More on the deflationary account of diachronic identity

[Cross-posted from Matters of Substance.]

First, the easy version of the deflationary account. Here is a question about diachronic identity: What makes it be the case that:

1. Some F0 at t0 is diachronically identical with some F1 at t1.

Deflationary answer:

2. There exists an x such that x is an F0 at t0 and x is an F1 at t1.

Observe that (2) does not make use of "diachronic identity" in its statement. Moreover, all of the conceptual ingredients that (2) uses are ones that any substantive account of diachronic identity (the memory or bodily continuity theories in the case of persons are paradigms) will also have to use in analyzing (1): being an F0 at t0, being an F1 at t1, quantification and conjunction (I have a hard time imagining any substantive account of diachronic identity that somewhere doesn't presuppose conjunction!) So, (2) is simpler, and if it is conceptually circular, so is any substantive account.

Now, the somewhat harder version, the question of analyzing diachronic identity wffs. Question: What makes it be the case that:

3. x at t0 is diachronically identical with y at t1.

Deflationary answer:

4. x exists at t0 and x exists at t1 and y exists at t1 and x is synchronously identical at t1 with y.

Since we all need synchronous identity, and it does not seem to be posterior to diachronic identity, it seems fair to presuppose it in an account of diachronic identity. The result seems to be an account of diachronic identity much simpler than any substantive account.

If one is worried that "x exists at t" presupposes diachronic identity, consider this. What is it to exist at t? Here are some standard proposals:

• Presentism: At t: x exists.
• Perdurantism: a part of x is located within the spacelike hypersurface t.
• Eternalist endurantism: x is wholly located within the spacelike hypersurface t.

None of these proposals seem to presuppose diachronic identity. Now, the last two proposals require an analysis of being located or wholly located in a region R. But this could be just a matter of instantiating a primitive located-at relation to R, or a matter of having R if regions just are properties (I am fond of--though I do not endorse--the proposal that regions are properties, with containment being entailment, and that to be in a region is to have the region as a property), or a matter of being appropriately related to other entities by the nexus of spatiotemporal relations.

In any case, substantive accounts of diachronic identity do not clarify what it is to be located in a region of spacetime or what it is to exist at t. Substantive accounts of diachronic identity explain what it is for an object that is located in one region to exist in another region, but that still doesn't explain what it was for the object to be located in the first region. In fact, there is something really weird about substantive accounts of diachronic identity here. It would be very strange to claim to have a good account of what it is for a person who is queen of country x to also be queen of country y (for general non-identical x and y) without that account also being an account of what it is for a person to be queen of x (for a general x). Surely we all need an account of what it is for a person to be a queen of x, and once we have that, the account of what it is for the queen of country x to also be the queen of country y is just a matter of applying that account twice (and using synchronic identity to take care of the definite articles). But like the queen-identity theorist, the substantive diachronic identity theorist has an account of what it is for, say, a person who occupies R1 to also occupy R2, without having an account of what it is to occupy R1. And once we have an account of what it is to occupy R1, we get for free an account of what it is to occupy R1 and R2, at least if we have synchronic identity.

Maybe the simplest way to summarize the deflationary account is this. It is no more mysterious how it is that x at t0 is identical with y at t1 than it is how it is that x who is the Queen of England is identical with y who is the Queen of Canada.

However, the above arguments presupposed that we're dealing with entities facts about which do not wholly reduce to facts about some other entities. In the case of wholly reducible entities, my arguments fail. The reason for that is that in the case of a wholly reducible entity, what it is to exist at t will be reducible to facts about some other class of entities. For instance, for a reducible x to exist at t will not be a matter of x's instantiating some primitive located-at relations. In that case, the conceptual baggage of "exists at t" might be the same as the conceptual baggage of the substantive account of diachronic identity, and so the deflationary account may be incorrect. (I think of wholly reducible entities as akin to wholly stipulative meanings. In the case of words with wholly stipulative meanings, we might not expect deflationary accounts of truth and meaning to apply--we might want the stipulations to be expanded out, like abbreviations, before the deflationary account is applied.)

If I am right, then someone giving a substantive account of what diachronic identity for Ks consists in is committed to Ks being reducible.

Deep Thoughts XXV

Every effect has a cause.

[Cf. Deep Thought VI.]

Deep Thoughts XXIV

One can try without succeeding.

Deep Thoughts XXIII

One cannot succeed without trying.

Truth supervenes on being

Truth supervenes on being (TSB) holds that any two worlds that differ in the truth of a proposition differ in what exists. Here's a fun thought: Suppose divine believings are entities, and that they essentially have the property of being divine believings and they essentially have the content they do. Suppose God exists necessarily. Then TSB holds trivially, because any two worlds that differ in the truth of a proposition also differ in what beliefs God has. It's hard to run this argument given divine simplicity, though.

More on the correspondence intuition

Introduce the notion "SatCorr", where SatCorr(p,T) iff p is a proposition, T is a partial theory of truth, and T satisfies the correspondence intuition in respect of p. I think the following are true:

1. If SatCorr(p,T) and SatCorr(q,T), then SatCorr(p or q,T), SatCorr(p and q,T) and SatCorr(not p,T).
2. If T says that singular existential propositions are made true by and only by the the objects they report the existence of, and p is any singular existential proposition, then SatCorr(p,T).

A consequence of (1) and (2) is that the correspondence intuition does not require truthmakers for all truths. For if we accept (1) and (2), any theory like T in (2) will automatically satisfy the correspondence intution for conjunctions, disjunctions and negations of singular existential propositions—even if it does not provide truthmakers for these.

