Sunday, April 22, 2007

The Truth™

Three challenges to truth

Part 1: The Truth™
Part 2: No truth
Part 3: Truthiness

The foundation of non-bullshit metaphysics is the discussion, construction and defense of the notion of "truth". What is this notion?

We can first look at the cognitive/linguistic job for which we employ the notion of "truth". Regardless of of the specific word we use, we still want some word to denote this job, and "truth" is at least as good a word as any other, with the advantage of historical use.

The first job we want to do is discuss distinctions. Thus the notion of truth defines the notion of falsity: If we discuss something as true then it follows that we discuss something else as false—we are making a distinction. The second job we want to do is discuss universal distinctions: If we discuss something as true for someone, somewhere, at some time, we discuss it as true for everyone, everywhere, always; likewise for falsity.

These are not the only cognitive/linguistic jobs we want to do, but we have perfectly good words, sanctified by historical use, to label those other jobs. The most important of these jobs is to discuss non-universal distinctions; we label that job as "opinion".

Since truth refers to a specifically cognitive/linguistic job, it follows that truth and falsity are properties of statements or sets of statements, in the extended sense that we can discuss particular states of mind or neural states in the same sort of language we use to discuss written or spoken statements in a natural language such as English. Mind/brain states are physical, symbolic representation with a vocabulary and grammar, just like statements in natural language.

There are three challenges to this job, hence three challenges to truth.

The first challenge to truth is the "modernist" notion of The Truth™. The Truth™ is a challenge to ordinary small-t truth because it attempts to over-determine truth by privileging a particular context evaluating statements.

We know from Quine et al. that no statement even has meaning, much less truth, by itself. To understand a statement, we need a context. There are two important contexts: the intensional and the extensional[1]. The intensional context governs how we interpret the statement, how the words or concepts or mental states hook up with other mental states. Examples of components of this intensional context applied to natural language statements are dictionaries, thesauri, and grammars. Another example of an intensional context is an axiom set, such as Peano's arithmetic, coupled with the grammar of propositional calculus. The extensional context is just the real world.

The Truth™ is a challenge to truth because it privileges a specific intensional context as true (and thus implies that alternative intensional contexts are false), and therefore the evaluations made under the privileged context become not just true (i.e. true in that context) but The Truth™, as all other contexts are false.

For instance, it is an ordinary truth that "2+2=4" is a theorem of the intensional context of ordinary integer arithmetic. When this intensional context is used to evaluate extensional reality, it is true in the sense that if you put two stones in a jar, and then put two more in, and then count the stones in the jar, you will count to four.

To construct an obviously absurd example, The Truth™ would declare ordinary integer arithmetic a privileged "true" context. Thus "2+2=4" is not just a truth about arithmetic, or a truth about some particular set of stones in a jar, but The Truth™. Of course, once we start applying the underlying concepts of our arithmetical context to other extensional realities, such as the motion of the hour hand of an ordinary 12 hour clock, we start running into silly contradictions: "7+8=15" is a valid statement of ordinary arithmetic and a true statement about stones in jars, but "7+8=3" is a valid statement of modulo-12 arithmetic and a true statement about the position of an hour hand.

Obviously, the statement "7+8=15" means different things in different intensional and extensional contexts; we are entirely justified in considering the same set of symbols to represent different statements in different contexts.

I constructed the above example specifically to highlight the absurdity, but the concept of privileging an intensional context crops up time and again in more subtle ways. For instance modernist meta-mathematics privileged the abstract conjecture-proof intensional context, making alternative contexts false (or at least marginalized as non-mathematics). Postmodernist[2] mathematicians are now exploring a rich vein of alternative contexts, including computational, representational, and probabilistic mathematics[3].

The most historically egregious example of privileging an intensional context to establish The Truth™ is privileging specific cultural and religious contexts to establish The Truth™ in the realm of ethics.

