sábado, 24 de junho de 2017


DRAFT for the book Philosophical Semantics to be published by Cambridge Scholars Publishing in 2017/2. 

– V –


There is no distinction of meaning so fine as to consist in anything but a possible difference in practice.
C. S. Peirce

Verificationism is today commonly viewed as a relic of philosophy in the first half of the 20th century. Although initially advocated by members of the Vienna Circle, it soon proved incapable of withstanding the increasing variety of opposing arguments, which came from both within and outside of the Circle. My aim in this chapter is to show that we can find a version of the principle of verifiability that is both intuitively acceptable and resistant to the most widespread objections. In my view, the Vienna Circle failed to successfully defend verificationism because it used the wrong approach of beginning by formally clarifying the principle of verification initially proposed by Wittgenstein, without paying sufficiently detailed attention to what we really do when we verify our statements. When their arguments in favor of the principle were shown to be faulty, most of them, followed by their offspring, unwisely concluded that the principle itself should be abandoned. They were reacting like the proverbial fox in Aesop’s fable: unable to reach the grapes, he consoled himself by imagining they were sour anyway...
   Returning to the methodology and assumptions of the later Wittgenstein, my aim in this chapter is twofold: first to sketch a plausible version of what can be called semantic verificationism, which consists in the proposal that the epistemic (cognitive, factual…) contents of declarative sentences, that is, the s-thoughts, thought-contents or propositions expressed by them, are constituted by their verifiability rules; second, to confirm and better explain semantic verificationism by answering its main counter-arguments.

1. Origins of semantic verificationism
The first point to be remembered is that, contrary to mistaken popular belief, the idea that a sentence’s meaning is its method of verification is not attributable to the logical positivists. The first to propose the principle was actually Wittgenstein himself, as the Vienna Circle always acknowledged (cf. Glock: 354). Indeed, if we review his works, we see that he formulated the principle in 1929 conversations with Waismann and mentioned it repeatedly in texts over the course of the following years. Furthermore, there is no solid evidence that he abandoned the principle later, replacing it with a purely performative conception of meaning as use, as some have argued. On the contrary, there is clear evidence that from the beginning his verificationism and his subsequent thesis that meaning is a function of use seemed mutually compatible to him. After all, Wittgenstein did not hesitate to conflate the concept of meaning as verification with meaning as use and even with meaning as calculus. As he said:

If you want to know the meaning of a sentence, ask for its verification. I stress the point that the meaning of a symbol is its place in the calculus, the way it is used.[1] (Wittgenstein 2001: 29)

It is always advisable to consult what the original author of an idea really said. If we compare Wittgenstein’s verificationism with the Vienna Circle’s verificationism, we can see that there are some striking contrasts. A first one is that Wittgenstein’s main objective with the principle always seems to have been to achieve a grammatical overview (grammatische Übersicht), that is, to clarify central principles of our factual language, even if this clarification could be put at the service of therapeutic goals. On the other hand, he was against the positivistic-scientistic spirit of the Vienna Circle, which in its incipient, precocious desire to develop a purely scientific philosophy had the strongest motivation to develop the verification principle as a powerful reductionistic weapon, able to vanquish once and for all the fantasies of metaphysicians. Wittgenstein, for his part, didn’t reject metaphysics in this way. For him the metaphysical urge was a kind of unavoidable dialectical condition of philosophical inquiry, and the truly metaphysical mistakes have the character of depth (Wittgenstein 1984c sec. 111, 119). It was this rejection of positivistic-scientistic reductionism that gradually estranged him from the Logical Positivists. For him, metaphysical errors were intrinsically necessary for the practice of philosophy as a whole:

The problems arising through a misinterpretation of our forms of language have the character of depth. They are deep disquietudes; their roots are as deep in us as the forms of our language and their significance is as great as the importance of our language. (1984c, sec. 111)

In these aspects Wittgenstein was much closer to that great American philosopher, C. S. Peirce. According to Peirce’s pragmatic maxim, metaphysical deception can be avoided when we have a clearer understanding of our beliefs. This clarity can be reached by understanding how these beliefs are related to our experiences, expectations and their consequences. Moreover, the meaning of a concept-word was for Peirce inherent to the totality of its practical effects, the totality of its inferential relations with other concepts and praxis. So, for instance, a diamond, as the hardest material object, can be partially defined as something that scratches all other things, but cannot be scratched by anything.
   Moreover, in contrast to the positivists, Peirce was aiming to extend science to metaphysics, instead of reducing metaphysics to science.[2] So, he was of the opinion that verifiability – far from being a weapon against metaphysics – should be elaborated in order to be applicable to it, since the aim of metaphysics is to say extremely general things about our empirical world. As Peirce wrote:

But metaphysics, even bad metaphysics, really rests on observations, whether consciously or not; and the only reason that this is not universally recognized is that it rests upon kinds of phenomena with which every man’s experience is so saturated that he usually pays no particular attention to them. The data of metaphysics are not less open to observation, but immeasurably more so than the data, say, of the very highly observational science of astronomy… (Peirce 1931, 6.2)[3]
Although overall Peirce’s views were as close to Wittgenstein’s as those of both were distant from the logical positivists, there is an important difference between both philosophers concerning the analysis of meaning. Peirce was generally interested in the connection between our concepts and praxis, including their practical effects, as a key to their clarification and a better understanding of their meaning. But by proceeding in this way he risked extending the concept of meaning too far; he took a path that can easily lead us to confuse the cognitive and practical effects of meaning with meaning itself. For as we already saw, the cognitive meaning of a declarative sentence, seen as a combination of semantic-cognitive rules, works as a condition for the production of inferential awareness, which consists in the kind of systemic openness (something like the ‘propagation of content’) that can produce an indeterminate number of subsequent mental states and actions.[4] Meaning as a verifiability rule is one thing; awareness of meaning and inferences that may result from this awareness, together with the practical effects of such inferences, may be a very different thing. Though they can be partially fused, they should be distinguished. Hence, within our narrow form of inferentialism, we first have the inferences that construct meanings (like those of the identification rules of singular terms, the ascription rules of predicates, and the verifiability rules of sentences). Then we have something usually beyond cognitive meaning, namely, the multiple inferences that enable us to gain something from our knowledge of meaning, along with the multiplicity of behavioral and practical effects that may result from them. Without this separation, we may even have a method that helps us clarify our ideas, but we will lack a boundary that can prevent us from extending our concept of meaning beyond a reasonable limit. For instance: the fact that something cannot be scratched helps to verify the sentence ‘This is a diamond,’ whereas the use of diamonds as abrasives will certainly be of little if any relevance as a proof. This is why I think that Wittgenstein, restricting cognitive meaning to a method of verification, that is, to combinations of semantic rules that make a proposition true, proposed a more adequate view of cognitive meaning and its truth.
   Looking for a better example, consider the statement: (i) ‘In October 1942 Chil Rajchman was arrested, put on a train, and deported to Treblinka.’ This promptly leads us to the inference: (ii) ‘Chil Rajchman was sent to be killed in a death camp.’ However, his probable fate would not be part of the verifiability procedure of (i), but rather of statement (ii). Thus, although (ii) is easily considered a consequence of (i), it isn’t a true constituent of the cognitive meaning, the thought-content expressed by (i). Statement (ii) has its own verifiability procedures, even if its meaning is strongly associated with that of statement (i), since it is our main reason for being interested in this last statement. So, we could say that there is something like a cloud of meaning surrounding the cognitive meaning of a statement S, which is formed by inferentially associated cognitive meanings of other statements with their own verifiability rules. But it is clear that this cloud of meaning does not properly belong to the cognitive meaning of S and should not be confused with it. In short: only by restricting ourselves to the constitutive verifiability procedures of a chosen statement are we able to restrict ourselves to the limits of its cognitive meaning.
   Opposition to a reductionist replacement of metaphysics by science was also one reason why Wittgenstein didn’t bother to make his principle formally precise, unlike positivists from A. J. Ayer to Rudolph Carnap. In saying this, I am not rejecting formalist approaches. I am only warning that such efforts, if not well supported by a sufficiently careful pragmatic consideration of how language really works, tend to put the logical cart before the linguistic horse. I want to show that unwise neglect of the most natural linguistic intuitions is what defeated the attempts of positivist philosophers to advocate their own principle.
   Having considered these differences, I want to start by examining some of Wittgenstein’s remarks regarding the verifiability principle, in order to find a reasonably adequate formulation and its justification. Afterwards, I will answer the main objections against the principle, demonstrating that they are much weaker than they seem at first glance.

2. Wittgensteinian verificationism
Here are some of Wittgenstein’s statements presenting the verifiability principle:

Each sentence (Satz) is a signpost for its verification. (Wittgenstein 1984e: 150)
A sentence (Satz) without any way of verification has no sense (Sinn). (Wittgenstein 1984f: 245)
If two sentences are true or false under the same conditions, they have the same sense (even if they look different). (Wittgenstein 1984f: 244)
To understand the sense of a sentence is to know how the issue of its truth or falsity is to be decided. (Wittgenstein 1984e: 43)
Determine under what conditions a sentence can be true or false, then determine thereby the sense of the sentence. (This is the foundation of our truth-functions.) (Wittgenstein 1984f: 47)
To know the meaning of a sentence, we need to find a well-defined procedure to see if the sentence is true. (Wittgenstein 1984f: 244)  
The method of verification is not a means, a vehicle, but the sense itself. Determine under what conditions a sentence must be true or false, thus determine the meaning of the sentence. (Wittgenstein 1984f: 226-7)
The meaning of a sentence is its method of verification. (Wittgenstein 1980: 29)[5]

