Requests and naturalism

If someone asks me to ϕ, typically that informs me that they want me to ϕ. But the normative effect of the request cannot be reduced to the normative effect of learning about the requester’s desires.

First, when you request that I ϕ, you also consent to my ϕ, and hence the request has the normative effects of consent. But one can want something done without consenting to it. For instance, if I have a lot of things on my plate, I might desire that a student give me their major paper late so that I don’t have to start grading yet, but that desire is very different in normative consequences from my agreeing to the lateness of the paper, much less my requesting that it be late.

Second, considerate people often have desires that they do not wish to impose on others. A request creates a special kind of moral reason, and hence imposes in a way that merely learning of a desire does not.

Moreover, we cannot understand requests apart from these moral normative effects. A request seems to be in part or whole defined as the kind of speech act that typically has such normative effects: the creating of a permission and of a reason. Moreover, that reason is a sui generis one: it is a reason-of-request, rather than a reason-of-desire, a reason-of-need, etc.

There is something rather impressive in this creation of reasons. A complete stranger has the power to come up to me and make me have a new moral reason just by asking a question, since a question is in part a request for an answer (and in part the creation of a context for the speech acts that would be constitute the answer). Typically, this reason is not conclusive, but it is still a real moral reason that imposes on me.

Consider the first time anybody ever requested anything. In requesting, they exercised their power to create a moral reason for their interlocutor. This was a power they already had, and the meaningfulness of the speech act of requesting must have already been in place. How? How could that speech act have already been defined, already understandable? The speech act was largely defined by the kinds of reasons it gives rise to. But the kinds of reasons it gave rise to were ones that had never previously existed! For before the first request there were no reasons-of-request. So the speech act had a meaningfulness without anybody ever having encountered the kinds of reasons that came from it.

This is deeply mysterious. It suggests an innate power of the human nature, a power to request and thereby create reasons. This power seems hard to reconcile with naturalism, though I do not have any knock-down argument here.

Meaning

1. A thing with no meaning cannot cause a thing with meaning.
2. There was a first meaningful thing (e.g., a thought) in the physical universe.
3. Every thing in the physical universe has a cause.
4. So, there was a meaningful thing not in the physical universe that caused the first meaningful thing in the physical universe.

Meaning and beauty

1. Only intelligent beings and things produced by them have objective meaning.
2. Something that is objectively meaningless is not objectively beautiful.
3. The earth is objectively beautiful.
4. The earth is not intelligent.
5. So, the earth is produced by an intelligent being.

Sex as an iconic partially self-representing gesture

“Iconic representational gestures” are like a gestural onomatopoeia: their physical reality resembles in some way what they signify. For instance, blowing a kiss signifies a kiss, running a finger across a throat signifies a killing, and a baptism signifies cleansing from sin.

An interesting special case of iconic representational gestures is one where the physical reality of the gesture itself itself accomplishes a part of what it represents. A slap in the face is an iconic gesture that represents the punishment that the other party deserves for bad behavior and is itself physically a part of the punishment. Intercourse is an iconic gesture that signifies a union of persons and its physical reality constitutes the physical part of that union. And, on views on which Christ’s body is present in the Eucharist, the reception of the Eucharist is also such an iconic gesture representing union with Christ and physically effecting an aspect of that union. We can call such gestures partially self-representing.

Now, normally meaning gets attached to symbolic acts like words and gestures through other symbolic acts (you point to a “zebra” and say “Let’s call that ‘zebra’”). This threatens to lead to a regress of symbolic acts. The regress can only be arrested by symbolic acts that have an innate meaning. Now, while there is often an element of conventionality even in iconic representational gestures, just as there is in onomatopoeia, nonetheless I think our best candidate for symbolic acts that have an innate meaning is iconic representational gestures. Moreover, if the gesture has an innate meaning, it is plausible that it was used at least as long as humankind has been around.

If we think about the best candidates for such gestures, we can speculate that perhaps pointing or punching has been around as long as humans have been around. But that’s speculation. But it’s not speculation that sex has been around as long as humans have been around. Thus, sex is an excellent candidate for a gesture that has the following features:

• iconic representational

• partially self-representing

• innate meaning.