It is a straightforward truth that people in Western societies approve of democracy, a truth in the sense that it is unproblematic that even an alien species observing us from galaxy NGC 6745—regardless of their particular characteristics, assuming only they were able to rationally discuss the subject at all—would conclude that common approval of democracy is a true statement about the people in Western societies.

However, if we arbitrarily privilege this particular social/cultural context as the true context, then "democracy is good" becomes not just a truth but The Truth™; if a society or culture does not embrace democracy, then their own context is false. Likewise for Christianity or Islam, sexual morality and driving on the right-hand side of the road.

Any time you hear someone talking in terms of The Truth™ (you can actually hear the capital letters and the ™ symbol), look carefully and you'll see they're always privileging some particular intensional context for establishing The Truth™.

The Truth™ is fundamentally a challenge to truth because small-t truth is always dependent on intensional context. (The context dependence does not entail subjectivism, though, because context is a particular subjective state, it is not established by particular subjective states.[4]) There is no way of establishing the truth of an intensional context, in the sense of applying to contexts the job we expect of "truth". Specifically we have no basis other than the arbitrary (non-universal) imposition of a context to distinguish a true context from a false one. Thus in making the distinction we just push the arbitrary non-universalism around; we don't eliminate it.

The Truth™ fundamentally, then, is revealed as bullshit in the philosophical sense: Using truth-language while being fundamentally indifferent to truth.


[1] For the purpose of this discussion, we will presuppose the notion of scientific realism, that a real world exists independent of our minds and—usually directly but often indirectly—causes our perceptual experiences. All the same sorts of conclusions, however, apply mutatis mutandis to Phenomenalism, with perception standing in for extension, from which we can construct the notion of scientific realism.

[2] Postmodernism will get its share of criticism in the next installment: "No truth".

[3] See A Glance at Postmodern Pedagogy of Mathematics (h/t to philosophical bits).

[4] My apologies: This comment is the soul of (bad) obscurity. I promise to clarify in the future.

14 comments:

  1. I thought "extension" generally was what a term denoted ("American presidents" denotes T. Jefferson. along with the others--the extension is all American presidents), and intension more a matter of connotation, possible attributes (head of state, commander in chief,etc.).

    But I think any discussion--any non-bullshit discussion-- of Truth starts with epistemology: how does knowledge function, accumulate, develop: language/semantic issues are separate, or subsequent to that discussion. The axioms of Peano arithmetic for instance are not really that similar to say the periodic table. And since you pride yourself on empiricism, and scientific materialism, it would seem that you would agree that mathematics is a type of language which developed over centuries, and really so is logic: in other words, it seems a scientific materialist would be required to hold to a sort of nominalism (as Quine suggested as well). Nominalism is of course not some postmodernist or relativistic view; but does mean things could be done differently, at least at level of semantics and mathematics: as say using binary instead of base 10 number systems. Trivial perhaps but axiomatic "truths" are quite different than statements about empirically observable events, objects, processes.

    While I will not join you on your excursion through truth theory, I would like to state, however vulgar it seems, that scientific materialism also entails a certain economic and political awareness. That was the point on rights discussion that I think you overlook or ignore: Gewirth is not just fiddling away on the "generic features of action" for sh**ts and giggles. Reason and Morality is a non-arbitrary foundation for an economic-political system, more or less: and to reduce it to just prudential advice misses the point. Lacking some objective validation for economic rights and entitlement, politics become more a matter of aesthetics (as Hume himself seems to suggest), if not the old state of nature. That's the truth.

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  2. jeff.maynes4/22/07, 9:02 PM

    Can your point be put the following way:

    1. As Tarski showed us, truth is a predicate that applies to languages.
    2. Only necessary truths are "The Truth."
    3. Quine undermined necessity with his critique of analyticity.
    4. Kripke salvaged some necessity by going back to a Millian picture of names, where names only have an extension.
    5. So, Kripkean necessity claims (e.g., "Hesperus is Phosphorus") are "the Truth."
    6. Since that is the only class of necessary truths we've got (since Quine's critiques still apply to things like mathematics), only extensional claims in the Kripkean vein count as "the Truth" and all other truths are merely "truths."