What calls attention to statements like these is their strongly intuitive appeal: they seem to be true. They satisfy our methodological starting point of clinging to our common knowledge beliefs. To a great extent they even seem to corroborate Wittgenstein’s controversial view according to which philosophical theses are in the end trivial because they do no more than make explicit what we already know. They are what he would call ‘grammatical sentences’ expressing the rules grounding the linguistic practices that constitute our factual language. In the end the appeal to meaning verificationism involves what we might call a ‘transcendental argument’: we cannot reasonably conceive a different way to analyze the cognitive meaning of a declarative sentence except by appealing to verifiability; hence, assuming that meaning is analyzable, some form of semantic verificationism must be right.
   There are some points to be added here. The first is terminological and already well explained in this book: we should not forget that the verifiability rule must be identified with the cognitive content of a declarative sentence. This cognitive content is what I called in my discussion of Frege’s semantics the thought-content (s-thought) expressed by the declarative sentence, being called by others the descriptive, informative or factual content of the sentence, if not its propositional content. A complementary point is that we should never confuse cognitive content with grammatical meaning. If you do not know who Tito and Baby are, you cannot understand the cognitive meaning of the sentence ‘Tito loves Baby,’ although you are already able to understand its gram­matical meaning.
   Another point to be noted is that the verifiability rule includes both the verification and the falsification of the statement.[6] The reason is that this rule either applies to the verifier as such – the truthmaker that in the last chapter we usually unequivocally identified with some cognitively independent fact in the world – which verifies the rule – or it does not apply to any expected verifier or fact in the world – which falsifies the rule. Consider, for example, the statement ‘Frege was bearded.’ Here the verifiability rule applies to a circumstantial fact intended in the world that makes the rule effectively applicable, which means that the thought-content, the verifiability rule expressed by the statement is true. Consider, by contrast, the statement ‘Wittgenstein was bearded’: here the rule of verification does not apply to the intended contextual fact in the world, since this fact does not exist, which falsifies it. So the thought-content expressed by this sentence is false.
   These remarks also lead us to conclude against the existence of negative facts: a negative statement never states this phantasmagoric thing called a negative fact; what it really does is to deny the existence of a positive fact. The true thought expressed by the sentence ‘Teetetus is not flying’ does not properly apply to a negative fact – the fact that he is not flying – but rather to no fact at all. It is so because ‘Teetetus is not flying’ means the same as ‘It is not the case that Teetetus is flying,’ which in turn has the same sense as ‘It is false that Teetetus is flying’; but this means only that the here expressed thought-content, that is, the verifiability rule, whose application in this case can only be imagined, does not definitely apply to any real fact in the world. This real fact, the truthmaker, should be the fact of Teetetus flying. But after identifying Teetetus we see that he is in fact sitting, and that the ascription rule for ‘…is flying’ does not apply to him. (Due to the flexibility of language you can say ‘It is a fact that Teetetus isn’t flying’; but here you are using the word ‘fact’ derivatively in the sense of ‘is true.’)
   It is important to consider that we can imagine or conceive the application of the verifiability rule of a false statement to be a possible fact, knowing in this way that it could be satisfied and that proves its meaningfulness: Plato could imagine his friend Teetetus flying. But this possible fact isn’t a negative fact.
   Next, consider the universal negative statement ‘There are no yetis.’ Here as well there is no negative fact to consider. For calling ‘… is a yeti’ Y, we can formalize ‘There are no yetis’ as ~Ǝx (Yx) or (x) (~Yx). This is the same as {~Ya1 & ~Ya2… & ~Yan}, where each negative singular statement is false and the ascription rule for characterizing yetis fails to be applied to any given object, since the expected positive fact of the existence of at least one yeti cannot be found. The false statement ‘There are yetis’ remains only a logically and empirically conceivable fact, though with all probability not a real, empirical fact.
   A final point concerns my reading of Wittgenstein’s distinction between the verification of a sentence (Satz) and of a hypothesis (Hypothese), which he made in the obscure last chapter of his Philosophical Remarks. As he wrote:

A hypothesis is a law for the building of sentences.
One could say: a hypothesis is a law for the building of expectations.
A sentence is, so to speak, a cut in our hypothesis in a certain place.  (1984e XXII, sec. 228)

In my understanding, the hypothesis is distinguished here by being more distant from sensory-perceptual experience than what he calls a sentence. As a consequence, only the verification of a sentence (statement) is able to give us certainty (for instance, ‘I am seeing a chair now’). However, this does not mean that the verification of this sentence is infallible. So, when Wittgenstein writes that we verify the truth of the sentence ‘Here is a chair’ by looking only at a side of the chair (1984e, Ch. XXII sec. 225), it is clear that we can increase our degree of certainty by adding new facets, aspects, modes of presentation, sub-facts. We could, e.g., look at the chair from other angles, or make tests to show what the chair consists of, whether it is solid enough to support a person, etc.
   Thus, my view is that what he calls the certainty of a sentence is only postulated as such after what we consider sufficient verification in the context of some linguistic practice. This is why things can be seen as certain and yet remain fallible, as practical certainties. By contrast, the verification of hypotheses, like those stating scientific laws, as it is realized only derivatively, gives us comparatively lower degrees of probability, though they are also assumed to be true.

3. A Verifiability rule as a criterial rule
A more important point emphasized by Wittgenstein and ignored by others is that we usually have a choice of ways to verify a statement, each way constituting some different, more or less central aspect of its meaning. As he noted:

Consideration of how the meaning of a sentence is explained makes clear the connection between meaning and verification. Reading that Cambridge won the boat race, which confirms that ‘Cambridge won,’ is obviously not the meaning, but is connected with it. ‘Cambridge won’ isn’t the disjunction ‘I saw the race or I read the result or...’ It’s more complicated. But if we exclude any of the means to check the sentence, we change its meaning. It would be a violation of grammatical rules if we disregarded something that always accompanied a meaning. And if you dropped all the means of verification, it would destroy the meaning. Of course, not every kind of check is actually used to verify ‘Cambridge won,’ nor does any verification give the meaning. The different checks of winning the boat race have different places in the grammar of ‘winning the boat race.’ (2001: 29)


All that is necessary for our sentences to have meaning is that in some sense our experience would agree with them or not. That is: the immediate experience should verify only something of them, a facet. This picture is taken immediately from reality because we say ‘This is a chair’ when we see only a side of it. (1984f: 282, my italics)

In other words: one can verify through the direct observation of facts, that is, by seeing the Cambridge boat winning the race or by hearing the judge’s confirmation, or both. These forms of verification are central to the meaning of ‘Cambridge won the boat race.’ Here it is worth remembering that even this direct observation of the fact is aspectual: each person at the boat race saw the fact from a different perspective, they saw different sub-facts: different aspects (facets) of the same event. However, we also say that they did see the grounding fact in the sense that they inferred its totality in the most direct way possible; this is why we can say that the fact-event of Cambridge winning was directly experienced. In the same way, we are allowed to say that we see a ship on the sea (the inferred grounding fact), while what we phenomenally see is only one side of a ship (a given aspectual sub-fact).
   However, often enough the way we can know the truth-value of a thought-content like that expressed by the sentence ‘Cambridge won the boat race’ is more indirect: someone can tell us, we can read this in the internet or in a magazine or we can see a trophy in the clubhouse… These ways are secondary, and for Wittgenstein they participate only secondarily in the sentence’s meaning. Finally, they are causally dependent on the first ones. If the first form of verification did not exist, these dependent forms would lose their reliability.
   Using Wittgensteinian terms, we can say that the verifiability rule applies when we achieve awareness of a fact, which means that we are in a position that allows us to make the relevant inferences from our factual knowledge. This awareness is the most direct when the criterial configuration (a configuration of p-properties or tropes) that satisfies the verifiability rule is constitutive of the fact, for instance, when we observe the competition being won. But more often the verification is indirect, namely, by means of symptoms, e.g., a sum total of symptoms making the thought-content more or less probably true.
   Criteria tend to be displayed in the form of criterial configurations. Thus, the verifiability rule applies when the criterial configurations demanded by the semantic-cognitive criterial rule are objectively given as belonging to the objective facts as their tropes. Furthermore, the satisfaction of the criterial rule seems to have as a minimum condition of satisfaction a structural isomorphism between, on the one hand, the interrelated internal elements originating as constituents of the thought-content-rule, and, on the other hand, the interrelated objective elements (tropical combinations) that make up the grounding fact in the world – this would constitute the grounding fact isomorphism. Since experience is always aspectual and often indirect, this also means that the internal criterial configurations belonging to the rule must also show a structural isomorphism with aspectual configurations of external criterial tropes (given in the world and experienced by the epistemic subject) generating what we could call isomorphic relations with a sub-fact (say, a ship on the sea seen from one side), allowing us to infer the whole grounding fact (say, a whole ship on the sea). I will try to say more about this complicated issue in the last chapter.
  As this reconstruction of Wittgenstein’s views shows, a sentence’s meaning should be constituted by a verifiability rule that usually ramifies itself, requiring the actual or possible fulfillment of a multiplicity of criterial configurations, allowing us to infer facts in more or less direct ways. Hence, there are definitional criterial configurations (primary criteria) such as, in Wittgenstein’s example, those created from direct observation by a spectator at the boat race. But there is also an indefinite number of secondary criterial configurations depending on the first ones. They are secondary criteria or symptoms, allowing us to infer that Cambridge (more or less probably) won the boat race, etc. Here too, we can say that the primary criteria have a definitional character: once we accept them as really given and we can agree on this, our verifiability rule should apply with practical certainty. On the other hand, secondary criteria and symptoms make the application of a verifiability rule only more or less probable. Thus, if an unreliable witness tells us that Cambridge won, we can conclude that it is probable that Cambridge won. However, what makes this probability acceptable is, as we noted, that we are assuming it is backed by some primary criterial observation of the fact by judges and eye-witnesses.
   Investigating the structure of verifiability rules has some consequences for the traditional concept of truth-conditions. The truth-condition of a statement can be defined as the condition sufficient for a thought-content S to actually be the case. The truth condition for the statement ‘Frege had a beard’ is the condition that he actually did have a beard. This means that the truth-condition of S is the condition that a fact is given as S’s truthmaker. The truthmaker is an objective actualization of the truth-condition. That’s why we can say that the truthmaker necessitates the truth of the thought-content. Thus, the philosophical belief is a misconception (used as a basis for anti-realism) that a true condition should be able to exist without at least some conception of criterial configurations (tropes that could possibly warrant its existence) and its related verifiability rules.
   Now, considering our analysis of the identification rules of proper names (Appendix of Chapter I) and of the application rules of predicative expressions (Ch. II, sec. 6), we must consider the verifiability rule of a singular predicative statement as a combination of both. We can see this by examining a very simple predicative statement: ‘Aristotle was bearded.’ For this we use as a definitional identification rule for Aristotle the same rule already presented:

IR-Aristotle: The name ‘Aristotle’ is applicable iff its bearer is the human being who sufficiently and more than any other person satisfies the condition(s) of having been born in Stagira in 384 BC, lived the main part of his life in Athens and died in Chalcis in 322 BC and is/or was the philosopher who developed the main ideas of the Aristotelian opus. (Auxiliary descriptions may be helpful, though they do not belong properly to the definition…)

And for the predicative expression ‘…was bearded’ we may formulate the following definitional ascription rule:

AR-bearded: The predicate ‘…was bearded’ is ascribable iff its bearer was a human being who had as tropes facial hair grouth on the chin and/or cheeks and/or neck.

Now, as we already know, we first apply the identification rule of the singular term in order to identify the object, subsequently applying the ascription rule of the general term by means of which we select the trope of the object identified by the first rule. Not only are there many possible ways in which the identification rule and the ascription rule can be satisfied, there are still more ways of verification for the thought-content stated by ‘Aristotle was bearded.’ One of them is by examining the well-known marble bust of Aristotle found in Athens, another is by accepting the testimony of contemporaries, and still another is by learning that most ancient Greeks (particularly among the peripatetic) customarily wore beards as a badge of manhood, which allows the satisfaction of AR-Aristotle for that human being, in addition to the satisfaction of IR-Aristotle. As we noted, we postulate or assume this criterially-based verification as practically certain, so that we can say we know (K) that Aristotle was bearded even if we are aware that this is only indirectly proven as highly probable. We can summarize this knowledge in the formula:

K[[IR-Aristotle is applicable to its bearer]AR-bearded is applicable to the same bearer].