Moreover, given that the physical aspect of sex is a thorough biological union, it is very reasonable to think that this innate meaning is a thorough personal union. But, as Vincent Punzo has noted in his work on sex, a thorough personal union needs to include a normative commitment for life. And that is marriage. Thus, sex signifies marriage.

Some paradoxes of reference

Liar-like:

• one plus the biggest integer that can be expressed in English in fewer than fifty words
• one; two; three; one plus the biggest integer mentioned in this list
• one; two; three; one plus the last integer mentioned in this list
• one plus the last integer mentioned in this list; two; three; one plus the first integer mentioned in this list
• one plus this integer

Truthteller-like:

• one; two; three; the biggest integer mentioned in this list
• one; two; three; the last integer mentioned in this list
• the last integer mentioned in this list; two; three; the first integer mentioned in this list
• this integer
• the square of this integer

Whatever content can be conveyed metaphorically can be said literally

Suppose you say something metaphorical, and by means of that you convey to me a content p. I now stipulate that "It's zinging" expresses precisely the content you conveyed. Technically, "It's zinging" is a zero-place predicate, like "It's raining." And now I say: "It's zinging." The literal content expressed by "It's zinging" is now equal to the metaphorical content conveyed by what you said. A third party can then pick up the phrase "It's zinging" from me without having heard the original metaphor, get a vague idea of its literal content from observing my use of it, and now a literal statement which has the same content as was conveyed by the metaphorical statement can start roaming the linguistic community.

Thus: If you cannot say something literally, you cannot whistle it either. For if you could convey it by whistling, you could stipulate a zero-place predicate to mean that which the whistling conveys.

Objection 1: My grasp of "It's zinging" is parasitic on your metaphor, while the third-party doesn't have any understanding.

Response: Yes, and so what what? I wasn't arguing that you can usefully get rid of metaphor. It may well be essential to understanding the content in question. My point was simply that there can be a statement whose literal semantic content is the same as the content conveyed by your metaphor. Understanding is something further. This is very familiar in cases of semantic deference. (I hear physicists talking about a new property of particles. I don't really understand what they're saying, but I make the suggestion that they call that property: "Zinginess." My suggestion catches on. I can say: "There are zingy particles", and what I say has the same content as the scientists' attribution of that property. But while the scientists understand what they're saying, I have very little understanding.) The third party who hasn't heard the original metaphor may not understand much of what he's saying with "It's zinging." But what he's saying nonetheless has the literal semantic content it does by deference to my use of the sentence, and my use of the sentence has the literal semantic content it does by stipulation. All this is quite compatible with the claim that any decent understanding of "It's zinging" will require getting back to the metaphor. But, nonetheless, "It's zinging" literally means what the metaphor metaphorically conveyed.

Objection 2: The stipulation does not succeed. (This is due to Mike Rea.)

Response: Why not? If I can refer to an entity, I can stipulate a name for it, no matter how little I know about it. I may have no idea who killed certain people, but I can stipulate "Jack the Ripper" names that individual. My stipulation will succeed if and only if exactly one individual killed those people. Similarly, if I can refer to a property, I can stipulate a one-place predicate that expresses that property. (If a certain kind of Platonism is true, this just follows from the name case: I name the property "Bob", and then I have the predicate "instantiates Bob".) In cases without vagueness, contents seem to be propositions, and zero-place predicates express propositions, so just as I can stipulate a one-place predicate to express a property, I should be able to stipulate a zero-place predicate to express a propositions. And in cases of vagueness, where maybe a set of propositions (or, better, a weighted set of propositions) is a content, I should be able to stipulate a similarly vague literal zero-place predicate as having as its content the same set of propositions.

There are many ways of introducing a new term into our language. One way is by stipulating it in terms of literal language. That's common in mathematics and the sciences, but rare in other cases. Another way is by ostension. Another is just by talking-around, hoping you'll get it. One way of doing this talking-around is to engage in metaphor: "I think we need a new word in English, 'shmet'. You know that butterflies in the stomach feeling? That's what I mean." We all understand what's going on when people do this kind of stipulation. For all we know, significant parts of our language came about this way.

What can we learn from the Contingent Liar?

Start with this:

• The last bulleted item in this post is not true.