Spatiotemporal position

Here is a regulative principle for metaphysics: As much possible, treat spatiotemporal position on par with other properties, like wisdom, mass, momentum, fearsomeness, beauty, tallness, charge, etc. (I leave it open whether spatiotemporal position is a relational property or not.)

Basic entities and predication

Suppose that trope theory is correct. Then what it is for x to have a given property P is to have a trope, say P_x, associated with it. But suppose now that x is a reducible entity—one facts about which reduce to the existence and functioning of other entities (e.g., x might be a table—table-facts reduce to facts about particles and societies). In that case, it is surely not the case that what it is for x to have P is for x to have associated with it P_x. For if x has P_x associated with it, then x is no longer reducible. For consider the fact that x has P. For this fact is the same as the fact that x is associated with P_x. But that x is associated with P_x does not reduce to facts about how, say, the components of x are arranged. For the latter facts are constituted by association with certain tropes of the components; but the fact we are interested in involves P_x. The only way x's having P could reduce would be if facts about the existence of P_x somehow reduced to facts about other things. But then P_x wouldn't really be a trope. The point of tropes is that they are ontologically basic—facts about them don't reduce.

Therefore, if trope theory is correct, then it does not apply to cases where we predicate something of a reducible entity. This, I think, gives one good reason to say that the reducible entity does not really exist in the same sense of "exist" that the other entities do. After all, if predication means something different in its case from what what it means in the other cases, it seems plausible its entitihood is not univocal with theirs.

I ssupect that the same argument might work with other theories of predication as well. If so, then reducible entities don't really exist in the full sense of the word.

Correspondence theory of truth

A correspondence theory of truth is sometimes presented as making sense of our intuition about the correspondence between true statements/beliefs/propositions and the world. However, Correspondence Theory(tm) holds more specifically that every true proposition corresponds to something in the world. And that is surely not intuitive. Certainly, Aristotle who said that to speak truly is to say of what is that it is and of what is not that it is not did not think that negative propositions corresponded to something that is. There is no widely held intuition that the proposition that there are no unicorns is made true by a thing. In fact, the idea that it is is counterintuitive, as are particular fleshings out of it. This is not a decisive count against it, but it seems that the Correspondence Theorist(tm) may have engaged in a bait and switch—done justice to the letter of the correspondence intuition but not in the way that that intuition called for, while committing us to a highly counterintuitive thesis.

Suppose Aristotle were right that all statements can be classified into the positive and the negative, and that the positive ones are made true by something that is, and the negative true are true because there is nothing that makes their negations true. Surely that would fully satisfy our correspondence intuition, though it would not be a Correspondence Theory(tm).

A theory of spacetime

I am not saying this theory is correct—it's too platonic for my taste. But it's suggestive. There are special properties called "locators". Moreover, as it happens, the collection of all locators forms a topological space (one can think of the open sets as corresponding to certain distinguished properties of locators). This space we can call the Receptacle. The Receptacle partitions into topologically connected subspaces. Each of these we can call a spacetime. Thus, a spacetime is a maximal connected set of locators. Some spacetimes have an additional structure, say a metric or manifold one.

The points of a spacetime are simply the locators that make it up. They are, thus, Platonic entities. An entity x occupies a point P if and only if x has the property P. Occupation, then, is simply exemplification. A spacetime is said to be actualized if and only if some point in it is occupied.

Question: Wherein do locators differ from other properties, like mass-properties (having mass x grams), that also have a topological (and even metric) structure?

A theory of personal identity with no counterexamples

This is likely equivalent to Merricks' proposal—I still need to think about whether it is—but I like it. Question: When is it the case that the same person is located at spatiotemporal location y and at spatiotemporal location z? Answer: When and only when there exists an x such that (a) x is a person, (b) x is located at y, and (c) x is located at z. Note that the answer does not use the concept of identity, and all the concepts it uses are ones that substantive theories of personal identity also presuppose.

Vagueness

A guiding intuition in much of my thinking in metaphysics is that no vague fact is to be taken metaphysically seriously. I don't have an account of the seriousness, though. Still, the intuition has some nice consequences. Psychological theories of personal identity make diachronic identity vague—but diachronic identity should be taken seriously, so the theories are false. Materialism makes it vague where there is intentionality (because it makes all interesting macroscopic properties vague), hence materialism is false.

The problem of animal pain

Supposedly intense pains that non-human animals undergo provide significant evidence against theism. Why? Well, the thought is that, if he existed, God could have done things better. But how?

Suggestion 1: He could have made something that has the same motivational effects that pain has but that doesn't hurt.

Response: It's not clear that this is possible—it may be that the qualia of pain reduce to motivational effects and cognitive content. But let's grant it's possible. Now we can ask: Do we have good reason to think God hadn't done this? After all, if the pain-replacement, call it shpain, had the same motivational effects, we would observe the same kinds of aversive responses to shpain as to pain. Maybe we wouldn't expect certain kinds of whimpering. But a dog's whimpering is not quite like human whimpering. I think the reason we see the two as species of the same behavior is because both are associated with similar triggers and similar motivational states. But if the objection to theism that we are evaluating is that God instead of creating pain in animals should have created shpain, then we need evidence that animals experience pain instead of shpain, and if I am right about why we see whimpering as a pain behavior, the whimpering does not provide such evidence.