These brief comments on verificationism à la Wittgenstein suggest the need for more intensive pragmatic research on ways of verification. As we noted, the structure of a verifiability rule is often very ramified, and its details should vary in accordance with the kind of statement that expresses it. A detailed pragmatic investigation of the diversified forms of verifiability rules seems to me an important task that until now was never really attempted. In what follows, I will not attempt to correct this deficiency. I will limit myself to answering the main objections to the verifiability principle as explained above.

4. Objection 1: The principle is self-refuting
The first and most notorious objection to the principle of verifiability is that it is self-defeating. The argument is as follows. The principle of verifiability must be either analytic or synthetic. If it is analytic it must be tautological, that is, non-informative. However, it seems clearly informative in its task of elucidating cognitive meaning. Furthermore, analytic statements are self-evident, and denying them is contradictory or inconsistent, which is not the case with the principle of verifiability. Therefore, the principle is synthetic. But if it is synthetic, it needs to be verifiable in order to have meaning. Yet, when we try to apply the principle of verifiability to itself we find that it is unverifiable. Therefore, the principle is devoid of meaning. The principle is meaningless by its own standards; and one cannot decide meaningfulness by means of what is meaningless.
   Logical positivists tried to circumvent such objections by responding that the principle of verifiability has no truth-value, for it is nothing more than a proposal, a recommendation, or a methodological requirement.[7] A. J. Ayer advocated this view by challenging his readers to suggest a more persuasive option (1992: 148). However, a reader with very different convictions could respond that he simply doesn’t feel the need to accept or to opt for anything of the kind... In effect, the thesis that the principle is a proposal appears to be clearly ad hoc. It goes against Wittgenstein’s assumption that all we are doing is exposing the already given intuitions underlying our natural language, the general principles embedded in it. Hence, to impose on our language a methodological rule that does not belong to it would be arbitrary and misleading as a means of clarifying meaning.[8]
   My suggestion is simply to keep Wittgenstein’s original insight, according to which a principle of verifiability is nothing but a very general grammatical sentence stating the way all our factual language must work in order to have cognitive content, a content to which a truth-value can be assigned. Once we understand that the principle should make explicit our pre-existing linguistic dispositions, we are entitled to think that it must be seen as an analytic-conceptual principle. More precisely, this principle would consist in the affirmation of a hidden synonymy between the expressions ‘meaning as the cognitive content (thought-content) expressed by a declarative sentence’ and ‘the procedures (combinations of rules) by which we may establish the truth-value of this same cognitive content.’ Thus, taking X to be any declarative sentence, we can define the epistemic value (sense, meaning, thought-content) of X by means of the following analytic-conceptual sentence stating the verifiability principle:

VP (Df.): Cognitive meaning (thought-content…) of the declarative sentence X = the verifiability rule for X.

Against this, a critic can react by saying that this claim to analytic identity isn’t transparent. Moreover, if the principle of verifiability were analytic, it would be non-informative, its denial being contradictory or incoherent. However, it appears that VP says something and that in principle it can be denied. Thus, it seems conceivable that the cognitive meaning of the statement X, the thought-content expressed by it, isn’t a verifiability rule.
   My reaction to this objection is to remember that an analytic sentence does not need to be transparent; it does not need to be immediately seen as necessarily true, and its negation does not need to be clearly seen as contradictory or incoherent. Assuming that mathematics is analytic, consider the case of the following sentence: ‘3,250 + (3 × 896) = 11,276 ÷ 2.’ At first glance, this identity neither seems to be necessarily true nor does its negation seem incoherent; but a detailed presentation of the calculation shows that it must be the case. This can be seen as a hidden analytic truth, at first view ungraspable because of its derivative character and our inability to see its truth at first glance.
   This can be suggested by means of a thought-experiment. We can imagine a person with a better grasp of arithmetic than ours. For a child, 2 + 3 = 5 can be analytically transparent, as it is for me. For me, 12 × 12 = 144 is also transparently analytic (or intuitively true), though not to a child who has just started to learn arithmetic. But 144 × 144 = 20,736 isn’t transparently analytic for me, although it may be so for a person with much greater arithmetical skill. Indeed, I would guess that some persons with great arithmetical skill (as in the case of some savants) can see at a glance the truth of the identity ‘3,250 + (3 × 896) = 11,876 ÷ 2.’ This means that the boundary line between transparent and derived or non-transparent analytic truths is moveable, depending on our cognitive capacities and to some degree affected by training. Thus, from an epistemically neutral point of view the two types are on the same level, since for God (the only epistemic subject able to see all truths at a glance) analytic truths would all be transparent.
   In searching for a better-supported answer, we can now distinguish between transparent and non-transparent analytic-conceptual knowledge.[9] The sentences ‘A triangle has three sides,’ ‘Red is not green’ and ‘Three is greater than two’ express transparent analytic knowledge, since these relations are self-evident and their negation clearly contradictory. But not all analytic sentences are so. Sentences about geometry such as the one stating the Pythagorean theorem express (I assume) analytic truths in Euclidean geometry, although this isn’t transparent for me. Non-transparent analytic knowledge is based on demonstrations whose premises are made up of transparent analytical knowledge, namely, analytical truths we can intuitively grasp. Hence, this kind of knowledge is only elucidative, which can mislead us to think that it is informative in the proper sense of the word. Hence, it also seems very possible that the principle of verifiability is a non-transparent, hidden analytic statement.
   Against this last suggestion, one could object that the principle of verifiability cannot be stated along the same lines as a mathematical or geometrical demonstration. After all, in the case of a proved theorem it is easy to retrace the path that leads to its demonstration; but there is no similar way to demonstrate the principle of verifiability.
   More plausibly, the key to an answer may be found if we compare the principle of verifiability with statements that at first glance do not seem to be either analytic or demonstrable. Close examination reveals that they are in fact only non-transparent analytic truths. A well-known statement of this kind is the following:

The same surface cannot be simultaneously red all over and green all over (under the same conditions of observation).

This statement isn’t analytically transparent. In fact, it has been regarded by logical positivists and even contemporary philosophers as a serious candidate for what might be called a synthetic a priori judgment (cf. Bonjour 1998: 100 f.). Nevertheless, I think it isn’t difficult to show that it is actually a hidden analytic statement. We begin to see this when we consider that it seems transparently analytic that (i) visible colors can occupy surfaces, (ii) different colors are things that cannot simultaneously occupy the same surface all over, and (iii) red and green are different colors. From this it seems to follow that the statement (iv) ‘The same surface cannot be both red and green all over’ must be true. Now, since (i), (ii) and (iii) seem to be intuitively analytic, (iv) should be analytic too, even if not so intuitively. Here’s how a similar argument can be better formulated:

(1)  Two different things cannot occupy the same place all over at the same time.
(2)  A surface constitutes a place.
(3)  (1, 2) Two different things cannot occupy the same surface all over at the same time.
(4)  Colors are things that can occupy surfaces.
(5)  (3, 4) Two different colors cannot occupy the same surface all over at the same time.
(6)  Red and green are different colors.
(7)  (5, 6) Red and green cannot occupy the same surface all over at the same time.

To most people, premises (1), (2), (4) and (6) can be clearly seen (preserving the intended context) as definitely analytic. Therefore, conclusion (7) must also be analytic, even if it does not appear to be so.
   The suggestion that I want to make is that the principle of verifiability is also a true, non-trivial and non-transparent analytic sentence, and its self-evident character may be demonstrated through an elucidation of its more transparent assumptions in a way similar to that of the above argument. Here is how it could be made plausible:

(1)  Semantic-cognitive rules are criterial rules applicable to objective criterial configurations: configurations of (tropical) properties.
(2)  Cognitive (descriptive, representational, factual…) meanings (thought-contents or s-thoughts) expressed by statements are constituted by combinations of (referential) semantic-cognitive rules applicable to arrangements of (tropical) properties called facts.
(3)  The cognitive meanings of statements (thought-contents) depend on ways of determining their truth by means of facts.
(4)  (1, 2, 3) The truth-determination of cognitive meanings or contents of statements lies in the effective application of their combinations of semantic-cognitive criterial rules to the arrangements of (tropical) properties called facts.
(5)  (by definition) Combinations of semantic-cognitive criterial rules determining the truth of statements by their effective application to facts constitute what we have decided to call their verifiability rules.
(6)  (4, 5) The cognitive meanings or contents of statements consist in their verifiability rules.

 For me, at least, premises (1), (2), (3), and (5) (which is definitional) sound clearly analytic, although not the conclusion (6). I admit that my view of these premises as analytic derives from the background of assumptions gradually reached in the earlier chapters of this book: it is analytically obvious to me that contents, meanings or senses are constituted by the application of rules or combinations of rules. It is also analytically obvious to me that the relevant rules are semantic-cognitive rules that can combine to form cognitive meanings or thought-contents expressed by statements. Moreover, once these combinations of rules are satisfied by the adequate criterial configurations formed by facts understood as arrangements of (tropical) properties, they allow us to see them as effectively applicable, that is, as having a verifying fact as their referent and truthmaker. Such semantic-criterial combinations of (normally implicit) cognitive rules, when judged as effectively applicable to their verifying facts, are called true, otherwise they are called false. And these semantic-criterial combinations of cognitive rules can also be called s-thoughts, thought-contents, propositional contents or simply verifiability rules.
   I know that some stubborn philosophers of language would still vehemently disagree with me, saying that they have different intuitions originating from different starting points. But since I cannot extend this argument further, I prefer to avoid discussion, invoking as an excuse the words of a character created by J. L. Borges: ‘Their impurities forbid them to recognize the splendor of truth.’[10]

5. Objection 2: A formalist illusion
Logic can be illuminating but also deceptive. An example is offered by A. J. Ayer’s attempt to formulate a precise version of the principle of verifiability in the form of a criterion of factual meaningfulness. In his first attempt to develop this kind of verifiability principle, he suggested that:

…it is the mark of a genuine factual proposition… that some experiential propositions can be deduced from it in conjunction with certain other premises without being deducible from these other premises alone. (Ayer 1952: 38-39)

That is, it is conceivable that a proposition S is verifiable if together with the auxiliary premise P1 it implies an observational result O, as follows:

1.     S
2.     P1
3.     O

Unfortunately, it was soon noted that Ayer’s criterion of verifiability was faulty. As Ayer himself recognized, his formulation was ‘too liberal, allowing meaning to any statement whatsoever.’ (Ayer 1952: 11) Why? Suppose that we have as S the meaningless sentence ‘The absolute is lazy.’ Conjoining it with an auxiliary premise P1, ‘If the absolute is lazy, then snow is white,’ we can – considering that the observation that snow is white is true and that the truth of ‘The absolute is lazy’ cannot be derived from the auxiliary premise alone – verify the sentence ‘The absolute is lazy.’
   Now, the core problem with Ayer’s suggestion (which was not solved by his later attempt to remedy it[11]) is this: In order to derive the observation that snow is white, he assumes that a declarative sentence (which he mistakenly called a ‘proposition’) whose meaningfulness is questioned is already able to attain some truth-value. But meaningless sentences cannot attain any truth-value; and if a sentence has a truth-value, then it must also have a meaning, it must also express a propositional content as a thought-content or a verifiability rule that is true only if effectively applicable. By assuming in advance a truth-value for a sentence under evaluation, Ayer’s principle implicitly begs the question. Moreover, he does not allow the empirical statement in question to reveal if it has a proper method of verification and, if it has one, to show what this method is.[12]
   In fact, we cannot imagine any way to give a truth-value to the sentence ‘The absolute is lazy,’ even a false one, simply because it is a grammatically correct but cognitively meaningless word combination. As a consequence, the sentence ‘If the absolute is lazy, then snow is white’ cannot imply that the conclusion ‘Snow is white’ is true in conjunction with the sentence ‘The absolute is lazy.’ To make it clearer, suppose we replace ‘The absolute is lazy’ with the equally meaningless symbols @#$, producing the conjunction ‘@#$ & (@#$  Snow is white).’ We cannot apply a truth-table to show the result of this because @#$ expresses no proposition at all. Even if the statement ‘Snow is white’ is meaningful, we cannot say that this formula allows us to derive the truth of ‘Snow is white’ from ‘The absolute is lazy,’ because @#$, being a meaningless combination of signs, cannot even be considered false in order to imply the truth of ‘Snow is white.’ The unassailable conclusion is that Ayer’s solution begs the question regarding the verifiability principle, since it implicitly works as if sentences like ‘The absolute is lazy’ had the status of meaningful sentences before he applies his criterion to them.[13]
   I can develop my point further by giving a contrasting suggestion as a criterion of meaningfulness, more akin to Wittgenstein’s views. Consider the sentence ‘This piece of metal is magnetized.’ The question of its cognitive meaningfulness suggests verifiability procedures. An affirmative answer results from the application of the following verification procedure that naturally flows from the statement ‘This piece of metal is magnetized’ conjoined with some additional information:

(1)  This is a piece of metal (observational sentence).
(2)   If a piece of metal is magnetized, it will attract other objects made of iron (criterion for being magnetized),
(3)  This piece of metal has attracted iron coins, which remained stuck to it (observational application of the criterion).
(4)  (From 1 to 3): It is certainly true that this piece of metal is magnetized.
(5)  If we have a reliable procedure to show the truth of an empirical statement, then the sentence has cognitive meaning as a principle of verifiability.
(6)  The procedure bringing us from (1) to (4) is reliable.
(7)  (From 4 to 6): The statement ‘It is certainly true that this piece of metal is magnetized’ is cognitively meaningful (expresses a thought-content).

Notice that here the verifying procedure flows naturally from our understanding of the declarative sentence that we intend to verify, once the conditions for its verification are given. However, in the case of meaningless sentences like ‘The absolute is lazy’ or ‘The nothing nothings,’ we can find no verification procedure following naturally from them, and this is the real sign of their lack of cognitive content. Ayer’s statement ‘If the absolute is lazy, then snow is white’ does not follow naturally from the sentence ‘The absolute is lazy.’ In other words: the multiple ways of verifying a statement – themselves expressible by other statements – must contribute, in different measures, to make it fully meaningful; but they must contribute by building its cognitive meaning and not by being arbitrarily attached to it, as allowed by Ayer’s proposal. They must be given to us intuitively as the declarative sentence’s proper way of verification. The neglect of real ways of verification built into any meaningful declarative sentence is the fatal flaw in Ayer’s criterion.

6. Objection 3: Verificational holism
A sophisticated objection to semantic verificationism is found in W. V-O. Quine’s generalization of Duhem’s thesis, according to which it is impossible to confirm a scientific hypothesis in isolation, that is, apart from the assumptions constitutive of the theory to which it belongs. In Quine’s compressed sentence: ‘our statements about the external world face the tribunal of sense experience not individually but only as a corporate body.’ (Quine, 1951: 9)[14]
   The result of this is Quine’s semantic holism: our language forms a so interdependent network of meanings that it cannot be divided up into verifiability procedures explicative of the meaning of any isolated statement. The implication for semantic verificationism is clear: since what is verified must be our whole system of statements and not any statement alone, it makes no sense to think that each statement has an intrinsic verifiability rule that can be identified with a particular cognitive meaning. If two statements S1 and S2 can only be verified together with the system composed by {S1, S2, S3Sn}, their verification must always be the same, and if the verifiability rule is the meaning, all the statements should have the same meaning, which is so absurd it leaves room for skepticism, if not about meaning, as Quine would like, at least about his own arguments.
   In my view, if taken on a sufficiently abstract level, on which the concrete spatio-temporal confrontations with reality to be made by each statement are left out of consideration, the idea that the verification of any statement in some way depends on the verification of a whole system of statements – or, more plausibly, of a whole molecular sub-system – is very acceptable. This is what I call abstract or formal confirmational holism, and this is what can be meant in Quine’s statement. However, his conclusion, according to which the admission of structural holism destroys semantic verificationism, does not follow. It requires admitting that structural holism implies what could be called a concrete or performative or procedural verificational holism, i.e., a holism regarding the concrete spatio-temporal verification procedures of individual statements, which are constitutive of the cognitive meaning. But this just never happens.
   Putting things in a somewhat different way: Quine’s holism has its seeds in the fact, well known by philosophers of science, that in order to be true the verification of an observational statement always depends on the truth of an undetermined multiplicity of assumed auxiliary hypotheses and background knowledge. Considered in abstraction from what we really do when we verify a statement, at least a form of molecularism is true: verifications are interdependent. After all, our beliefs regarding any domain of knowledge are more or less interdependent, building a complex network. But it is a wholly different matter if we claim that from formal or abstract confirmational holism, a performative procedural or verificational holism follows on a more concrete level. Quine’s thesis is fallacious because, although at the end of the day a system of statements really needs to confront reality as a whole, its individual statements do not confront reality, either conjunctively or simultaneously.
   I can clarify what I mean with the help of a well-known example. We all know that by telescopic observation Galileo discovered the truth of the statement: (i) ‘The planet Jupiter has four moons.’ He verified this by seeing and drawing, day after day, four luminous points near Jupiter, and observing that these points were constantly changing their locations in a way that seemed to keep them close to the planet, crossing it, moving away and then approaching it again, repeating these same movements in a regular way. His obvious conclusion was that these luminous points could be nothing other than moons orbiting the planet. His contemporaries, however, were suspicious of the results of his telescopic observation. How could two lenses magnify images without deforming them? Some even refused to look through the telescope, fearing it could be bewitched… Philosophers of science today have realized that Galileo’s contemporaries were not as scientifically naive as they often seem to us.[15] As was noted (Salmon 2002: 260), one reason for accepting the truth of the statement ‘Jupiter has four moons’ is the assumption that the telescope is a reliable instrument. But the reliability of telescopes was not sufficiently confirmed at that time. To improve the telescope as he did, Galileo certainly knew the law of telescopic magnification, whereby its power of magnification results from the focal length of the telescope divided by the focal length of the eyepiece. But in order to guarantee this auxiliary assumption, one would need to prove it using the laws of optics, still unknown when Galileo constructed his telescope. Consider, for instance, the fundamental law of refraction. This law was established by Snell in 1626, while Galileo’s telescopic observations were made in 1610. With this addition, we can state in an abbreviated form the formal procedure of confirmation as it is known today and which I claim would be unwittingly confused by a Quinean philosopher with the concrete verification procedure. Here it is:

1. Repeated telescopic observation of four points of light orbiting Jupiter.
2. Law of magnification of telescopes.
3. Snell’s law of refraction: sinθ1/sinθ2 = v1/v2 = l1/l2 =n2/n1.
4. A telescope cannot be bewitched.
5. Jupiter is a planet.
6. The Earth is a planet.
7. The Earth is orbited by a moon.
8. (All other related assumptions.)
9. Conclusion: the planet Jupiter has at least four moons.

If Galileo did not have knowledge of premise 3, this only weakens the inductive argument, which was still strong enough to his lucid mind. From a Quinean verificationist holism, the conclusion, considering all the other constitutive assumptions, would be that the conclusive statement 9 does not have a proper verification method, since it depends not only on observation 1, but also on the laws expressed in premises 2 and 3, the well-known premises from 4 to 7, and an undetermined number of other premises constitutive of our system of beliefs, all of them having their own verifiability procedures... As he wrote: ‘our statements should face the tribunal of experience as a corporate body.’ Indeed.
    In this example, the problem with Quine’s reasoning becomes clear. First, we need to remember that the premises belonging to confirmation procedure (I) are not simultaneously checked. The conclusion expressed by statement 9 was actually verified only as a direct consequence of statement 1, resulting from the daily drawings made by Galileo of his observations of variations in the positions of the four ‘points of light’ aligned around Jupiter. However, Galileo did not simultaneously verify statement 2 when he made these observations, nor the remaining ones. In fact, as he inferred conclusion 9 from premise 1, he only assumed a previous verification of the other premises, as was the case with premise 2, which he verified as he learned how to build his telescope. Although he didn’t have premise 3 as a presupposition, he had already verified or assumed as verified premises 2, 4, 5, 6, 7 and 8. Now, because the verifications of 2 to 8 are already presupposed in the verification of 9, it becomes clear that these verifications are totally independent of the verification of 9 by means of 1. The true form of Galileo’s concrete verification procedure was much simpler than the abstract (holistic or molecularist) procedure of confirmation presented above. It was:

1. Repeated telescopic observation of four points of light orbiting Jupiter.
2. Conclusion: the planet Jupiter has at least four moons.