Call this token bulleted linguistic item p. Then p is, in fact, the last--and the only--item prefixed with a bullet point in this text. If it's not true, then it seems it's true. But if it's true, then it seems it's not. Oops! That's a contradiction in classical logic. But, famously, sentences like this are only contingently paradoxical. If I were to add a bullet point followed by "2+2=4" at the end of the post, then p would be unparadoxically false, while if I were to end the post with a bullet point followed by a piece of nonsense or a falsehood, then p would be unparadoxically true (nonsense is not true).

Here is an assumption that I think is implicit in the above derivation:

1. The item p is true if and only if the last bulleted item in this post is not true.

The argument needs some bridge like this between the truth of the linguistic item p and the last bulleted item not being true. Once we have (1), then the argument is quick, using only uncontroversial premises. If item p is true, then the last bulleted item is not true by (1). But empirically the last bulleted item is p. So if p is true, then it's not true. But if it's not true, then by (1) it's not the case that the last bulleted item is not true. Since empirically the last bulleted item is p, it follows that it's not the case that p is not true, i.e., that p is true. So p is true if and only if it's not true, a contradiction in classical logic.

Since we should not deny classical logic or obvious empirical truths, it follows that (1) is false. Now, if p expresses a proposition, then it's got to express a proposition that makes (1) be true--that's both intuitively obvious and a consequence of the Tarski T-schema. (Doesn't (1) follow from the T-schema absent the expression assumption? It had better not. If "s" is meaningless, then the instance "'s' is true if and only if s" does not express a proposition, too, and hence is not true. So the T-schema had better apply only to meaningful items.) So p doesn't express a proposition. But that's a contingent fact, since in another possible world I screw up and end this post with a bulleted "2+2=5" thereby making p both meaningful and true.

So, whether a linguistic item expresses a proposition is in general a contingent matter. We already should have known this in the case of linguistic items using names, indexicals and demonstratives, and indeed p contains the demonstrative "this". But nothing hangs on p containing the demonstrative "this"--one could just replace it with some complex definite description--so I will ignore this demonstrative. If we think that whether a linguistic item expresses a proposition determines whether it's a meaningful sentence, then it follows that whether a linguistic item is a meaningful sentence is contingent, even in the absence of names, indexicals and demonstratives.

Further, not only is it a contingent matter whether a linguistic item expresses a proposition, but whether it does so can vary from token to token, again in the absence of names, indexicals and demonstratives. After all, I just gave a conclusive argument p does not express a proposition, and hence that the last bulleted item in this post does not express a proposition, and thus is not true:

2. The last bulleted item in this post is not true.

Item token (2) is true (note that numerals aren't bullets) and hence expresses a proposition. But s, which is a token of exactly the same type, does not. And that's not due to names, indexicals or demonstratives.

These conclusions are interesting independently of the paradox. But somehow it feels wrong to use the paradox to reach them. Is it?

The start of meaning

The first meaningful performance did not gets its meaning from earlier meaningful performances. So it seems that meaning preceded meaningful performances. Let's say the first meaningful performance was a pointing to a distant lion. Then pointing had a meaning before anybody meaningfully pointed.

Well, things aren't quite so simple. Maybe there is no "before" before the first meaningful performance, since maybe the first meaningful performance is an eternal divine meaningful performance (perhaps the generation of the Logos?). Or maybe the first meaningful performance got its meaning from later meaningful performances (Sellars seems to think something in this vicinity with respect to the relationship between thoughts and concepts) in some sort of virtuous circularity.

The theistic move seems just right to me. The virtuous circularity move is, however, not going to work. For the circle of performances then had a meaning independently of itself, and so we still get a meaningful performance—perhaps by a community—that doesn't get its meaning from anywhere else.

One may have vagueness worries about the idea of a "first meaningful performance". Still, in a supervaluatist framework we can fix a precisification of "meaningful performance", and then the argument will go through.

Meaning

1. Every meaning derives from components to which intelligent beings have assigned a meaning.
2. Some things that have a meaning that does not derive from components to which earthly beings have assigned a meaning.
3. Therefore, there is a non-earthly intelligent being.

I suggest two examples for premise (2).