Maybe we can get some evidence for animals having pain rather than shpain by looking at neurological similarities between humans and animals. This may, however, presuppose the supervenience of the mental on the physical, which is controversial. Furthermore, we do not know enough about how pain systems in the brain work. We know that in addition to similarities between human and non-human brains there are differences. Given that shpain and pain have similar triggers and similar motivational results, on the hypothesis that animals have pain rather than shpain, we would expect a lot of neurological similarity and some difference between animal brains and our brains—and that's exactly what we observe.

Suggestion 2: God could have miraculously prevented pain in those cases in which the motivational role of pain is not important to the animal's flourishing, say when the animal is certain to die.

Response: Let's consider the hypothesis that he has, in fact, done so, and see how strong the disconfirming evidence is. It is plausible that God's miracles would be calculated to produce a particular effect and would be in some way minimal as deviations from the ordinary operations of nature. The reason for that is that there is a great value in the ordinary operations of nature. If so, then what we would expect as a miraculous intervention would be a minimal deviation—one sufficient to relieve the pain. Now, the pain has certain neural correlates. A minimal miraculous intervention might well keep most (if materialism is true) or all (if dualism is true) of these correlates intact. And in particular it might very well be that pain behaviors continue because of the remaining correlates. Now, granted, the fact that we still observe the pain behavior is some evidence against the hypothesis that God has eliminated pain in these cases by being evidence against the hypothesis that God has eliminated pain in a way that eliminates pain behaviors. But unless it was very plausible that the latter is how God would eliminate pain, the evidence against the hypothesis that God has eliminated pain behaviors is not that strong.

Suggestion 3: God could have made a world where animals don't need pain or anything like it, because conscious non-human animals are never endangered by anything.

Response: To evaluate this would require the evaluation of a different argument from the argument from animal pain—the argument from the red-in-tooth-and-claw nature of our world, bracketing the question of pain. I think it is plausible that animal death is not an evil in itself—animals do not naturally have immortality. But death is an ultimate kind of danger, and if so, then the plausibility of the suggestion is decreased. Maybe we could imagine a world where nobody dies before reproducing, but that would be a world where it would be hard for evolution to work, and evolution is valuable.

Conclusions: The problem of animal pain only becomes a problem when one adds some reason to think that God could have done better here. There are three suggestions to that effect. On the first two, the theist can make the reasonable response that we do not have very strong reason to think God hadn't done that allegedly better thing. On the last one, we have a broader problem than that of animal pain.

Verificationism and idealism

I just realized (thinking about Quine's description of verificationist reductionism in "Two Dogmas") that there does not seem to be any difference between verificationism and idealism.

Real numbers

For a long time I've been puzzled—and I still am—by this. Our physics is based on the real numbers (complex numbers, vectors, Banach spaces—all that is built out of real numbers). After all, there are non-standard numbers that can do everything real numbers can. So what reason do we have to think that "the" real numbers are what the world's physics is in fact based on?

I think one can use this to make a nice little argument against the possibility of us coming up with a complete physics—we have no way of telling which of the number fields is the one our world is based on.

Color perception

Here's another data point towards a theory of perception. My son, 4, is colorblind (or color perception deficient or whatever the right term these days is). He was looking at the dark red flowers on his mom's blouse, and said they were black. He was told they were red, and he accepted that—he is very accepting of the fact that colors aren't what they seem to him as. I then asked him if they looked red to him after he was told they were red. He was very definite about an affirmative answer to this question.

Neonates' cries influenced by native language

This is rather neat.

Curry sentences

Curry sentences are of the form:

1. If (1) is true, then p,

where I shall stipulate the "If ... then ..." to be a material conditional, and where p abbreviates something not paradoxical. If p is false (in an unparadoxical way—maybe, p is "snow is red"), (1) is paradoxical because it provides an argument for p. Now, it is clear that whatever we say about (1) we should also say about:

2. If not-p, then (2) is not true.

Now, go back to my old favorite, the contingent liar paradox. There are many versions. One of them is this. Let D be some definite description of a sentence which picks out different sentences in different worlds. Then consider:

3. The sentence satisfying D is not true.

Paradox ensues in worlds where D picks out (3). Now, consider:

4. The contingent liar (3) is unparadoxical if D picks out a first-order sentence that is unproblematically true or unproblematically false, in which case (3) has the opposite truth value to that of that sentence.

Then, consider this:

5. The following sentence is not true: "1=1" if p and (5) if not-p.

By (4), sentence (5) is unparadoxically true if p. We ought to, however, say about (5) exactly whatever we say about:

6. "1=1" is true if p, and (6) is not true if not-p.

Thus, we ought to say that (6) is unparadoxically true if p. But we observe that the first conjunct in (6) is trivially true, at least if p is not itself paradoxical. So, surely, we ought to say about (6) exactly what we say about:

7. Sentence (7) is not true if not-p.

Thus, (7) is unparadoxically true if p.

But we ought to say the same thing about (2) as we say about (7), and about (1) as about (2). So, the Curry sentence (1) is unparadoxically true if p. And if p is false, it is a liar sentence, and a contingent liar sentence if p is contingently false. All this means that the Curry paradox is not very different from the contingent liar.

Sex solely for pleasure

Is there an intrinsic morally significant difference between having sex solely for one's pleasure and having sex solely for money? To sharpen the question, let's ask: Is there a morally significant difference between having sex solely for one's pleasure and having sex for money which one intends to use solely as a means to one's pleasure?