Generalizing: If we call the statement to be verified S, and the statements of the observational and auxiliary hypotheses O and A respectively, the structure of the concrete verifiability procedure of S is not

     A1 & A2… & An

But simply:
     (Assuming the prior verification of A1 & A2... & An)

This assumption of an anterior verification of auxiliary hypotheses in a way that might hierarchically presuppose sufficient background knowledge is what in fact makes all the difference, as it allows us to separate the verifiability procedure of S from the verifiability procedures of the involved auxiliary hypotheses and the many background beliefs which are already assumed to have been successfully verified.
   The conclusion is that we can now clearly distinguish what verifies each auxiliary hypothesis. For example: the telescope’s law of magnification was verified by very simple empirical measurements; and the law of refraction was established later, based on empirical measurements of the relationship between variations in the angle of incidence of light and the density of the medium. Thus, while it is true that on an abstract level a statement’s verification depends on the verification of other statements of a system, on the level of its proper cognitive and practical procedures, the successful verification of auxiliary statements is already assumed, which allows us to isolate the verifiability procedure proper of our statement as what is actually being verified, identifying it with what we mean with the statement, with its true cognitive meaning.
   In the same way, we are able to distinguish the specific concrete modes of verification of each distinctive auxiliary or background statement, whose truth is assumed as verified before employing the verification procedure that leads us to accept S as true. This allows us to distinguish and identify the concrete procedure whereby each statement of our system is cognitively verified, making the truth of formal or structural holism irrelevant to the performative structure of semantic verificationism.
   By considering all that is formally involved in confirmation, and by simultaneously disregarding the difference between what is presupposed and what is performed in the concrete spatio-temporal verification procedures, Quine’s argument gives us the illusory impression that verification as such should be a holistic procedure. This seems to imply that the meaning of the statement cannot be identified with a verifiability procedure, since the meanings of statements are diverse and differentiated, while the holistic confrontation of a system of beliefs with reality is unique and as such undifferentiated.
   Finally, if we remember that each different statement must have a meaning of its own, it again becomes perfectly reasonable to identify the cognitive meaning of a statement with its verifiability rule. For both the verifiability rule and the meaning are once more individuated together as belonging to each statement, and not to the system of statements or beliefs assumed in the verification. Molecular holism is true regarding the ultimate form of confirmation. But it would be disastrous regarding meaning, since it would dissolve all meanings into one big, meaningless mush.
   The inescapable conclusion is that Quine’s verificational holism is false. It is faulty because the mere admission of formal holism, that is, of the fact that statements are in some measure inferentially intertwined with each other is not sufficient to lead us to conclude that the verifiability rules belonging to these statements cannot be identified with their meanings because these rules cannot be isolated, as Quine suggests. Finally, one should not forget that in my example I gave only one way of verification for the statement ‘The planet Jupiter has at least four moons.’ Other ways of verification can be added, also belonging to the meaning and enriching it.
    Summarizing my argument: an examination of what happens when a particular statement is verified shows us that even assuming formal holism (which I think is generally correct particularly in the form of a molecularism of linguistic practices), the rules of verifiability are distinguishable from each other in the same measure as the meanings of the corresponding statements – a conclusion that only reaffirms the expected correlation between the cognitive meaning of a statement and its method of verification.

7. Objection 4: Existential-universal asymmetry
The next objection is that the principle of verifiability only applies conclusively to existential sentences, but not to universal ones. To verify an existential sentence such as ‘At least one piece of copper expands when heated,’ we need only observe a piece of copper that expands when heated. To conclusively verify a universal claim like ‘All pieces of copper expand when heated’ we would need to observe all the pieces of copper in the entire universe, including its future and past, which is impossible. It is true that absolute universality is a fiction and that, when we talk about universal statements, we are always considering some limited domain of entities – some universe of discourse. But even in this case the problem remains. In the case of metal expanding when heated, for instance, the domain of application remains much broader than anything we can effectively observe, making conclusive verification practically impossible. Therefore – mainly because scientific laws usually take the form of universal statements – some would ask whether it wouldn’t be better to admit that the epistemic meaning of universal statements consists of falsifiability rules instead of verifiability rules. . However, in this case existential sentences like ‘There is at least one flying horse’ would not be falsifiable, since we would need to search a too wide domain of entities in the past and in the future in order to falsify it. Anyway, one could suggest that the meaning of universal statements were given by falsifiability rules, while the meaning of existential and singular statements would be given by verifiability rules. Wouldn’t this be a more felicitous answer? (cf. Hempel 1959)
   I think this would not do. We can, for example, falsify the statement ‘All ravens are black’ simply by finding a single white raven. In this case we verify the statement ‘This raven is white.’ In this way of course the verifiability rule of this last statement is such that, if applied, it falsifies the statement ‘All ravens are black.’ But if the meaning of the universal statement may be a falsification rule, a rule able to falsify it, and the verifiability rule of the utterance ‘That raven is white’ is the same rule that when applied falsifies the statement ‘All ravens are black,’ then – admitting that the verifiability is the cognitive meaning of singular statements – it seems that we should admit that the statement ‘All ravens are black’ must have the same meaning as ‘That raven is white.’ However, this would be absurd: the meaning of ‘This raven is white’ has nearly nothing to do with the meaning of ‘All ravens are black.’
   The strongest argument against falsifiability rules is that they do not exist. As already noted, there seems to be no proper falsifiability rule for a statement, as there certainly is no counter-assertive force (or a force proper to negative judgments, as was once believed), no rule of de-identification of

 counter-assertive force (or a force proper to negative judgments, as was once believed), no rule of de-identification of a name, and no rule for the de-ascription or de-application of a predicate. This is because what satisfies a rule is a criterion and not its absence, even when in some cases by common agreement the criterion is the absence of something normally expected, as in the case of a hole when someone says: ‘Your shirt has a hole’ or ‘This big hole has water inside.’  In such cases the ascription rule for ‘…has a hole’ and for the identifying rule ‘This big hole’ have negative criteria, but what they satisfy is seen as a verifiability rule and not a falsifiability rule.[16]
   It seems, therefore, that we should admit that the cognitive meaning of a statement can only be its verifiability rule, applicable or not. But in this case it seems inevitable to return to the problem of the inconclusive character of the verification of universal propositions, leading us to the admission of a ‘weak’ together with a ‘strong’ form of verificationism (Ayer 1952: 37).
   I think, however, that this does not seem to be the best path to reach the right answer. My suggestion is that the inconclusiveness objection is simply faulty, since it emerges from a wrong understanding of the true logical form of universal statements; a brief examination shows that these statements are in fact both probabilistic and conclusive. Consider again the statement:

1.     Copper expands when heated.

It is clear that its true logical form is not, as it seems:

2.     I state that it is absolutely certain that all pieces of copper expand when heated,

where ‘absolutely certain’ means ‘without possibility of error’. This form would be suitable for formal truths such as

3.     I state that it is absolutely certain that 7 + 5 = 12,

because here there can be no error (except procedural error, which we are leaving out of consideration). However, this form is not suitable for empirical truths, since we cannot be absolutely sure about their truth. The logical form of what we mean with statement (1) is a different one. This form is that of practical certainty, which can be expressed by

4.     I affirm that it is practically certain that every piece of copper expands when heated,

where ‘practically certain’ means ‘with a probability that is sufficiently high to make us disregard the possibility of error.’ In fact, we couldn’t rationally mean anything different from this. Now, if we accept this paraphrase, a statement such as ‘Copper expands when heated’ becomes conclusively verifiable, because we can clearly find inductive evidence protected by theoretical reasons that become so conclusive that we can be practically certain, namely, that we can assign a probability to the truth of the statement that all pieces of copper expand when heated that is sufficiently high to make us sure about it (we can say that we know its truth). In short: the logical form of an empirical universal utterance, assuming a domain of application, is not that of a universal statement like ‘├ All S are P,’ but usually:

5.     I affirm that it is practically certain that all S are P.

Or (using a sign of assertion or assertion-judgment):

6.     ├ It is practically certain that all S are P.

The objection of asymmetry seems to have been motivated by the assimilation of the logical form of formal universal statements in the logical form of empirical universal statements. The empirical universal statement is shown to be conclusively verifiable, since what it claims is nothing but a sufficiently high probability. Hence, the cognitive meaning of an empirical universal statement can still be seen as its verifiability rule. Verification allows judgment; judgment must be treated as conclusive; and verification likewise.

8. Objection 5: Arbitrary indirectness
Another common objection is that the rule of verifiability of statements with empirical content requires taking as a starting point at least the direct observation of facts that are objects of virtually interpersonal experience. However, many statements do not depend on direct observation to be true, as is the case with ‘The mass of an electron is 9.109 x 10 kg raised to the thirty-first negative power.’ Cases like this force us to admit that many verifiability rules cannot be based on more than indirect observation of the considered fact. As W. G. Lycan has noted, if we don’t accept this, we will be left with a grotesque form of instrumentalism in which what is real must be reduced to what can be inter-subjectively observed and in which things like electrons and their masses do not exist anymore. But if we accept this – admitting that many verifiability rules are indirect – how do we decide what the direct and indirect observations are? ‘Is this not one of those desperately confusing distinctions?’ (2000: 121 f.)
   Here again, problems only emerge if we embark in the narrow formalist canoe of logical positivism and paddling straight ahead trample on natural language with inappropriate requirements. Our assertive sentences are uttered or thought of in linguistic regions, practices, circumstances, language-games, speech acts. The verification procedure must be adapted to the linguistic practice in which the statement is uttered. Consequently, the criterion to distinguish direct observation from indirect observation should always be relative to the linguistic practice that we take as a model. We can be misled by the fact that the most common linguistic practice is (a): our wide linguistic practice of everyday direct observational verification. The standard conditions for singling out this practice are:

Virtually interpersonal observation made by epistemic subjects under normal internal and external conditions and with unbiased senses of solid, opaque and medium sized objects, which are close enough and under adequate lighting, all other things remaining the same.

This is how the presence of my laptop, my table and my chair are typically checked. Because it is the most usual form of observation, this practice is seen as the archetypical candidate for the title of direct observation, to be contrasted with, say, indirect observation through perceptually accessible secondary criteria like the use of mirrors, optical instruments, etc. However, it is an unfortunate mistake that some may tend to use model (a) to evaluate what happens in other, sometimes very different, linguistic practices. Let us consider some of them.
   I begin with (b): the bacteriologist’s linguistic practice. Usually the bacteriologist is concerned with the description of the micro-organisms visible under his microscope. In this practice, seeing a bacterium under a microscope is called by him a direct observation and set as the model for verification. But the bacteriologist can also say, for example, that he has verified the presence of a virus indirectly, due to changes he found in the form of the cells he saw under a microscope, even though viruses are for him not directly observable except under an electron microscope that he does not possess. Almost nobody would say that a bacteriologist’s procedures are all indirect, unless when having in mind a comparison with our everyday linguistic practices (a). Anyway, although unusual, this would be possible. In any case, the right context can clearly show what the speaker has in mind.
   Let us consider now (c) the linguistic practice of paleontology. The discovery of fossils is seen here as a direct way to verify the real existence of extinct creatures that died out millions of years ago, such as dinosaurs, since live observation is impossible. (It would become possible if such species could be discovered on other planets, or if we invented a time machine, or if there were a Jurassic Park method of recreating such creatures). But the paleontologist can also speak of indirect verification by comparison and contrast within his practice. So, consider the conclusion that hominids once lived in a certain place based only on damage caused by stone tools to the fossil bones of animals that these early hominids once hunted and used for food or clothing. This finding may be regarded as resulting from an indirect verification in paleontological practice, in contrast to finding fossilized remains of early hominids, which would be considered a direct form of verification. Of course, here again any of these verifications will be considered indirect when compared with verification produced by the most common linguistic observational practice of everyday life, namely, (a). However, the context can easily show what sort of comparison we have in mind; a problem would arise only if the language used raises doubts about the model of comparison employed.
   If the practice is (d) of pointing to linguistically describable feelings, the verification of a sentence will be called direct when made by the speaker himself, albeit subjective, while the determination of feelings by a third person, based on behavior or verbal testimony, will generally be taken (by non-behaviorists and those who believe in my objections to the private-language argument) as indirect. There isn’t any easy way to compare practice (d) with the everyday practice (a) of observing medium-sized physical objects in order to say what is more direct, since they belong to very different domains of verification.
   My conclusion is that there is no real difficulty in distinguishing between direct and indirect verification, insofar as we have clarity about the linguistic practice with which the verification is being made, that is, about the model of comparison we have chosen. Contrasted with philosophers, speakers share the contextually bounded linguistic assumptions needed for the applicability and truth-making of verifiability rules. To become capable of reaching agreement on whether a verificational observation or experience is direct or indirect, they merely need to be aware of the contextually established model of comparison that is being considered. 