    Is that a fair characterization of your point?

    If so, then while it's fair to warn us from saying too many of our claims are necessary truths, not all claims (such as in ethics) of objective truth are necessity claims. So while the Quinean point is certainly true, it isn't enough to rule out rejecting ethical relativism. (Though likewise it isn't clear whether you are using ethical relativism as an example or a consequence).

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  3. Perezoso:
    I thought "extension" generally was what a term denoted.

    I agree. I gave extension very short shrift in the essay. The extension is, as you say, what a term denotes. The extensional context, in which the things denoted "live", is the real world.

    But I think any discussion--any non-bullshit discussion-- of Truth starts with epistemology

    I don't think there's any good place to start in philosophy. Everything is interlinked and cross-referenced. In any event, I do discuss epistemology in my series on The Scientific Method.

    [I]t seems a scientific materialist would be required to hold to a sort of nominalism.

    Agreed. The operative word being a sort of nominalism; I don't agree with everything that's been said about nominalism.

    Nominalism is of course not some postmodernist or relativistic view...

    There are those who would disagree, and call Quine a postmodernist. I'm not that stuck on labels, myself. And "relativism" by itself doesn't mean anything; it's often used as an irritating synonym for nihilism.

    [S]cientific materialism also entails a certain economic and political awareness. That was the point on rights discussion that I think you overlook or ignore.

    I can write about only one thing at a time. I think it's important per se to clear away myths and fallacies of ethical discourse. I also do talk positively about ethical discourse as well as polemically and politically about what I strongly approve and disapprove of.

    Reason and Morality is a non-arbitrary foundation for an economic-political system, more or less: and to reduce it to just prudential advice misses the point. Lacking some objective validation for economic rights and entitlement, politics become more a matter of aesthetics (as Hume himself seems to suggest), if not the old state of nature. That's the truth.

    To some extent I agree. Lacking an objective basis, politics is indeed a matter of subjectivity (although I will repeat my consistent objection that aesthetics and taste are not the whole of subjectivism).

    But it's not sufficient that we want an objective basis. There has to actually be one, and it has to be rationally justifiable. I don't find it at all satisfying to simply make up some ethical basis, call it "objective" and pretend it really is.

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  4. jeff.maynes:

    2. Only necessary truths are "The Truth."

    Depends on what you mean by "necessary truths". If we look at propositional calculus in a purely mathematical way, there are statements that always evaluate to the constant "true" over all possible values of the variable(s) (e.g. "p or not-p", which is a true statement about propositional calculus). There are analytical statements, which are statements about a language (e.g. "all bachelors are unmarried", a true statement about the English language). It's difficult to understand in what sense these statements are "necessary". The statement, "All bachlors are unmarried," is certainly false in Hsilgne, an invented language that uses all the same words as English but each word has a completely different meaning than its English equivalent.

    I'm not sure, for instance, that "Hesperus is Phosphorus" is a necessary truth. It seems easy to simply call it a contingent truth about a particular language.

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  5. jeff.maynes4/23/07, 6:41 AM

    If not necessity, then I'm curious what you mean by "the Truth." The use of intension/extension seems to indicate that saying something is "the Truth" means saying something about how things really are. Well, since the truth predicate applies to sentences, any truth is going to be relative to a language. That's the force of Tarski's work (which I take as a powerful constraint on a theory of truth). So if that understanding is correct, then either "the Truth" is incoherent or there are no examples of it. But perhaps I have misunderstood you.

    I'll play the Kripkean for a moment and defend "Hesperus is Phosphorus," since on my initial understanding of your point, this makes sense of it. So, if we follow Kripke and take names to be rigid designators then they specify the same thing in all possible worlds. So since "Hesperus" and "Phosphorus" always specify the same thing, the truth is metaphysically necessary.

