Falsehood and Meaning

In a famous paper entitled “Truth and Meaning” Donald Davidson argues that meaning is constituted by truth conditions. A recursive theory of truth for a language in the style of Tarski is thus a theory of meaning for that language. Understanding a sentence consists in grasping its truth conditions. The meaning of a word is its contribution to determining truth conditions. Truth is the central concept of semantic theory. Davidson says nothing about falsity in relation to meaning; that concept has no place in the theory of meaning. Perhaps the reason is obvious: falsity conditions are not what a sentence means. Suppose we say, evidently correctly, that “snow is white” is false (in English) if and only if snow is not white—the falsity condition is given by inserting negation into the sentence whose meaning is in question. Then clearly it would be wrong to say that “snow is white” means that snow is not white—it means the opposite of that! So falsity conditions don’t constitute meaning. I will return to this point, but at present, I merely observe that falsity is not the concept chosen to characterize meaning, by Davidson or by the many others who have seen meaning as residing in truth conditions. I propose to argue that this is a mistake—that falsehood is as closely intertwined with meaning as truth.

The first point to make is that understanding a sentence involves knowing under what conditions it is false. If I understand “snow is white” I know that this sentence is false if and only if snow is not white—just as I know that it is true if and only if snow is white. I know its truth conditions and I know its falsity conditions. It is perfectly true that we cannot replace “is false if and only if” with “means that”, but this doesn’t imply that knowing falsity conditions isn’t part of understanding a sentence. For the same thing is true of many sentences in relation to truth: we can’t replace a statement of truth conditions for indexical sentences with a “means that” clause either (“I am hot” uttered by me doesn’t mean that Colin McGinn is hot at the time of utterance), and most sentences of a natural language are at least implicitly indexical. Similarly, a biconditional for “Shut the door!” employing the concept of obedience doesn’t license the proposition that the sentence means such a condition (the sentence doesn’t mean that the addressee shuts the door in response to the command to shut it). And there is really no reason to suppose that what constitutes grasp of meaning should be susceptible of statement in the “means that” form. It is just an accident that this holds for truth conditions in the case of context-independent sentences (actually it doesn’t even hold for “snow is white” because of the indexicality of tense). If you say that meaning is use, you are not saying that a given word or sentence means anything about use. In any case, it is not an objection to a claim about meaning that it won’t go over into the “means that” form; and intuitively it is a platitude that to understand a sentence (in the indicative) one needs to know under what conditions it is false. You wouldn’t understand “snow is black” unless you knew that the circumstance of snow being white renders that sentence false. We could test someone’s grasp of meaning precisely by asking her whether the sentence would be true or false under such and such conditions.

But is it possible to give a Tarski-type theory of falsehood analogous to his theory of truth? That was certainly part of the appeal of a truth conditions theory of meaning for Davidson: it permits the employment of Tarski’s powerful and rigorous theory of truth. If falsehood cannot be treated in this way, then it lacks one of the most attractive aspects of the concept of truth in semantic theory. To my knowledge neither Tarski nor anyone else has investigated this question, so mesmerized are they by Tarski’s formidable apparatus; but the question is easily answered in the affirmative—falsehood is just as amenable to recursive formal treatment as truth (which is just what we should expect). I will run quickly through the basic clauses for falsity; it is really a routine matter. For any sentence s, s is false if and only if not-p (where p is a sentence of the meta-language translating s). A conjunction “p and q” is false if and only if either p is false or q is false (not if and only if p is false and q is false). A disjunction “p or q” is false if and only if p is false and q is false (not if and only if p is false or q is false). Notice how disjunction is used in the meta-language to give falsity conditions for “and” and conjunction is used to give falsity conditions for “or”, instead of the usual alignment of connectives for truth conditions. A universal quantification “For all x, Fx” is false if and only if something x is not F. An existential quantification “For some x, Fx” is false if and only everything x is not F. Again notice the inversion of the quantifiers compared to the standard clauses for truth. With these clauses, we can construct a recursive theory of falsity entirely parallel to Tarski’s construction for truth. The analogue of a satisfaction clause will simply be: an object x counter-satisfies F if and only if x is not F, where “counter-satisfies” means the converse of “false of” (alternatively, “dissatisfies”). We can then speak of “Convention F” which specifies that a definition of falsehood should entail all instances of the schema, “s is false if and only if not-p”; and even define falsehood as “dissatisfaction by all sequences”. There would be F-sentences as well as T-sentences. The apparatus is exactly as for truth but with suitable amendments. Tarski could have written an appendix to his famous 1944 paper with the title “The Concept of Falsehood in Formalized Languages” and said much the same things as he said about truth. It would be surprising if he couldn’t, given the close connection between the two concepts—it would constitute an important theorem!