Life: Life has a meaning. But a meaning of life that derives from our assignments is not a meaning that matters to us. What we have assigned meaning to, we could reassign meaning to. If the meaning of life were merely a matter of human assignment, then humanity's search for meaning would be a mere matter of curiosity, of figuring out how our ancestors have assigned meaning and how those meanings combine. It would be either like searching for the meaning of an ancient inscription (a case where we don't know the meanings of the components) or like parsing a complex sentence in first order logic (a case where we know the meanings of the components but don't know how they go together). There would be no deep existential relevance in such a meaning, since we could just as well assign a meaning ourselves. It would be just a meaning assigned by peers.

This example shows that the meaning of life needs not just to be a meaning assigned by a non-earthly intelligent being, but by a being whose meaning-assignments have deep existential relevance to us. A being with a deep kind of authority. So not just some space alien that seeded life on earth, say.

The sublime: Any case of the sublime—say, the Orion Nebula or Beethoven's 9th—has a meaning that escapes us, all of us. Cases of the sublime can be natural or human-made, but in both cases they have a meaning beyond us. And that meaning-beyond-us isn't just a matter of being better at figuring out how components combine, in the way that the meaning of a sentence of First Order Logic is. In a piece of the sublime we don't know very well, but can only vaguely sense, what the meaningful components are, and we are not responsible for the mysterious meaningfulness of these components. Even in the human-made cases, the creator is a servant to that mysterious meaning of the components.

Moreover, the meaning of the sublime piece is one that we resonate with, one we have a kind of grasp of—or maybe that has a grasp on us—that ever eludes us. We have a resonance to the meaning of the sublime. So whatever story we give about that meaning, we also need to give a story about how it's a meaning we resonate to. There could be aliens that have assigned deep mythological interpretations to various components of the Orion Nebula. But that isn't the meaning we resonate to. So, once again, the argument not only yields a non-earthly intelligence, but one who can make us resonate to his designs.

Intensions

The intension of a referring expression e in a language is a partial function I_e that assigns to a world w the referent I_e(w) of e there, when there is a referent of e in w. Thus, the intension of "the tallest woman" is a partial function that assigns to w the tallest woman in w.

The intension of a unary predicate P is a partial function I_P that assigns to a world w the extension I_P(w) of P at w, i.e., the set of all satisfiers of P there.

Intensions are meant to capture the semantic features of terms, with respect to intensional semantics. Now let e be the referring expression:

• The set of even integers.

Let E be the predicate

• is an even integer.

Then the intension of e assigns to w the set of all even integers, for each w. And the intension of E assigns to w the set of all even integers, too. So I_e=I_E. But e and E are plainly not semantically equivalent, even within intensional semantics. So intensions are insufficient for characterizing the semantic features of expressions, even with respect to intensional semantics.

A longshot: Perhaps something like this led Frege to his weird "The concept horse is not a concept" claim.

Lying and being sincere at the same time

Sam is a politician speaking to a large multilingual audience, and is planning on offering them slogans that uniquely appeal to each language group. By coincidence, there is something, s, that he can say which is such that in Elbonian it means that he loves to hunt while in Baratarian s means that he is an avid cyclist. Sam actually loves to hunt but hates cycling, but knows that saying that he loves to hunt will tend to appeal to Elbonian speakers, whom he also tends to respect and does not wish to deceive, and that saying that he is an avid cyclist will tend to appeal to Baratarian speakers. So Sam utters s.

In so doing, Sam is sincerely asserting to Elbonian speakers that he loves to hunt and lying to Baratarian speakers that he is an avid cyclist. But there is Jane in the audience who is a completely bilingual Elbonian and Baratarian speaker. Did Sam lie to Jane?

One might say: It depends on how Jane understood him. But that's not right. To lie to someone does not require the interlocutor to understand one at all. If I write to you in a letter of recommendation that says that Jim is the worst student I have ever had, while in fact I know he is the best student I have ever had, and you misread the "worst" as "best" in the letter (after all, typically, in a letter of recommendation a superlative is positive, so you're primed to read it as "best"), nonetheless I lied to you, but unsuccessfully. Jane might have understood s in Elbonian, or in Baratarian, or just been confused by s. But nonetheless it seems that Sam both lied and spoke sincerely to Jane. He lied to Jane qua Baratarian speaker, since he asserted to all Baratarian speakers that he was an avid cyclist, and he spoke sincerely to all Elbonian speakers, including Jane, that he loved to hunt.

But this is odd. And it also means that it is difficult to make the token the unit of meaning. And that's a problem for nominalists of the Goodman and Quine variety.