Both are cases where the sex is engaged in solely for hedonistic ends, but in the one case the pleasure is achieved more indirectly. Still, in both cases there is some indirectness. Sex, in and of itself, need not be pleasurable. In both cases, it seems to be engaged in as a mere means to pleasure. The difference, however, is that in the one case, the pleasure is the pleasure of this very sexual act, while in the other case, the pleasure is a different pleasure (e.g., the pleasure of driving a nice car, or the pleasure of sex with someone else whom one wishes to seduce in an expensive way). So, in the case of sex solely for one's pleasure, the pleasure is more closely tied to the sex, and it may even be a mistake to talk of the pleasure as a distinct end. If so, then there is a significant—and perhaps morally so—difference between the two cases: in the money case, sex is engaged in purely instrumentally, while in the pleasure-of-sex case, the end is too close to the sex to call the sex purely instrumental.

This distinction, however, imports into the original question something that wasn't there. Granted, there is a difference between sex solely for the pleasure of the sex, and sex for the sake of money which one wants for the sake of some other pleasure. But in the case I originally specified, I did not suppose a case of sex for the sake of the pleasure of the sex; I supposed a case of sex for the sake of pleasure simpliciter. And when one's end is pleasure simpliciter, then one's action plan involves a fungibility of means: one looks around for the ways to get a lot of pleasure, considering whether it is more convenient to get pleasure by proving a new theorem, or having sex, or eating cake, or volunteering at a shelter—or by having sex for money and then using the money to buy a pleasure. Insofar as one is having sex solely for the sake of pleasure, one is prima facie indifferent between these options except insofar as they produce different levels of pleasure with different degrees of convenience.

And if so, then it does not seem that there is a significant moral difference between sex solely for money solely for pleasure and sex directly solely for pleasure. In particular, it follows that if we think that non-marital sex for money is always wrong, we will conclude that non-marital sex solely for pleasure is always wrong; and if we think that marital sex for money is always wrong, we will likewise conclude that marital sex solely for pleasure is always wrong. (To be honest, I think some cases of marital sex for money—say, when one is starving and one's spouse refuses to provide food except on condition of sex—are more defensible than marital sex solely for pleasure.)

However, there is a difference between sex for the pleasure of the sex and sex for money. Sex for the pleasure of the sex is not solely hedonistic. The hedonist as such does not care what she is taking pleasure in, convenience, consequences and intensity being kept constant. Insofar as one cares about what one is taking pleasure in, one is not a pure hedonist. In a case of sex for the pleasure of the sex, the sex is not present purely instrumentally. Here, we also should distinguish sex for the pleasure of sex from sex for the pleasure of the sex. The pleasure of sex can be achieved apart from sex, say by direct neural input. The pleasure of the sex can only be achieved through the sex. It may be that there is little moral difference between sex for the sake of the pleasure of sex and sex for the sake of money. After all, one could have sex for the sake of money in order to get the pleasure of sex—perhaps one is saving up for a neural sexual pleasure implant. But there is a moral difference between sex for the sake of the pleasure of the sex and sex for the sake of money. Say that a sophisticated hedonist is someone for whom not only the intensity, convenience and consequences of a pleasure matters, but the kind of pleasure also matters. Maybe the sophisticated hedonist wants to have a variety of kinds of pleasure, or maybe she has arbitrarily chosen some pleasures over others. In any case, the person who has sex for the sake of the pleasure of the sex is neither a pure hedonist nor a sophisticated hedonist, for she not only cares for the kind of pleasure, but also that which it is had in.

One is unlikely—perhaps it is even an impossibility—to value the pleasure of the sex without non-instrumentally valuing the sex. There may well be people who have sex solely for pleasure. For instance, if Sally wants to have some pleasure and goes through all the options and chooses the one with the best balance of intensity and convenience, and that happens to be sex, she may be having sex solely for pleasure. But such cases are, I think, rare. The pure case of someone who wants to have sex for the sake of the pleasure of sex is less rare. Such a case would require the person to be indifferent as to the gender, age, appearance and species of the sexual partner, except insofar as this impacts convenience, consequences and the pleasure received. Maybe some people do have such an indifference—the only reason, for instance, why they prefer their partners to be of their own species is that they find bestiality to lack something of pleasure.

There is a further kind of distinction we should draw at this point, a distinction between having sex for the sake of the pleasure of the sex—of this particular sexual act with this person at this time—and having sex for the sake of the pleasure of this sort of sex. Thus, the person who cares about the appearance of their sexual partner (typically) seeks the pleasure of sex with a good-looking person. The number of people who have sex for the sake of pleasure is probably small, the number of people who have sex for the sake of the pleasure of sex is probably also small, but the number of people who have sex for the sake of the pleasure of sex of a certain sort (where the sort is either specified by specifying the kind of sexual act or the kind of partner or both) is probably larger. And this, too, I think is not very different morally from sex for money. After all, one might well be having sex for money for the sake of the pleasure of sex of the preferred sort. And I think this is morally objectionable, and apt to make an object of the partner.

On the other hand, sex for the sake of the pleasure of the sex requires or at least tends to require valuing the sex with this person at this time non-instrumentally (actions are individuated by agent, time, patient, etc.) And that's different.

The Christian tradition has unanimously condemned sex for the sake of one's own pleasure. But it is not clear that this condemnation of hedonistic sex applies in the case of sex for the sake of the pleasure of the sex—for in that case, the intended end, "the pleasure of the sex", is partly constituted by the sex itself, and hence the sex is engaged in for the sake of the pleasant good of the sex, rather than for the sake of pleasure alone. And if the sex is intrinsically unitive, this may well be sex for the sake of pleasant union, which is a species of sex for the sake of union, which in turn is taken to be permissible by the tradition. Of course, this is very speculative, and the tradition is authoritative while my interpretation of it is not.