So we now add a Tarski-style theory of falsehood to a Davidson-type theory of meaning to produce a theory of falsity conditions for sentences of natural language (or disobedience conditions for the case of imperatives). This will be part of our theory of meaning for the language. It joins with a theory of truth conditions to give (allegedly) a complete theory of meaning. Both theories are necessary and neither is sufficient by itself. A speaker of the language grasps both the truth conditions and the falsity conditions of the sentences of that language. Thus I know that “snow is white” is true if and only if snow is white and that “snow is white” is false if and only if snow is not white. These are separate pieces of knowledge concerning distinct properties and employing different concepts (notably negation in the case of falsity). We can imagine possible beings that embrace one sort of knowledge while eschewing the other—they might be softhearted relativists that reject the notion of falsity altogether or stern skeptics about truth that recognize only falsity—but in our case, we have and embrace both sorts of knowledge. Our understanding of sentences includes both truth-conditions knowledge and falsity- conditions knowledge. This implies that a theory of meaning is based around two central concepts, truth and falsehood, not a single concept—which is not what we have been traditionally taught. Word meaning is now geared to two concepts: this is not truth-theoretic semantics but truth-value–theoretic semantics. Truth and falsehood play coordinate roles in the overall theory. Linguistic understanding has two parts or aspects. We could say that a meaning is a location in logical space that comprises both a positive condition and a negative condition: both snow being white and also snow not being white. Meanings are both inclusive and exclusive.

This opens up some interesting perspectives. Suppose you are a hardboiled Popperian: you don’t think truth can ever be established, but you do think falsehood can be. You hold that “all swans are white” cannot be confirmed as true, but can be falsified by observing a single instance of a non-white swan. You believe the concept of truth is irrelevant to science, but you think the concept of falsehood plays an important role. Verification is out of the question, but falsification is the engine of progress. Suppose you even go so far as to believe truth should be eliminated from our conceptual scheme, while retaining falsehood. You accordingly don’t accept that meaning is constituted by truth conditions (any more than you accept that scientific progress is the accumulation of truths) or by verification conditions (there are no such conditions): but you do believe that sentences can be false and can be established to be false. Then you may well find yourself attracted to a pure falsity conditions theory of meaning: the meaning of “all Fs are G” is given by the condition that this sentence is falsified by the fact that an F has been observed not be a G. That is, we understand a sentence by constructing its falsification conditions, which embed its falsity conditions, and truth conditions be hanged. You thus don’t much care for Tarski’s definition of truth—for what use is the concept of truth?—but you do fancy his implied definition of falsity. It enshrines your general “critical epistemology”—your dedication to the notion of falsification. You embrace falsity-theoretic semantics done in the general style of Tarski, as adopted by Davidson. This seems like a coherent position, however radical or misguided it may be. It serves to bring out the change of perspective that results from taking falsehood seriously in semantics.