9. Objection 6: Empirical counter-examples
Another kind of objection relates to statements that seem to have meaning, but lack any apparent verifiability rule. I think that this kind of objection demands consideration on a case-by-case basis.
   Consider, to begin with, the statement ‘John was courageous,’ spoken under circumstances in which John died without having had any opportunity to demonstrate courage (Dummett 1978: 148 f.), say, shortly after birth. If we add the stipulation that the only way to verify that John was courageous would be by observing his behavior, the verification of this statement becomes practically (and probably physically) impossible. Therefore, in accordance with the verifiability principle, this statement has no cognitive meaning. However, it seems to remain more than just grammatically meaningful.
   The answer is that in the circumstances portrayed, the statement ‘John was courageous’ only appears to have a meaning. It belongs to the set of statements whose cognitive meaning is only apparent. Although the sentence has an obvious grammatical sense, given by the combination of a non-empty name with a predicate, we are left without any criterion for the application or non-application of the predicate. Thus, such a statement has no function in language and is not able to tell us anything. It is part of a set of statements such as ‘The universe doubled in size last night’ and ‘My brother died the day after tomorrow.’ Although these statements may at first appear to make some sense, what they possess is no more than the expressive force of suggesting images in our minds. But they are devoid of cognitive meaning, since we cannot test or verify them.
   Wittgenstein considered an instructive case in his work On Certainty. Consider the statement ‘You are in front of me right now,’ said under normal circumstances for no reason by someone to a person standing before him. He notes that this statement only seems to make sense, given that we are able to imagine situations in which it would have some use, for example, when a room is completely dark, so that it is hard for one person to identify another person in the room (1984a, sec. 10). John’s case is in this aspect similar. We are inclined to imagine counterfactual situations in which he would or would not have demonstrated courage, and we can think of them as possible situations. This invites us to project courage into these possible situations and get the mistaken impression that the statement has a workable epistemic sense.
   What can we say of statements about the past or the future? Here too, it is necessary to examine them on a case by case basis. Suppose that someone says: ‘Earlier Java man lived about 1 million years ago.’ This statement was fully verified by a fossilized skull and a reliable carbon dating procedure. The direct verification of past events in the same way that we observe present events is practically (and supposedly physically) impossible, but it is not part of the verifiability rule, whose application warrants the truth of the statement on the basis of a standard adopted in practice (a). Here direct verification is made on the basis of verifiable empirical traces left by past events (practice (c)).
   There are other, more indirect verifications of past events. The sentence ‘Neptune existed before it was discovered’ can be accepted as certainly true. Why? Because our knowledge of physical laws (which we trust as sufficiently verified) combined with information about the origins of our solar system allow us to conclude that Neptune certainly existed a long time before it was discovered, and this inferential procedure is suitable as a form of verification.
   Very different is the case of statements about the past such as:

1. On that rock an eagle landed exactly ten-thousand years ago.
2. Napoleon sneezed more than 30 times while he was in Russia.
3. The number of human beings alive exactly 2,000 years ago was an odd number.

For such supposed thought-contents there are no empirical means of verification. Here we must turn to the old distinction between practical, physical and logical verifiability. Such verifications are not practically or technically achiev­able, and as far as I know, they are not even physically realizable (it is improbable that we will ever visit the past in a time-machine or through a worm-hole in space). The possibility of verification of such statements seems to be only logical. But it is hard to believe that an empirical statement whose verifiability is only logical can be considered as having a useful cognitive sense (cf. Reichenbach 1953: sec. 6).
   To explain this point better: it seems that the distinction between logical, physical and practical verifiability influences meaning according to the respective fields of verifiability to which the statements in question belong. Statements belonging to a formal field need only be formally verifiable to be fully meaningful: the tautology (PQ ) ↔ (~P v Q), for instance, is easily verified by the truth-table applying the rules for material implication, bi-implication, negation and disjunction. But statements belonging to the empirical domain (physical and practical) must be not only logically, but also at least in principle empirically verifiable in order to really have cognitive meaning. As a consequence, a supposedly empirical statement that is only logically verifiable must be devoid of cognitive significance. This seems to be the case of a statement such as ‘There is a nebula that moves away from the earth at a speed greater than the speed of light.’ This statement is empirically devoid of sense, insofar as according to relativity theory it is impossible. Similarly, in examples (1), (2) and (3), what we have are empirical statements whose verification is empirically inconceivable. Consequently, though having grammatical and logical meaning and invoking images in our minds, these statements lack any relevant cognitive meaning, for we don't know what to make of them. Such statements aren’t able to perform the specific function of an empirical statement, which is to be able to truly represent an actual state of affairs. We do not even know how to begin the construction of their verifiability rules. All that we can do is to imagine or conceive the situations described by them; but we know of no rule or procedure to link the conceived situation to something that possibly existed in the real world. Although endowed with some expressive meaning, they are devoid of genuine cognitive meaning. Finally, we can reformulate statements (1), (2) and (3) as meaningful empirical possibilities, e.g. ‘It is possible that Napoleon sneezed more than 30 times when he was invading Russia.’ These modal statements are true and verifiable by their coherence with our belief-system.
   Something similar can be said of statements about the future, with the difference that here direct verification is in many cases physically possible. Consider the sentence (i) ‘It will rain in Caicó seven days from now.’ When a person seriously says something of this sort, what she usually means is (ii) ‘Probably it will rain in Caicó seven days from now.’ And this probability sentence is conclusively verifiable, albeit indirectly, by a weather forecast. Thus, we have a verifiability rule, a cognitive meaning, and the application of this rule  gave the statement a real degree of probability. However, one could not in anticipation affirm (iii) ‘It certainly will rain in seven days.’ Although there is a direct verifiability rule – to look at the sky for seven days – it has the disadvantage that we will only be able to apply it if we wait out the seven days, and we will only be able to affirm its truth (or deny it) afterwards. It is true that one could use this sentence in some situations, for example, when making a bet about the future. But in this case we would not affirm (iii) from the start, since we cannot apply the rule in anticipation. In this case, what we mean with sentence (iii) can be only in fact (iv) ‘I bet that it will rain in Caicó seven days from now,’ which without any empirical justification has again only an expressive-emotive meaning and no truth-value.
   A similar statement is (v) ‘The first baby to be born on Madeira Island in 2050 will be female,’ which has a verifiability rule that can only be applied in the future. This sentence lacks a practical meaning insofar as we are unable to verify and state it at the present moment; presently this sentence expreses no proposition and has no truth-value. Nonetheless, in a proper context the sentence may have the meaning of a guess: (vi) ‘I guess that the first baby to be born…’ or (vii) a statement of possibility regarding the future ‘It is possible that the first baby to be born…’ In these cases, we are admitting that the sentence has a cognitive meaning, since all we are saying is that it has an observational verifiability rule that can be applied (or not) in the future. But as an affirmation of something that will be the case in the year 2050, this sentence has no cognitive meaning, for in order to be true this affirmation requires awareness of the effective applicability of the verifiability rule. When we consider what is really meant in statements regarding future occurrences, we see that even in these cases verifiability and meaning go together.
   Now consider the statement: ‘In about eleven billion years the Sun will expand and engulf Mercury.’ This statement in fact only means ‘Very probably in about eleven billion years the Sun will expand and engulf Mercury’; this prediction can be inferentially verified today, based on what we know of the fate of other stars in the universe that resemble our Sun but are much older.
    We conclude that there is no general formula detailing the structure of a verifiability procedure. Sentences about the future can be physically and to some extent practically verifiable. They cannot make sense as warranted actual assertions, since such affirmations require the possibility of present verification. Most of them are concealed probability statements. The kind of verifiability rule required varies with the utterance and its insertion in the linguistic practice in which it is made, showing what it really means. This may again lead us to the mistaken belief that there are unverifiable statements with cognitive meaning.
   Finally, a word about ethical statements. Positivist philosophers have maintained that they are unverifiable, which has led some to adopt implausible emotivist moral theories. Once again we find the wrong attitude! I would suggest that ethical principles are scarcely verifiable, like metaphysical statements and indeed like most philosophical statements. They aren’t decisively verifiable because we are still unable to state them in adequate ways, making them sufficiently precise, since we lack consensual agreement regarding adequate verifiability rules about these matters. Like their verifiability, their cognitive meaningfulness is dubious. Philosophy is nothing more than a conjectural activity.

10. Objection 7: Formal counterexamples
The verificationist thesis is naturally understood as extensible to the statements of formal sciences. In this case, the verifiability rules or procedures (combinations of rules) that demonstrate their formal truth endow a form of cognitive content deductively within the formal system in which they are considered. A fundamental difference with respect to empirical verification is that in the case of formal verification, to have a verifiability rule is the same as being able to definitely apply it, since the criteria to be ultimately satisfied are the own axioms already assumed as such by the system.
   A much discussed counter-example is Goldbach’s conjecture. This conjecture is usually stated as G:

G: Every even number greater than 2 can be expressed as the sum of two prime numbers.

The usual objection is that this conjecture has cognitive meaning, it expresses a thought-content even if we never manage to prove it, even if the procedure for formal verification of G has not yet been found. Hence, its significance cannot be equated with a verifiability procedure.
   The answer to this objection is too simple and stems from the perception that Goldbach’s conjecture is what its name says: a mere conjecture. Well, what is a conjecture? It’s not an affirmation, a proven theorem, but rather the recognition that a thought-content has enough plausibility to be taken seriously as possibly true. One would not make a conjecture if it seemed fundamentally improbable. Thus, the true form of Goldbach’s conjecture is:

It is plausible that G.