    It is, of course, true-in-L(english), but so are all sentences. That's the way the truth predicate applies (which is why I was confused by your respond to my post attacking the necessity of H=P on these lines). So your example of homophonic translation changes the word and it is a new sentence (because now it is a sentence of a different language). No matter how you change the symbols, if the words remain the same, then they will always specify the same thing. The homophonic translation changes the words, so it does not affect the truth value of H=P. In all possible worlds, H=P is always true, and is therefore necessary.

    Also, I don't think truths of mathematics, logic, etc. are necessary. I think Quine is correct on that issue.

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  6. jeff.maynes:

    If not necessity, then I'm curious what you mean by "the Truth."

    By The Truth™ I mean something more prosaic than what you're talking about. I'm talking about stuff like, "Only that mathematics susceptible to the conjecture-proof method are The Truth™." And I'm talking about "Since secular democracy is good for the United States, it's The Truth™, and therefore it must be good for Iraq; if they don't want it, there's something wrong with them."

    The use of intension/extension seems to indicate that saying something is "the Truth" means saying something about how things really are.

    The small-t truth is about a true way of talking about how some things really are in a context. The Truth™ consists of privileging a context as the only way of talking about those things.

    So, if we follow Kripke and take names to be rigid designators then they specify the same thing in all possible worlds.

    This I think is the crux of the biscuit, and a sense where philosophy, rather than seeking truth, is unproductively (if not fallaciously) seeking The Truth™.

    In what sense can a name be a "rigid designator"? Certainly not in any specific natural language, where the the designation is at best empirical and at worst arbitrary. "Phosphorous" means, in an extensional sense, those things when pointed to people who speak English typically assent to "Is this phosphorous?"

    We could translate a statement in natural language into an artificial language with an intensional context of rigid designation, but then we would be forced to translate "Hesperus is Phosphorous" to "Phosphorous is Phosphorous", which is just an instance of an always true-valued statement about propositional calculus (i.e. p=p), presumably the grammar of our artificial language.

    We get into all sorts of trouble, though, trying to come up with such an artificial language with truly rigid designators, because nouns in this language have meanings which are ambiguous precisely to the extent of our epistemic limitations, and this ambiguity contradicts our intention of rigid designation.

    Putnam's Twin Earth style paradoxes highlight this ambiguity: Precisely what does a rigid designator that corresponds to the English word "water" designate? To the extent that the speaker does not know that his water is composed of two Hydrogen molecules and one Oxygen molecule, by what means are we justified in translating "water" to a rigid designator that designates only H2O?

    We can talk in an airily abstract way about rigid designators, but when we actually get down to cases, we find that we've just moved the ambiguity from the natural language to the translation process.

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  7. jeff.maynes4/23/07, 9:01 AM

    I'm not sure my disagreement with you is substantial, or merely over the details of your argument. I'll stick to the latter in tihs reply.

    I find your use of Putnam's Twin Earth case curious. The point of Putnam's work is similar to Kripke - he wanted an extensional theory of meaning. So what Kripke did for proper names, Putnam does for natural kind terms. Putnam's very point is that "water" in Earth and "water" in Twin Earth have different meanings, despite the fact that the two Oscar's are in identical psychological states. Putnam's very conclusion is his famous line that "meaning just ain't in the head." That is, the meaning of the two terms is determined its extension. This is the same side of the street that Kripke works in Naming and Necessity.

    So what are Kripke and Putnam really up to here? They are doing semantics. They are offering theories (well, Kripke isn't, but that's unrelated) about how we ought to conceive of meaning. The essential evidence both rely on are linguistic intuitions. Thought experiments like Twin Earth and the Godel case are designed to show that our intuitions do in fact support the claim that the meaning of names/natural kind terms is the extension of the term.