The paradox of Shakespeare's last words

Let p be the proposition that the last thing asserted by Shakespeare in his life is not true. This is a perfectly good proposition, and it is one that we can easily assert. Moreover, it is a proposition that Shakespeare could easily have asserted many times—but only if these times weren't the last moment of his life. Suppose in our world, w₀, Shakespeare asserted p at time t₁. (For all we know, he did!) Surely there is a world, w₁, which is just like our world, but where Shakespeare is killed instantly after t₁. In w₁, then, Shakespeare did not assert p, since p is something that it is logically impossible for Shakespeare to assert as the last assertion of his life. But of course, in w₁, Shakespeare uses the exact same words at t₁ as he does in w₀, and seemingly with the same intention.

So, what are we to make of this? On pain of contradiction, we must hold that in w₁, Shakespeare fails to assert p in his last moment. If we think that words plus intention suffice to determine a proposition asserted (and even if we don't, we can perhaps stipulate a sense of "asserted" in which that is true, and make sure that that's the sense in p), it follows that what intentions one has can depend on what will happen later or that one's "words" include contextual features such as whether one dies shortly thereafter or when one utters them. In other words, we get a temporal externalism about intentions, or else a very weird notion of "words".

And we get an argument from this liar paradox against open futurism. For in w₀ at t₁, it is open whether Shakespeare will die right after t₁ or not. But if he dies right after t₁, he is not intending p. But it is true at t₁ that he is intending p. Hence, it is true at t₁ that he does not die after t₁, which contradicts open futurism. Or, to put it differently, according to the open futurist, there is no fact at t₁ as to what Shakespeare intends at t₁.

Let's make the open futurist even more uncomfortable. Suppose at t₁, you say:

1. One day, I will open my mouth and utter a noise that does not express a true proposition.

This is a perfectly ordinary locution, and one that all of us can reasonably make in light of our fallibility, unless we're expecting to die shortly. Surely you've said something, indeed something most likely true. But this is not the case if open futurism is true. For it is open for you next to say:

2. I just uttered a noise that did not express a true proposition

and then die. Our options are: (a) take (1) to be true and (2) to be either false or nonsense; (b) take (2) to be true and (1) to be either false or nonsense; and (c) take both (1) and (2) to be nonsense—i.e., to fail to express a proposition. There seems to be no reason to prefer (a) to (b) or (b) to (a). So we should go for (c). But if we take (c) as the right solution, and open futurism is true, then we have to say that whenever (1) is uttered, there is not yet a fact about whether it expresses a proposition. This is really weird. Not that it's not weird without open futurism. But it's less weird.

Fun with substitutional quantification

Stipulate that "x strongly believes p" iff x believes p and it is not the case that x believes not-p. Consider the argument:

1. For anything that Freddie believes, there is a possible world where Sally strongly believes it.
2. Freddie believes the negation of Sally's deepest held belief.
3. Therefore, there is a possible world where Sally strongly believes the negation of Sally's deepest held belief.

Isn't it fun to derive an impossibility from two propositions whose conjunction is possible?

We learn from this that if we are to read (1) substitutionally, we need a substitutional quantification in which we are only allowed to substitute names. In that case, (3) does not follow from (1) and (2), because if "Xyzzy" is the name of the negation of Sally's deepest held belief, then instead of (3) all we get to conclude is:

4. There is a possible world where Sally strongly believes Xyzzy.

But there is no contradiction here, because in the relevant possible world, Xyzzy isn't the negation of Sally's deepest held belief. But still, wasn't (1)-(3) fun?

Is quantification substitutional?

Consider:

1. Possibly, something exists which could not be referred to with a linguistic expression.

If quantification is at base substitutional, then (1) is false. But the negation of (1) is:

2. Necessarily, everything can be referred to with a linguistic expression.

Call this "referential universalism". Now, there presumably are worlds where there is no language. Could there be entities that could exist only in such worlds? If so, then, most likely (2) would be false (some such individuals could be referred to in a cross-worldly way by appropriate definite descriptions, but there is little reason to think they all could be). So, referential universalism is not particularly plausible.

The substitutionist could affirm that referential universalism is a trivial truth. In English, some names, like "Alex", ambiguously refer to multiple entities, and are disambiguated contextually. Presumably, there is an extension English* of English which has the name "Ting" that is much more ambiguous—it can refer to anything at all. Thus, "George loves Sally" is appropriately translated by "Ting loves Sally" as well as by "George loves Ting", in different contexts. But then (2) is a trivial truth—"Ting" can refer to anything at all.

It is a fine question how to allow for ambiguous reference and remain a substitutionist. One way is not open: take substituents to be pairs consisting of an ambiguous referring term and a referent. For if one did that, one is doing objectual quantification over referents. So, probably, what one needs to do is to substitutionally quantify over pairs <e,c> where e is an ambiguously referring expressing and c is a description of a context (it can't just be a context as then we'd be objectually quantifying over contexts). But then our substitutionist becomes committed to the highly non-trivial truth:

3. Necessarily, everything is such that in some context there is a linguistic expression that unambiguously refers to it.

Now, maybe it will be said that I haven't offered an argument against (2) or (3). True. But I now make this move. Look: (2) and (3) are trivially true when read substitutionally. Our understanding of (2) and (3) as non-trivial truths shows that we do not, in fact, read their quantifiers substitutionally, and hence substitutionism is false.