But ‘It is plausible that G,’ i.e., ‘[I state that] it is plausible that G,’ or (using a sign of assertion) ‘├It is plausible that G,’ is something other than

 I state that G (or ├G),

which is what we would be allowed to say if we wanted to enunciate Goldbach’s proved theorem. If our case were to uphold the statement ‘I state that g,’ namely, an affirmation of the truth of Goldbach’s theorem as something cognitively meaningful, the required verifiability rule would be the whole procedure for proving the theorem, and this we simply do not have. In this sense G is cognitively devoid of meaning. However, the verifiability rule for ascribing mere plausibility is far less demanding than the verifiability rule able to demonstrate or prove G.
   The plausibility ascription is ‘[I state that] it is plausible that G’, whereby the verifiability rule consists in something much weaker, namely, in a verification procedure able to suggest that G can be proved. Now this verification procedure does in fact exist. It consists simply in considering random examples, such as the numbers 4, 8, 12, 124, etc., and showing that they are always the sum of two prime numbers. This verifiability rule not only exists; it has been applied up until now without exception to every even natural number ever considered! This is the reason why we really do have enough support for Goldbach’s conjecture: it has been fully verified as a conjecture. If an exception had been found, the conjecture would have been proved false, for this would be incompatible with the truth of ‘[I state that] it is plausible that G.’
   Thus, in itself the conjecture is verifiable and – as a conjecture – has been definitely verified: It is true that it is really plausible that G can be true. And this explains its cognitive meaningfulness. What remains beyond verification is the statement affirming the necessary truth of G. And indeed, this statement doesn’t really make sense; it has no cognitive content, since it consists in a proof, a mathematical procedure to verify it. The error consists in the confusion of the statement of a mere conjecture which is true with the ‘statement’ of a theorem that does not exist.
   A contrasting case is Fermat’s last theorem. Here is how this theorem (F) is usually formulated:

F: there are no three positive numbers x, y and z that satisfy the equation xⁿ + yⁿ = zⁿ, if n is greater than 2.

This theorem had been only partially demonstrated up until 1995, when Andrew Wiles finally succeeded in working out a full formal proof.  Now, someone could object here that even before Wiles’ demonstration, F was already called ‘Fermat’s theorem.’ Hence, it is clear that a theorem can make sense even without being proved.
   There are, however, two unfortunate confusions in this objection. The first is easy to spot. Of course, Fermat’s last theorem has a grammatical sense: it is syntactically correct. But it would be an obvious mistake to confuse the grammatical meaning of F with its cognitive meaning. An absurd identity, for instance, ‘Napoleon is the number 7,’ has a grammatical sense.
   The second confusion concerns the fact that the phrase ‘Fermat’s theorem’ isn’t appropriate at all. We equivocally call F a ‘theorem’ because before his death Fermat wrote that he had proved it, but couldn’t put this proof on paper, since the margins of his notebook were too narrow for this…[17] For these reasons, we have here a misnamed opposite of ‘Goldbach’s theorem’. Although F was called a theorem, it was in fact only a conjecture of the form:

   [I state that] it is plausible that F.

It was a mere conjecture until Wiles demonstrated F, only then effectively making it a theorem. Hence, before 1995 the cognitive content that could be given to F was actually ‘[I state that] it is plausible that F,’ a conjecture that was demonstrated by the fact that no one had ever found numbers x, y and z that could satisfy the equation. Indeed, the cognitive meaning of the real theorem F, better expressed as ‘I state that F’ or ‘├ F’ (which very few really know), should include the demonstration or verification found by Wiles, which is no more than the application of an exceptionally complicated combination of mathe­matical rules.
   Some would complain that if this is the case, then only very few people really know the cognitive meaning of Fermat’s last theorem. I agree with this: The cognitive content of this theorem, its full thought-content, like that of many scientific statements, is really known by very few people indeed. What most of us know is only the weak conjecture falsely called ‘Fermat’s last theorem.
   Finally, there are phrases like (i) ‘the lesser convergent series.’ For Frege, this definite description has sense but not reference. We can add that there is a rule that allows us to always find series that are less convergent than any given one, making them potentially infinite. We can state this as LC: ‘For any given convergent series, we can always obtain a less convergent one.’ Since LC implies the truth of statement (ii) ‘There is no lesser convergent series,’ we conclude that (i) has no referent. Now, what is the identification rule of (i)? What is the sense or meaning of (i)? One answer would be to say that it is given by failed attempts to devise the series (i) ignoring LC. It would be like the meaning of any mathematical falsity. For instance, the identity 321 + 427 = 738 is false. Now, what is its meaning? I believe that it also resides in the failed attempt to verify it, showing that this is a false identity. Attempting to verify this identity we add 321 to 427, obtaining the result 748. Since 748 is different from 738, we conclude that the identity 321 + 427 = 738 is false, and it is such an operation that gives some kond of cognitive sense to the false identity. The same regarding false statements like 3 > 5. They express thoughts consisting in the formation of unaplicable combination of rules.

11. Objection 8: Skepticism about rules
One could still say that Wittgenstein (1984c, sec. 185 f.) formulated a skeptical riddle that endangers the possibility of an ongoing common interpretation of rules and, consequently, the idea that our language may work as a system of rules, and in this way also threatens the proper concept of meaning. A similar skeptical riddle was imaginatively formulated by Saul Kripke (1982, Ch. 1). Answering this riddle interests us here because if the argument were correct, it could imply that it is a mistake to accept that there are verifiability rules responsible for the cognitive meanings of sentences.
   Wittgenstein introduced his riddle with the following example. Let’s say that a person learns a rule to add 2 to natural numbers. If you give her the number 6, she adds 2 and writes the number 8. If you give her the number 73, she adds 2, writing the number 75... But imagine that for the first time she is presented with a larger number, say the number 1,000, and that she then writes the number 2,004. If you ask why she did this, she responds that she understood that she should add 2 up to the number 1,000, 4 up to 2,000, 6 up to 3,000, etc. (1984c, sec. 185). According to Kripke’s version, a person learns the rule of addition, and it works well for additions with numbers below 57. But when she performs additions with larger numbers, the result is always 5. So for her 59 + 67 = 5… This occurs because she understood ‘plus’ as the rule ‘quus,’ according to which ‘x quus y = x + y if {x, y} < 57, otherwise 5’ (1982: 9).
   What these examples demonstrate is that a rule can always be interpreted differently from the way it was intended, no matter how many specifications we include in our instructions for using the rule, since these instructions can also be differently interpreted. The consequence is that we cannot be assured that everyone will follow our rules in a similar way or that people will continue to coordinate their actions based on them. And as meaning depends upon following rules, we cannot be certain about the meanings of the expressions we use. How could we be certain, in the exemplified cases, of the respective meanings of ‘add two’ and ‘plus’? 
   In my view, neither Wittgenstein nor Kripke gives a satisfactory answer to the riddle. Both assume a Humean-kind skeptical solution. Wittgenstein’s answer can be interpreted as saying that we follow rules blindly, as a result of training in the conventions of our social practices (1984c sec. 201, 202, 211, 219). Kripke’s answer is similar: following a rule is justified not by truth-conditions derived from correct interpretation, but by assertability conditions (1982: 74) based on the fact that any other user in the same language community can assert that the rule follower ‘passes the tests for rule following applied to any member of the community’ (1982: 110). However, against both one could insist that the simple fact that in our community we have so far openly coordinated our linguistic activity according to rules does not imply that these coordinations need to work this way, and does not even imply that they should continue to work this way, which shows that the riddle remains basically unsolved.
   For my part, I always thought that the ‘paradox’ had a more straightforward solution. A central point can be seen as in some way suggested by Wittgenstein’s philosophy, namely, that we learn rules in a similar way because we share a similar human nature modelled in our form of life (Costa 1990: 64-66).  This makes it easy for us to interpret the rules we are taught in the same manner, and means that we must also be naturally endowed with innate, internal corrective mechanisms able to reinforce agreement.
   I think, however, that if we follow this path further, the decisive solution of the riddle can be found in Craig DeLancey (2004). According to him, we are biologically predisposed to construct and interpret statements in the most economical possible way. Or, as we could also say, we are innately disposed to put in practice the following principle of simplicity as a pragmatic maxim:

PS: We should interpret (and establish) a semantic rule in the simplest way possible.

Because of this principle, we prefer to maintain the interpretation of the rule ‘add 2’ in its usual form, instead of complicating it with the further condition that we should add twice two after each thousand. And because of the same principle, we prefer to interpret the rule of addition as a ‘plus’ instead of a ‘quus’ addition, because with the ‘quus’ addition we would complicate the interpretation by adding the further condition that any sum with numbers above 57 would give as a result the number 5. The application of such a principle of simplicity allows us to harmonize our interpretations of semantic rules, thus solving the riddle.[18]
   One might ask: what warrants the assumed similarity of human nature or that we are innately equipped to develop such a heuristic principle of simplicity? The obvious answer lies in the appeal to Darwinian evolution. Over long periods of time, a process of natural selection has harmonized our learning capacities, eliminating individuals with deviant, less practical dispositions. Thus, within our human form of life the principle of simplicity offers a plausible explanation of our capacity to share a sufficiently similar understanding and meaning of semantic rules. If we add to this the assumption that human nature and recurring patterns in the world will not change in the future, we can be confident in the expectation that people will not deviate from the semantic rules they have learned. Of course, underlying this last assumption is Hume’s much more defiant criticism of induction, which might remain a hidden source of uneasiness. But this is a further issue that goes beyond our present concerns (for a short answer see the Appendix of the present chapter).[19]
   Summarizing: Our shared interpretation of learned rules only seems puzzling if we insist on ignoring the implications of the theory of evolution, which supports the principle of simplicity. By ignoring considerations like these, we tend to ask ourselves (as Wittgenstein and Kripke did) how it is possible that these rules are and continue to be interpreted and applied in a similar manner by other human beings, losing ourselves within a maze of philosophical perplexities. For a similar reason, modern pre-Darwinian philosophers like Leibniz wondered that our minds are such that we are able to understand each other, appealing to the Creator as producing the necessary harmony among human souls. The puzzle about understanding how to follow a rule arises from this same old perplexity.