Searching for meaning in one's suffering

Here is a logically valid argument:

1. If theism is false, most evils are meaningless.
2. If most evils are meaningless, it is inadvisable for sufferers to put significant effort into searching for meaning in their suffering.
3. It is not inadvisable for sufferers to put significant effort into searching for meaning in their suffering.
4. So, theism is true.

All the conditionals here are material conditionals and I am not claiming any kind of necessity for them. I do find the premises fairly plausible. I am least sure of (2). I not clear on what "meaning in suffering" is, but there does seem to be such a thing—at least, many people report finding it.

Meaning and use

Consider the thesis:

1. The meaning of a word is defined by how it is used.

This thesis seems false. I hereby stipulate that "Xozhik" is a name for me. As soon as I have made the stipulation, "Xozhik" has acquired a meaning. However the word did not get used, but was only mentioned, and it could be that nobody ever uses it.

This nit-picking point does not affect more sophisticated theses about meaning and use.

Eternal significance

I find myself pulled to the following two claims:

1. If nothing lasting can come from human activity (think of Russell's description of everything returning "again to the nebula"), then no human life has much meaning.
2. If nothing lasting can come from human activity, some human lives (e.g., lives lived in loving service to others) still have much meaning.

I don't think I am alone in finding myself pulled in these two directions. It would be nice if one could reconcile these two intuitions.

If the conditionals in (1) and (2) are material, then there is an easy way to reconcile these two intuitions. For if they are material conditionals, then (1) and (2) together entail:

3. Something lasting can come from human activity.

And given (3), there is no contradiction between (1) and (2)—both are trivially true because their antecedents are false.

This seems too facile. (Maybe only because I am not sufficiently convinced by my arguments here. But I also think that this interpretation ignores the anti-material marker "still" in (2).) But here is a more sophisticated hypothesis about these two intuitions. Suppose that God has designed our world so that only events that can have eternal significance are deeply morally significant. Then it is contingently true that:

4. Nothing that lacks eternal significance has deep moral significance.

Moreover, suppose that God implants in us a strongly engrained intuition that (4) is true. He does this in order to set our sights on eternity and to comfort us under the slings and arrows of outrageous fortune. (I think here of Boethius' Consolation of Philosophy.) At the same time, the moral significance of events does not entirely come from their eternal significance. Thus, such counterfactuals as

5. If lives of loving service to others lacked eternal significance, they would still have deep moral significance

are true, and moral reflection can discover these truths.

This hypothesis would explain why we are drawn to (1). We are drawn to (1) because we have a deep divinely implanted intuition that (4) is true, and (4) makes (1) very plausible. Moreover, the hypothesis can explain why we are drawn to (2), namely that with reflection we discover (5) to be true. (Contrary to what the name "subjunctive conditional" suggests, we do use the indicative mood for subjunctive conditionals sometimes.)

The hypothesis also explains why it is hard to find arguments for (1), why belief in (1) is more of a gut feeling than an argued position, but nonetheless a gut feeling that it is hard to get rid of.

Finally, the hypothesis is compatible with the possibility of there being non-theists like Russell who overcome their pull to (1). The intuition isn't irresistable. The only plausible story as to how (4) can be true is that, in fact, God makes all morally significant things have potential eternal effects. So a non-theist is likely to realize that (4) fits poorly with her overall view, and hence get rid of (4).

This hypothesis about (1) and (2) charitably does about as much justice as can be done to both intuitions simultaneously. This gives us not insignificant reason to think the hypothesis is true, and hence that there exists a God who makes morally significant events have potentially eternal effects.

Of course, one might come up with naturalistic explanations of the pull to (1) and (2). But I suspect that these naturalistic explanations will end up simply denying one of the two intuitions, and then explaining why we have this mistaken view. An explanation of our intuitions on which the intuitions are true is to be preferred for anti-sceptical reasons.

Water

I've been making myself more of a nuisance than usual. I've been asking people whether ice and steam are water. Does it matter? Well, if ice or steam isn't water, then water is not just H₂O. And that is good to know. But the question sort of grew on me, as questions often do.