None of this affect the claim that there is a perfectly good substitutional quantifier--only the claim that all quantification is to be understood in terms of it.

Experiences and presentism

That x is having a certain kind of conscious experience at t is not just a claim about what is happening right at t. If mental processes are in some way correlated with physical processes, then this follows from the fact that it does not really make sense to talk of the instantaneous state of the physical process (think, for instance, of wave phenomena or classical momenta—these are defined in terms of what happens at other times). But even without this correlation, this is plausible. Thought experiment: imagine seeing a red circle for a tenth of a second with no after image and no memory (the memory is wiped instantly). You see an obvious flash. Shorten the amount of time you're seeing the red circle. Eventually, you don't see it at all.

But if presentism is true, isn't this really weird? It would be really weird if my present conscious state were partly constituted by past-tensed states of affairs. The eternalist (or even growing block theorist) can talk of a temporally extended conscious state. That's not a problem. But the presentist can only talk of the present conscious state together with some (dodgy) past-tensed states, like having seen a red circle a quarter of a second ago. Of course, folks who think that beings coming out of swamps at random couldn't be conscious even if they had souls will not be bothered by this.

Why can't the past change?

If you're a B-theorist, it is no puzzle that the past can't change. It can't change because we are always in the same world, and so neither the past, nor the present nor the future can change. Today, let us suppose (I think correctly) that it is the case that on Wednesday it was raining. Could it tomorrow be the case that it wasn't raining on Wednesday? Not at all—for the very same world, the very same events, that make propositions true today is the one that we evaluate against tomorrow. The fact that the past can't change, thus, is a matter of mere logic—it just follows from the truth conditions for sentences.

But what if you're an A-theorist? So, you think that things will be objectively different tomorrow. Indeed, you already do think that some things about Wednesday will objectively change. For instance, while today (Saturday) Wednesday is objectively three days in the past, tomorrow it will objectively recede one more day into the past. So in fact we already have a change, but a change that the A-theorist doesn't mind. (Though she should.)

In any case, logic alone doesn't do the job. One way to see this is that some A-theorists actually think the future changes. Thus, today, it is false that either I am at Mass on November 8 or that I am absent from Mass on November 8. But come November 8, this disjunction will be true. But the clever tricks that open futurists use to make sense of an open future could be used, equally well, to make sense of an open past. (The parallel holds for B-theory. The B-theorist is committed to the claim that the future cannot change. This sounds fatalistic, but we must distinguish the ability to change the future from the ability to affect the future.)

In the setting of my earlier post on A-theory, the claim that the past cannot change corresponds fairly closely (and in fact exactly, if we assume a closed past) to the claim that the earlier-than relation is transitive. If today, a world where it rains on Wednesday is is past, tomorrow that world will also be past. So in the setting of that post, the explanatory challenge to the A-theorist is why the earlier-than relation E is transitive. The A-theorist who takes E to be fundamental can only say that it is a brute fact that it is necessarily transitive.

There may be A-theorists who can meet the challenge, however. Suppose that you think that there is a TimeShift operator which shifts tensed propositions time-wise. Thus, if p is the proposition that it is sunny, TimeShift(+1 day, p) is the proposition that in a day it'll be sunny. Suppose, further, we take worlds to be maximal consistent collections of propositions, or maximally specific consistent propositions. Then the TimeShift operator can also operate on worlds, and we can define E(w₁,w₂) to hold iff there is a t<0 such that w₁=TimeShift(t,w₂). Then it really is a matter of simple logic that E is transitive, and we have a perfectly good explanation of why the past cannot change.

Note, however, that an open-futurist cannot take this explanation. For her, the fixeity of the past remains a surd.

If this is right, then Tom Crisp is mistaken in taking the earlier-than relation between abstract times (which are just worlds in my terminology) to be primitive. An A-theorist should not say it's primitive—it needs explaining. Or at least I remember him taking it to be primitive, but my memory isn't so good.

The changing past

A decade ago, the end of World War II was 54 years in the past. Right now, the end of World War II is 64 years in the past. If A-theory is true, these are genuine properties of WWII, and it has changed in respect of them. But something in the past cannot change. So A-theory is false.

The A-theorist's best answer to this argument is, I think, that this is a mere Cambridge change. A mere Cambridge change is when an object does not change in respect of intrinsic properties, but something else around it changes, which makes appropriate the application of a different predicate to it. The classic example is that x may grow shorter than y without changing in height—simply because y grew taller. The change in x was Cambridge and that in y was real.

A mere Cambridge of an object x change requires something else, a y, that really changes, where x's change consists in x having a description that makes reference to x's unchanged and y's changed qualities. Let us try to see how to do this for WWII.

Option 1: WWII has the unchanging property of ending in 1945. But 1945 has a changing property—it once was future, then was present, then was past, eventually being 54 years in the past, and now being 64 years in the past. So WWII, or WWII's end, undergoes a Cambridge change in virtue of 1945 (or a specific date in 1945) undergoing a real change. But the idea that 1945 should undergo a real change is at least a bit problematic, I think. It is plausible to say that 1945 is in the past, and so it shouldn't be able to really change. The alternative seems to be to makes times be something abstract—but the idea of abstract entities really changing is also troubling. So one would need to make 1945 be an enduring concrete entity. That's weird.