12. Quine’s objections to analyticity
Since I am assuming that the verifiability principle is an analytic-conceptual statement, before finishing I wish to say a word in defense of analyticity. I am satisfied with the definition of an analytic proposition as the thought-content expressed by a statement whose truth derives from the combination of its constitutive unities of sense. This is certainly the most common and intuitively acceptable formulation. W. V-O. Quine would reject it because he finds that it is based on the too vague and obscure concept of meaning.
   The answer to this is that there is nothing too vague or obscure in the concept of meaning used in our definiens, except from Quine’s own scientistic-reductionist perspective, which tends to confuse normal vagueness with a lack of precision or obscurity (see Grice & Strawson 1956: 141-158; Swinburne 1975: 225-243). Philosophy works with concepts such as meaning, truth, knowledge, good, beauty, which are felt as inevitably ambiguous and vague, as much as the concepts used in countless attempts to define them. In my view, the effort to explain away such concepts only by reason of their usual vagueness (or supposed obscurity) betrays an impatient scientistic-pragmatic disposition of mind that is anti-philosophical par excellence (which is not to defend the opposite: a methodology of hyper-vagueness or unjustified obscurity).
   Having rejected the above common definition, Quine tried to define an analytic sentence in a Fregean way, as a sentence that is either tautological (true due to its logical constants) or can be shown to be tautological by the replacement of its non-logical terms with cognitive synonyms. Thus, the statement (i) ‘Bachelors are unmarried adult males’ is analytic, because the word ‘bachelor’ is a synonym of the phrase ‘unmarried adult male,’ which allows us by the substitution of synonyms to show that (i) means the same thing as (ii): ‘Unmarried adult males are unmarried,’ which is a tautology. However, he finds the word ‘synonym’ in need of explanation. What is a synonym? Quine’s first answer is that a synonym of an expression is another expression that can replace the first in all contexts salva veritate. However, this answer does not work in some cases, particularly with phrases such as ‘creature with a heart’ and ‘creature with kidneys,’ which are not synonymous, but in many cases can be interchangeable salva veritate, since they have the same extension. In a last attempt to define analyticity, Quine makes an appeal to the modal notion of necessity: ‘Bachelors are unmarried males’ is analytic if and only if ‘Necessarily, bachelors are unmarried males.’ But he sees that the usual notion of necessity does not cover all cases. Phrases like ‘equilateral triangle’ and ‘equiangular triangle’ necessarily have the same extension, but are not synonyms. Consequently, we must define ‘necessary’, in this case, as the specific necessity of analytic statements, in order for it to hold in all possible circumstances. But as Quine puts it, his argument to explain synonymy, though not flatly circular, ‘has the form, figuratively speaking, of a closed curve in space.’ (Quine 1951: 8) Moreover, the necessity of analyticity is an obscure notion, if it really exists.
   A noteworthy problem is Quine’s apparent assumption that a word should be defined with the help of words that do not belong to its specific conceptual field. Thus, for him the word ‘analyticity’ should not be defined by means of words like ‘meaning,’ ‘synonymy,’ ‘necessity’… which seem to be too unspecific in their meaning to allow for an adequate definition. Nonetheless, when we consider the point more carefully, we see that the words belonging to a definiens should be relatively close in their meanings to the definiendum, simply because in any real definition the terms of a definiens must belong to the same semantic field as its definiendum. Thus, in order to define a conceptual word from ornithology, we would not use concepts from quantum physics, and vice versa. These conceptual fields are too distant from each other. Because of this, we define ‘arthropod’ as an invertebrate animal having an exoskeleton, all these terms being biological, which does not compromises the definition. Considering the abstractness of the semantic field, a corresponding level of vagueness can be expected. Hence, there is nothing wrong in defining analyticity using correspondingly vague words that belong to the same conceptual field, like ‘meaning’ and ‘synonymy.’
   A more specific and more serious objection is that Quine’s definition of synonymy simply followed a wrong path. Since there is probably no necessity of analyticity, the lack of synonymy of expressions that necessarily have the same extension like ‘equilateral triangle’ and ‘equiangular triangle’ remains unexplained.
   My alternative proposal, based on what we have learned about the meaning of our expressions is that any expressions A and B are synonymous if their semantic-cognitive rules (the concepts they express) are the same, which can be tested by adequate definitions expressing the criteria for the application of those rules. Consider the words ‘chair’ in English and ‘Stuhl’ in Germany. They are synonymous because they express the same semantic-cognitive rule: a criterial rule made explicit by their common definition as a moveable seat provided with a backrest, made for use by only one person at a time. The expressions ‘creature with a heart’ and ‘creature with a kidney’ are not synonymous because they express different semantic-cognitive rules, the first defined as a creature with an organ to pump blood, the second defined as a creature with an organ to clean waste and impurities in blood. Even if approximate in meaning, the expressions ‘equilateral triangle’ and ‘equiangular triangle’ are likewise not synonymous, for the same reason: the first is defined as a triangle whose three sides are equal, while the second is defined as a triangle whose three internal angles are congruent with each other and are each 60°. Hence, we can replace Quine’s insufficient definition of analyticity by the following more adequate definition:

A statement S is analytic (Df) = it can generate a tautology by means of substitution of cognitive synonyms, namely, of expressions with the same semantic-cognitive criterial rules (i.e., with the same definitions).

Besides this, if we identify any proposition, any thought-content, with a verifiability rule, it seems that we could say that an analytic proposition is a verifiability rule that is self-verifying. Or, somewhat better: It seems that the intertwining of rules that constitutes the verifiability rule of an analytic statement verifies not by its application to the world, but by means of an application of one rule to the other in a way that makes the whole true independently of any state of the world. For instance, ~(P & ~P) can be verified by its truth-table in which we combine the rules for the application of the negation and the conjunction in a way that always gives as a result the value true. We will come back to this point later, when discussing the concept of truth.
   A complementary point supported by Quine is that, contrary to what is normally asserted, he does not see any definite distinction between empirical and formal knowledge. What we regard as analytic sentences can always be falsified by greater changes in our more comprehensive system of beliefs. Even sentences of logic such as the excluded middle can be rejected, as occurs in some interpretations of quantum physics.
   Regarding this complementary point, it seems to me that it would not be correct to say that an analytic proposition turns out to be false as a result of new experiences. What more precisely occurs is that its domain of application can be restricted or even lost. For example: since the development of non-Euclidean geometries, the Pythagorean theorem has lost part of its theoretical domain; it is not the only usable geometry anymore. And since the theory of relativity has shown that physical space is better described as non-Euclidean, this theorem has lost its monopoly on describing physical space. However, this is not the same as to say that the Pythagorean theorem has been falsified in a literal sense. This theorem remains perfectly true within the framework of theoretical Euclidean geometry, where we can prove it, insofar as we assume the basic rules that constitute this geometry. This remains so even if Euclidean geometry’s domain of application has been theoretically restricted with the rise of non-Euclidean geometries and even if it has lost its application to real physical space after the development of general relativity theory. The case is different when a law belonging to an empirical science is falsified. In this case, the law definitely loses its truth, since its truth-value depends solely on its precise empirical application. Newtonian gravitational law was falsified by general relativity, even if it is still usable in some practical applications that do not require the highest level of accuracy. The best one could say in its favor is that it has lost some of its truth and try to make this idea clear by appealing to multi-valued logic.

13. Conclusion
There is still much more to be said about these issues. I believe, however, that the few but central considerations that were offered here are sufficient to convince you that semantic verificationism, far from being a useless hypothesis, comes close to being rehabilitated when investigated with a methodology that does not overlook and therefore does not violate the delicate tissue of natural language.

[1] As probably the best reader of Wittgenstein at the time, Moritz Schlick echoes a similar view: ‘Stating the meaning of a sentence amounts to stating the rules according to which the sentence is to be used, and this is the same as stating the way in which it can be verified. The meaning of a proposition is the method of its verification.’ (Schlick 1938: 340)
[2] See, for contrast, Carnap’s definition of scientific philosophy as ‘the logic of science’ in his 1937, § 72.
[3] C. S. Peirce’s view of metaphysics coincides with what is today the most accepted one (cf. Loux 2001, ix). On Peirce’s verificationism see also Misak 1995, Ch. 3. As I do, and following Peirce, Cheryl Misak favors a liberalized form of verificationism, opposed to the narrow forms advocated by the Vienna Circle.
[4]  See my analysis of the form of the semantic-cognitive rules in chapter 3, sec. 12, and of the nature of consciousness in chapter 2, sec. 12.
[5] I believe that the germ of the verifiability principle is already present in aphorism 3.11 of the Tractatus Logico-Philosophicus under the title of ‘method of projection.’ There he wrote: ‘We use the perceptible sign of a sentence (spoken or written) as a projection of a possible state of affairs. The method of projection is the thinking of the sentence’s sense.’
[6] This is why there is no falsifiability rule, as Michael Dummett suggested (1993, p. 93).
[7] This position was supported by A. J. Ayer, Rudolf Carnap, Herbert Feigl and Hans Reichenbach (Cf. Misak 1995: 79-80).
[8] Ayer’s view wasn’t shared by all positivists. Moritz Schlick, closer to Wittgenstein, defended the view according to which all that the principle of verifiability does is to make explicit the way meaning is assigned to statements, both in our ordinary language and in the languages of science (1936: 342 f.).
[9] This distinction is inspired by Locke’s original distinction between intuitive and demonstrative knowledge. I do not use Locke’s distinction because, as is well known, he questionably applied it to non-analytic knowledge. (cf. Locke 1975, book IV, Ch. II, § 7)
[10]  From J. L. Borges’ magnificent short tale, ‘El Tintorero Enmascarado Hákim de Merv’.
[11] The difficulty made him propose a more complicated solution that the logician Alonzo Church proved to be equally faulty (cf. Church 1949).
[12]  I am surely not the first to notice this flaw. As Barry Gower summarizes: ‘…the principle behind [Ayer’s] verifiability criterion requires that we recognize all statements involved in using it as having a truth-value, that is, as being either true or false, including the statement whose factual meaningfulness we are testing using the criterion. But if a statement has a truth-value, then it must be meaningful, and if it is about matters of fact then it is factually meaningful (2006: 200).
[13] C. G. Hempel (in Ayer ed. 1959: 112) pointed out that a sentence of the form ‘S v N’, in which S is meaningful, but not N, must be verifiable, in this way making the whole disjunction meaningful. He commits a similar mistake here. The form of this statement is ‘S v @#$.’ We cannot apply any truth-table to this. Here only the verifiable S has meaning and allows verification, not the whole disjunction, because this whole is nonsensical if taken as a disjunction.

[14] Later Quine corrected this thesis, advocating a verifiability molecularism restricted to sub-systems of language, since language has many relatively independent sub-systems. However, our counter-argument will apply to both cases.
[15] I think Galileo’s judges unwittingly did a great favor to science by sentencing him to house arrest, leaving him with nothing to do other than concentrate his final intellectual energies on writing his scientific testament, the Discorsi intorno a due nuove scienze.
[16]  Michael Dummett viewed the falsification rule as the ability to recognize under what conditions a proposition is false. But this must be the same as the ability to recognize that the proposition isn’t true, namely, that its verifiability rule isn’t applicable, which presupposes that we know its criteria of applicability. (cf. Dummett 1996: 62 ff.)
[17] Now we know that Fermat couldn’t have written this seriously, since the mathematics of his time did not provide the means to prove his conjecture.
[18] DeLancey clarifies ‘simplicity’ by remarking that non-deviant interpretations are formally more compressible than the deviant interpretations considered by Wittgenstein and Kripke. Moreover, a Turing machine would need to have a more complex and longer program in order to process these deviant interpretations.
[19] Curiously, in his book Kripke considers a criterion of simplicity, but discards it for the reason that although it allows us to choose between different hypotheses, it does not to establish what one has really understood as a rule (1982: 38-39). However, the paradox appears only when we can state it in the form of comparable hypotheses (‘plus’ versus ‘quus,’ etc), and it is to them that we apply the criterion of simplicity. In my view, the question regarding what someone ultimately understood as a rule independently of public check is simply empty.

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