    I'm not really sure what sense it makes to ever say a particular semantic theory is "the Truth" so I think this line of disagreement might be a useless excursus. Surely semantic theories cannot be read off either the world or language, and the one we choose will be heavily guided by pragmatic virtues, etc. It makes no sense to say that there is one semantic theory that is the way natural language works. Surely philosophy isn't going for "the Truth" here.

    That's all to say I don't really think semantics is at all related to your notion of "the Truth." Taken together with my point in my last post, I don't really see any problem. The truth predicate is relative to a language, and will hinge on the semantics of that language. Just as Tarski had to stipulate the satisfaction relation for his formal language, we'd have to offer a complete semantics to develop a truth theory. Surely that isn't going to happen, but that's why we are in the business of offering and revising hypotheses.

    So I'm not sure I feel the same pressure from the ambiguities of natural language that you do. It's trivial that "Hesperus = Phosphorus" is not necessarily true if you change the meanings of the terms. This is only to say that the truth of any sentence depends on the language in which it is uttered, and the semantics of that language. This is tricky in natural language because the meanings of our terms are ambiguous. I do not, however, see this as a problem. To even engage in truth-talk we've got to decide on the meanings of our terms.

    To sum up, my whole point can be distilled as such: truth-talk occurs within a single language, and essentially depends on semantic theory. When we say something is true, we mean that it is true within that language. We might, and probably do, apply the true sentence universally. A challenge to the semantic theory or language in which the truth is formulated might alter the truth conditions of the sentence, but it does not mean we cannot apply it to others.

    So the Democratic theorist would simply say that "democracy is the best form of government" is a universal truth, and that it depends on a certain set of facts and the meanings of the terms. The simple fact that we could keep the phonemes the same and alter the semantic theory such that the sentence means "facism is the best form of government" does not undermine the theorists attempt to apply his sentence across the board. His sentence might be false because certain facts he relies on are relative, but the universal application of a true-in-L sentence is not threatened by the in-L condition.

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  8. Are you saying that truth is exclusively a propositional function?

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  9. Deacon: Truth is relation between a statement and an intensional and extensional context.

    The same goes for analytic statements with the language (intensional context) itself treated as an object instantiated in a dictionary, etc. or as real mental states.

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  10. Putnam's very conclusion is his famous line that "meaning just ain't in the head."

    That is correct. The extension of the term is sort of provisional, depending on the definition of the term (which I think we could agree with Quine is not immutable): but the facts are the facts. Does Einstein encounter some semantic difficulties in his gen. and spec. theories of relativity? Not really. What is troubling the semanticists is "synonymy". I am not an expert in Kripke (however I think he misread Russell in Naming and Necessity), but one could take issue with the idea that synonymy is somehow necessary, but say the truths of the periodic table or relativity are not. That water freezes at 0 celsius seems pretty f-n necessary (along with countless other facts of physical science), regardless of what a Hume or german idealist might say. Or rather, there are NO necessary semantic truths, but sort of apparently immutable facts (physical/chemical reactions--drop K into H20 you get an explosion, etc.), and the semantics describes (and depends on) those external, objective facts/events/processes. And I think Quine suggests that too: the extension of a term (or statement), while not "fixed", relates to the extra-linguistic facts.

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  11. jeff.maynes

    The point of Putnam's work is similar to Kripke - he wanted an extensional theory of meaning.

    Indeed. My point is that an extensional theory of meaning doesn't get us any far, because of the ambiguity problem.

    Putnam's very conclusion is his famous line that "meaning just ain't in the head."

    Indeed. My point is that Putnam is incorrect—or at least irrelevant. Meaning is in the head.

    Thought experiments like Twin Earth and the Godel case are designed to show that our intuitions do in fact support the claim that the meaning of names/natural kind terms is the extension of the term.

    Except that I find Putnam's conclusions counter-intuitive.

    Surely philosophy isn't going for "the Truth" here.