Option 2: WWII has the unchanging property of ending, say, 15,000,001,945 years after the beginning of the universe, but the universe has a changing age. When we say that WWII ended n years ago, we mean that the year that WWII ended, say 15,000,001,945 cosmic era, is equal to the age of the universe minus n. So, the end of WWII doesn't change, but the age of the universe does. This seems to work, but leads to further puzzles. What kind of an enduring entity is the universe? What is this property of age that so inexorably grows?

Option 3: WWII has the unchanging property of ending in 1945, but there is an objectively changing fact—the fact of which time is present. And in virtue of the latter changing fact, which does not consist in a change in any entity, 1945 undergoes Cambridge change. This view requires a relaxation of the account of Cambridge change—it doesn't require entities to change. (One might try to say that propositions reporting what time is present change in truth value. But that had better be true in virtue of something else.) I think the idea of change that does not happen in virtue of anything's changing is dubious.

A-theory

Here is the right way to see A-theory (this is particularly accurate as an account of Tom Crisp's presentism). There are infinitely many possible worlds, one of which, w₀, is actual. Which world is actual changes with time: tomorrow, say, w₁₇ will be actual (a world encodes everything that is objectively the case—but the A-theorist thinks there is an objective difference between how things are today and how they will be tomorrow). Of course, w₀ and w₁₇ are not unrelated: at w₀ it is true that tomorrow* w₁₇ will be actual, while at w₁₇ it was true that yesterday* w₁₇ was actual (here, "tomorrow*" and "yesterday*" are narrow-scope versions of our usually wide-scope terms).

Moreover, there are three crucial relations that can hold between worlds: S and E.

We say that S(w₁,w₂) if and only if w₁ and w₂ are simultaneous—i.e., it is the same time in both of them. When I say that it might have been the case that right now I am writing a post on growing-block theories, this implies there is a world w simultaneous with the actual world w₀ such that at w, I am writing such a post. This relation is an equivalence relation—it is reflexive, symmetric and transitive.

The earlier-than relation E(w₁,w₂) holds if and only if at w₂ it is true that w₁ was actual. However, it is important to see that the S and E relations are not of a kind. S holds between the actual world and many, many worlds that have never been, are not, and never will be actual. E only holds (in some order) between the actual world and worlds that have been or will be actual. The relation E is transitive. Moreover, no two worlds related by S are related by E. In particular no world is earlier than itself..

Socrates was sitting if and only if there is a world w₁ such that E(w₁,w₀) and at w₁ Socrates is sitting.

The relations S and E probably have to be taken to be primitive.

If E(w₁,w₂) then I will say that w₂ is in w₁'s future and w₁ is in w₂'s past.

We can now precisely characterize closed-future and closed-past views. We have a closed future (past) if and only if the collection of worlds that the actual world is earlier (later) than the actual world is totally ordered by E. It is a consequence of this that no two worlds later (earlier) than the actual world are simultaneous. Everybody, I assume, believes in a closed past. Closed-futurist A-theory, then, is the view the collection of all worlds can be partitioned into disjoint subcollections, in one of which subcollections are all the worlds that aren't E-related to any world (these are the worlds that have no past or future), and each of the other subcollections is totally ordered by E.

Open futurists, on the other hand, think that there are two future worlds that are not E-related—in fact, they typically think there are two future worlds that are simultaneous.

Presentism then adds the further claim that at a world w, only those things are existent that are presently* existent. While A-theory is a theory of the structure of time, presentism is a theory of the ontology of each world. They neatly complement each other, because the presentist has an elegant answer to the question of what it is for an object or event to exist at a time:

1. x existed at t in w if and only if there is a world w₁ such that (a) it is t in w₁, (b) E(w₁,w) and (c) x exists in w₁
2. x exists at t in w (where w is such that it is t in it) if and only if x exists in w
3. x will exist at t in w if and only if there is a world w₁ such that (a) it is t in w₁, (b) E(w,w₁) and (c) x exists in w.

Our timeline (which is branching if open-futurism is true) is the collection of the actual world and all worlds that are E-related to the actual world.

This formulation shows the problem of how A-theory, divine immutability and omniscience could all be true (after all, doesn't it contradict immutability if God has to keep on updating his beliefs) is the same as the problem of how contingentism, strong aseity and omniscience could all be true, where contingentism is the doctrine that not everything is necessary and strong aseity is the doctrine that God has exactly the same intrinsic properties in all worlds. Moreover, this formulation also shows that an A-theorist who believes in divine immutability is someone who believes a restricted version of strong aseity—restricted to the worlds in our timeline. There is thus a good plausibilistic argument from A-theoretic immutability to strong aseity—why restrict to our timeline?

Where does the B-theorist stand in regard to all this? She insists that at every world it is true that in the past and the future, the very same world is actual. Of course, a different Lewisian "centered" world will be actual in the future. The above is really a matter of formalism, so it does not solve any really hard problems, so it does not solve the problem of how worlds and centered worlds differ.

The formalism does, however, highlight some problems for presentism. Consider the problem of induction for presentists. Normally, only what happens in the actual world is relevant for inductive inferences. We know that most worlds are different enough from the actual world that doing induction over them will mix us up completely. But to have any hope of induction being useful, the presentist has to insist on making use not just of data about what happens in the actual world, but also data about what happens in worlds earlier than the actual. I don't know that the presentist can answer this. Here's another problem. Finding out that I promise something in a world w₁ gives me very little reason to do the promised deed in w₀. But if I also find out that E(w₁,w₀), then I have reason to do this. This seems magical, and unless the A-theorist can give us a good substantive account of the E-relation, this will be unexplained.