The result of my informal survey is that there is simply no consensus on the question. A number of people told me that ice that is frozen water, and hence it's water. On the other hand, my five-year-old son thought that ice is frozen water, and hence it's not water. At issue here, I suppose, is whether "frozen" is an alienans adjective like "fake" in "fake silk" (fake silk isn't silk). After all, as a colleague pointed out, a vaporized human isn't a human. The best argument I heard for the "ice isn't water" position was that if someone gives you a glass of just ice, and you say "I'd like some water in it", nobody will say "There already is water in it." But, still, there is no consensus.

So this is interesting. The case of water and ice is not a far-fetched case, like many cases in metaphysics. It's an entirely familiar, day-to-day case. And yet, as far as I can tell, our use underdetermines our meaning. Scary. If that's what happens with water, what about substance and simultaneity?

My linguistic intuitions are so polluted that they're barely worth asking about. But my inclination is to say that "water" is ambiguous in the way "man" is: there is water in the generic sense and water in the specific sense, and the water in the specific sense is the liquid phase of water in the generic sense. But the informal discussions make me unsure about this.

What's wrong with Tarski's definition of application?

Tarski's definition of truth depends on a portion which is, essentially, a disjunctive definition of application. As Field has noted in 1974, unless that definition of application is a naturalistically acceptable reduction, Tarski has failed in the project of reducing truth to something naturalistically acceptable. Field thinks the disjunctive definition of application is no good, but his argument that it is unacceptable is insufficient. I shall show why the definition is no good.

In the case of English (or, more precisely, the first order subset of English), the definition is basically this:

1. P applies to x₁, x₂, ... (in English) if and only if:
   • P = "loves" and x₁ loves x₂, or
   • P = "is tall" and x₁ is tall, or
   • P = "sits" and x₁ sits, or
   • ...

The iteration here is finite and goes through all the predicates of English.

Before we handle this definition, let's observe that this is a case of a schematic definition. In a schematic definition, we do not give every term in the definition, but we give a rule (perhaps implicitly by giving a few portions and writing "...") by which the whole definition can be generated.

Now consider another disjunctive definition that is generally thought to be flawed:

2. x is in pain if and only if:
   • x is human and x's C-fibers are firing, or
   • x is Martian and x's subfrontal oscillator has a low frequency, or
   • x is a plasmon and x's central plasma spindle is spinning axially, or
   • ...

Why is this flawed? There is a simple answer. The rule to generate the additional disjuncts is this: iterate through all the natural kinds K of pain-conscious beings and write down the disjunct "x is a K and F_K(x)" where F_K(x) is what realizes pain in Ks. But this definition schema is viciously circular, even though the infinite definition it generates is not circular. If all the disjuncts were written out in (2), the result would be a naturalistically acceptable statement, with no circularity. However, the rule for generating the full statement—the rule defining the "..." in (2)—itself makes two uses of the concept of pain (once when restricting the Ks to pain-conscious beings and the other when talking of what realizes pain in Ks). Thus, giving the incomplete (2) does not give one understanding of pain, since to understand (2) one must already know what the nature of pain is. (The same diagnosis can be made in the case of Field's nice example of valences. To understand which disjuncts to write down in the definition in any given world with its chemistry, one must have the concept of a valence.)

Now, the Tarskian definition of application has the same flaw, albeit this flaw does not show up in the special cases of English and First Order Logic (FOL). The flaw is this: How are we to fill in the "..." in (1)? In the case of English we give this rule. We iterate through all the predicates of English. For each unary predicate Q, the disjunct is obtained by first writing down "P =", then writing down a quotation mark, then writing down Q, then writing down a quotation mark, then writing down a space followed by "and x₁" flanked by spaces, then writing down Q. Then we iterate through all the binary predicates expressible by transitive verbs, and write down ... (I won't bother giving the rule—the "love" line gives the example). We continue through all the other ways of expressing n-ary predicates in English, of which there is a myriad.

Fine, but this is specific to the rules of English grammar, such the subject-verb-object (SVO) order in the transitive verb case. If we are to have an understanding of what truth and application mean in general, we need a way of generating the disjuncts that is not specific to the particular grammatical constructions of English (or FOL). There are infinitely many ways that a language could express, say, binary predication. The general rule for binary predication will be something like this: Iterate through all the binary predicates Q of the language, and write down (or, more generally, express) the conjunction of two conjuncts. The first conjunct says that P is equal to the predicate Q, and the second conjunct applies Q to x₁ and x₂. We have to put this in such generality, because we do not in general know how the application of Q to x₁ and x₂ is to be expressed. But now we've hit a circularity: we need the concept of a sentence that "applies" a predicate to two names. This is a syntactic sense of "applies" but if we attempt to define this in a language independent way, all we'll be able to say is: a sentence that says that the predicate applies to the objects denoted by the names, and here we use the semantic "applies" that we are trying to define.