    Maybe, maybe not. ::shrugs:: I personally think that extensional meaning is an attempt to embed truth directly into language and meaning, a project I think is doomed in a fundamental way. That I call such a project a search for The Truth™ is, if you like, a manner of speaking or a metaphor.

    Keep in mind that I'm offering different examples of the The Truth™ as privileging some sort of context. In philosophy of language, that context is a mythical rigid designator language. In ethical/political philosophy, it's a particular cultural context—the language problem does not entail the political problem; they're merely similar.

    To even engage in truth-talk we've got to decide on the meanings of our terms.

    Precisely so! But this is not just a little chore we have to get out of the way to get to our real work, it's intrinsic to truth-talk.

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  12. Does Einstein encounter some semantic difficulties in his gen. and spec. theories of relativity? Not really.

    Au contraire, mon ami! Go back and re-read Einstein's own book. He redefines the semantics of "space" and "time": They are no longer even ontological extensional terms, they become epistemic terms: Space is what we measure with a ruler, time is what we measure with a clock. Minkowski comes along a few years later and defines a whole new extensional term: space-time.

    And it gets worse! Looking at SR & GR, we can formulate a bijective theory where space and time are extensional terms, and the things that they denote change shape.

    Even worse: We can form yet another bijective theory where space and time are constant, objects are constant, but light rays change shape.

    Not only does Einstein deny us a privileged frame of reference to measure absolute velocity, he denies us even a privileged language to talk about physics!

    That water freezes at 0 celsius seems pretty f-n necessary

    I think jeff.maynes means "necessary" in the sense of logical necessity. That water freezes at a particular temperature is true, but it's a contingent truth, a truth about this possible world. (Unless you mean "water freezes at 0C" in the analytic sense, in that 0C is defined to be the temperature at which water freezes; in which case we're back to linguistic philosophy.)

    You can say "fuck" here, BTW.

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  13. Merci boo-coo, but I have Einstein's own writings on Relativity, and while I am a not pro. physicist, I understand it fairly well (including the integrals). Einstein continually affirms he is an empiricist and determinist, and that physics is inductive (as Newton himself established); that spacetime takes on that 4 dimensional character, or that perspective may affect the perception of time, does not alter the fact that relativity still is a property of objective "reality" and not at all mental. Einstein is not some Kantian (or mystic, as some of the quantum physics people seem to suggest). He never doubts the reality of the perceived world, and the objectivity of the data. In terms of semantics, I think it is fair to term Einstein a "referentialist" as most "normal" scientists are. The propositions of natural science refer to perceivable facts "out there," even if subatomic or astronomical. Yes, inference and probability are important concerns, but that the truth of some events--say even the supposed indeterminacy of some quantum events---are provisional or contingent does not all all entail a sort of extreme subjectivism or Kantian sort of idealism; really, LaPlaceanism still holds for the vast majority of physical-chemical events and processes; it's a matter of not having enough information, not that "everything is random/chaotic, man".

    I suggest you read Bricmont (a Belgian physicist who has written some interesting things criticizing the chaos fetishists and subjective/mystical readings of quantum physics). The semantics simply describe/denote (and extension is merely a fancy name for denotation, whether in terms of nouns, or statements) those objective states of affairs. What's the alternative? Kant? Some bizarre possible worlds BS? Pulzeeze don't start with that. Probable/contingent events and situations (who will win the pennant) are not worlds or "places"--they aren't really anything, in terms of logic or empiricism: that attachment to contingency/modality is the schtick of the Kripke school.

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  14. And Bricmont also criticizes the sort of Humean/Popperian skepticism towards the truths of natural science (besides, you mentioned Quine, who more or less rejects analyticity, and WVOQ was hardly a Popperian-subjectivist either). You can call gravity contingent if you want; but how about we lay bets on whether your snapple bottle floats upwards at some time in the next 5 years when you drop it.

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