Falsity and negation go together—notice how often I used negation in explaining falsity conditions semantics. Similarly for Popperian epistemology: we are always discovering that theories are not true (i.e. false). So negation plays a critical role in the theory of meaning (and in Popperian epistemology): we don’t know the meaning of a sentence unless we know under what conditions it is not true. The concept of negation thus enters into our understanding of any and every sentence, even when the sentence doesn’t contain negation. Hence negation is integral to meaning as such. I doubt that so-called animal languages incorporate negation in this way, even if the animal in question possesses the concept of negation. We might then speak of negation-theoretic semantics—theories that emphasize the role of negation in constituting meaning. This makes a better understanding of negation desirable, and indeed I think negation is an underexplored topic (not counting Sartre’s Being and Nothingness). Would a good analysis of negation shed light on the nature of meaning?

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Prehension Prehended

Did I mention that my book Prehension recently came out? I have held it in my hands. It’s a funny book. It’s not really a philosophy book, but a science book. But it’s more like nineteenth century science, informal and personal, as well as “scientific”. The title alludes both to gripping with the hands and grasping with the mind (any reference to Whitehead is quite accidental). I adopt a very biological view of the mind, though without the usual reductionism. I intend it to be “meaningful” in the sense of summing up the human condition. We are very odd creatures when you look at it closely; my book is odd too.

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Quine and Groucho

I was watching the Marx brothers film Horse Feathers and noticed a reference to the distinction between de reand de dicto readings of vernacular sentences. Groucho says to Chico, “You have the brain of a four year old…and I bet he was glad to get rid of it”. The joke depends upon switching from a narrow scope reading of the quantifier to a wide scope reading–as if Chico had stolen the brain of an actual four year old. I wonder if Quine ever saw the film and had his attention drawn to the ambiguity of the original sentence. The unexpected reading is: “There is a four year old whose brain you have”.

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Prehension

My book on the hand finally comes out next week (August 14). I just got copies: nice cover, good paper. Oh what trouble that book has caused me! It is pretty academic stuff actually. I’m curious to know what people make of it. It’s really a science book, laced with philosophy. People might object that it is more than conceptual analysis, and don’t I say that philosophy is conceptual analysis? But philosophers can do things other than philosophy, and might even be helped by their strictly philosophical expertise. I am all in favor of cross-disciplinary work, though it is harder to do than people think.

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Kant

I’ve just been teaching Kantian ethics. The idea is that a right action is one the guiding maxim of which can be universalized without contradiction, and a wrong action is one that cannot be so universalized. So it is wrong to break your promises because if everyone did so there would be no institution of promising. It is contradictory to will universal promise-breaking, since there can be promises only when there is trust in them–which requires that they generally be kept. It’s a very clever idea, but one that only a rationalist philosopher could approve–that it’s actually contradictory to act immorally. The fault of the bad person is thus purely intellectual: he can’t see that his actions are guided by contradictory principles. Immorality is a form of incoherence. If only!

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Alien Matter

How alien is objective physical reality compared (a) to its perceptual appearance and (b) to our own consciousness? As to (a), it seems to lack secondary qualities like color; in which case, what makes it capabable of occupying space? As to (b), unless we go in for panpsychism it seems very remote from the nature of experience. So it must be quite alien to the things we know about most directly. Is it SO alien that we couldn’t represent it in our experience in principle? We’re accustomed to the strangeness of matter from contemporary physics, but is it so far removed from what we are familiar with that we have no hope of adequately representing it? Is it as remote from our understanding as a bat’s experience? Or is it remoter, because at least a bat has experience, which we also do–while matter sits at an opposite ontological extreme? Is the entire universe an alien form of life–though completely dead?

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U and I

The odd thing about utilitarianism is that what makes it most attractive is also what makes it most implausible. It seems good to require impartiality, so that no one is treated as privileged in making a moral decision–hence U doesn’t discriminate with respect to whose happiness is maximized. But this very feature of the theory is what leads to its hyperbolic demandingness–as when it obliges us to give away all our money to charity and neglect our own children in order to benefit remote individuals. The altruistic aspect of U comports well with the intuitive content of morality, but the slide into excessive altruism is immediate. To prevent this, we have to insist on partiality, but then we are back discriminating against certain people. Stressing special relationships quickly leads to favoring our own tribe at the expense of others. It’s either demandingness or discrimination.

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