It's worth, to get clear on the problem, to imagine the whole range of ways that a predicate could be applied to terms in different languages, and the different ways that a predicated could be encapsulated in a quoted expression. This, for instance, of a language where a subject is indicated by the pattern with which one dances, a unary predicated applied to that subject is indicated by the speed with which one dances (the beings who do this can gauge speeds very finely) and a quote-marked form of the predicate is indicated by lifting the left anterior antenna at a speed proportion to the speed with which that predicate is danced. In general, we will have a predicate-quote functor from predicates to nominal phrases and an application functor from (n+1)-tuples consisting of a predicate plus n nominal phrases to sentences. Thus, the Tarskian definition will require us to distinguish the application functor for the language in order to form a definition of truth for that language. But surely one cannot understand what an application functor is unless one understands application, since the application functor is the one that produces sentences that say that a given predicate applies to the denotations of given nominal phrases.

A not unrelated problem also appears in the fact that a Tarskian definition of the language presupposes an identification of the functors corresponding to truth-functional operations like "and", "or" and "not". But it is not clear that one can explain what it is for a functor in a language to be, say, a negation functor without somewhere saying that the functor maps a sentence into one of opposite truth value. And if one must say that, then the definition of truth is circular. (This point is in part at least not original.)

The Tarskian definition of truth can be described in English for FOL and for English. But to understand how this is to be done for a general language requires that one already have the concept of application (and maybe denotation—that's slightly less obvious), and we cannot know how to fill out the disjuncts in the disjunctive definition, in general, without having that concept.

Perhaps Tarski, though, could define things in general by means of translation into FOL. Thus, a sentence s is true in language L if and only if Translation(s,L,L*) is true in L*, where L* is a dialect of FOL suitable for dealing with translations of sentences of L (thus, its predicates and names are the predicates and names take from L, but its grammar is not that of L but of FOL). However, I suspect that the concept of translation will make use of the concept of application. For instance, part of the concept of a translation will be that a sentence of L that applies a predicate P to x will have to be translated into the sentence P(x). (We might, alternately, try to define translation in terms of propositions: s* translates s iff they express the same proposition. But if we do that, then when we stipulate the dialect L* of FOL, we'll have to explain which strings express which propositions, and in particular we'll have to say that P(x) expresses the proposition that P applies to x, or something like that.) The bump in the carpet moves but does not disappear.

None of this negates the value of Tarski's definition of truth as a reduction of truth to such concepts as application, denotation, negation (considered as a functor from sentences to sentences), conjunction (likewise), disjunction, universal quantification and existential quantification.

The meanings of life and "life"

The question of the meaning of life obviously differs from the also interesting question of the meaning of "life". The latter asks for the meaning of the word "life", while the former asks for the meaning of the thing which is signified by that word. Suppose we take seriously, however, the idea that in asking for the meaning of "life" and in asking for the meaning of life, we are using "meaning" univocally. Then the question presupposes that life, just like "life", is communicative unit. For it is only communicative units that have meaning.

But if life is a communicative unit, then who is communicating to whom? Is it the living person who is communicating, with her life? If so, to whom? Herself? But then living is like talking with oneself, which does not seem right, though I can see that it could be defended. So, maybe, with another. But which other? Presumably either God or fellow human beings (or both). No other options seem available. If only fellow human beings, then if someone is on a desert island and does not expect to meet anybody, her living is just like her talking to the wall—pointless. And that's not right. So, if it is the living person herself who is communicating with her life, she is communicating with God.

Suppose, then, that it is someone else who communicates by means of our lives. There are two options. One is God. The other is society. In the latter case, the life of the person on the desert island, largely formed by desert island experiences, is of questionable meaning.

So if life is a communicative unit, the communication is either by God or with God (or both, a gnostic might add). If so, then the meaning of life does depend on the actual or at least presupposed existence of God.