Presentism and "ago"

According to most proponents of presentism, propositions are tensed. Thus, when yesterday you said that it is raining and I said it today, we expressed the same proposition, which, perhaps, was false yesterday and is true today. Moreover, presentists believe that one cannot refer de re to non-present objects.

For presentism to have any hope of being able to express all of reality, the presentist needs an "Ago" operator, where Ago(t,p) is a proposition that backdates p by t (units of time). If p is expressed by a present tense sentence, Ago(t,p) can be expressed by a past tense sentence. Thus, if p is the proposition that it is raining, Ago(3 days,p) is the proposition that three days ago it was raining.

Here is a plausible fact about the logic of "Ago":

1. Ago(t,p) is now true iff p was true t units of time ago

The seriously actualist presentist adds this:

2. No proposition that refers de re to a presently non-existent entity can be true. (If we like, we can probably qualify this as: "no positive proposition".)

Let p be the proposition that there is someone who will vote for Obama. Then:

3. Ago(70 years,p) is true.

I.e., 70 years ago, there was someone who would vote for Obama. Thus, by (1):

4. p was true 70 years ago.

But p makes de re reference to Obama. Since Obama didn't exist 70 years ago, it follows by (2) that:

5. p was not true 70 years ago.

And this, of course, contradicts (4).

Thus, the presentist cannot hold (1)-(3) together.

Thus, the straightforward presentist reading of the claim that 70 years ago there was someone who would vote for Obama as the claim that 70 years ago someone existed who would vote for Obama is one that doesn't fit with (1) and (2). But there is a non-straightforward way of giving the truth-conditions that does:

6. There (is) a time t at which there (is) a person x who (votes) for Obama at t and who also existed on October 29, 1939,

where "(is)" is short for "was, is or will be" and "(votes)" is short for "voted, votes or will vote".

An interesting question is whether such truth conditions are available for all possible examples of this sort.

There is, however, a different route for the presentist. She could deny (1). This would be analogous to Robert Adams' move of allowing that a proposition might be true at a world without being such that were that world actual, the proposition would be true. Such a view a view, when married to Crisp's concept of abstract times, would have the problematic consequence, that in general, at a time t, the time t was not present. (For t will contain propositions that make de re reference to now-actual objects that didn't exist at t, and so at t the maximal proposition would have been different from what it actually is.) To me, (1) seems very plausible.

Probably, most presentists will simply deny (2), allowing for de re reference to non-existents by means of haecceities. They will then open themselves to Lewis's objection that they are not really presentists, but there is probably a way out of that. It would, however, be an interesting thing if they had to deny (2)—this would mean that presentists cannot be serious actualists in the sense involved in (2). And if presentists could not be are not serious actualists, then their claim that only present objects are actual is not quite as revolutionary as it seems.

Erotic love relationship needs

Bryan Weaver and Fiona Woollard seem to think that there are people whose needs for erotic companionship could not be met by one monogamous relationship. I hereby hypothesize that for all x, if x is such that his or her needs for erotic companionship could not be met by one monogamous relationship, then x is such that his or her needs for erotic companionship could not be met by any number of relationships.

Hating the devil

An interesting disagreement among orthodox Christians, even among orthodox Catholics, is whether the devil should be hated. I have run into a number of people who think in the affirmative. In fact, anecdotal evidence suggests that that is the more common position. On the other hand, I think we should not hate the devil—in fact, we should love him.

Here are some plausibilistic arguments for my position:

1. Surely, we should not hate the souls in hell. But if the reason for hating the devil is that he cannot repent of his wickedness, then the same applies to the souls in hell. And if the reason for hating the devil is his evil works and his empty promises, then that's a bad reason—it's a reason for hating the evil works and the empty promises, but not for hating the devil.
2. Anything that is good deserves to be loved to the extent that it is good. Anything that exists is good to the extent that it exists. Thus, the devil deserves to be loved to the extent that he exists. And to the extent that he does not exist, surely then it is not he, who exists, who is to be hated, but the fact that he does not exist fully should be hated. (Yes, one can hate its being the case that p.)
3. Love and hatred are closely tied to actions. Now the actions we should engage in with respect to the devil are ones that are good for him, and hence they are more like loving than like hateful actions. For instance, we should reject the devil's temptations. That is good, because by rejecting the temptations we make him be responsible for fewer evils than he would be responsible for if we yielded, and it is bad for one to be responsible for evils. We should shun the devil's company. But to be in the devil's company, we would have to be wicked. And it harms a person to be provided with wicked companions. Furthermore, we should strive to frustrate the devil's wicked plans. While the frustration of one's plans may be bad for one in one way, in a more salient way, it is good for one when the plans are wicked. It is a bad thing for one to succeed at evil.

On the other hand, one might worry that love has a unitive dimension, and then one might argue that we should, surely, not seek to be united to the devil—that is just too dangerous. However, we can be united simply by doing good to someone, and there are ways of doing good to the devil that do not carry undue danger—for instance, we can, as noted above, do good to the devil by frustrating his evil designs. Another good we could do to the devil, should God assign this to us (we are mysteriously told that we'll judge angels), could be to condemn him to punishment, if it is intrinsically good to be punished for one's wickedness.

At the same time, the love should not have much intensity. The devil is dangerous, and we should not think too much about him. Maybe I have already done too much.

Cleanliness is next to godliness

There is an interesting study on the effects of clean smells on virtuous behavior.

John Scalzi on Molinism

See this fun story.

Westlund on companion love

Andrea Westlund in her piece "The Reunion of Marriage" (in the Monist's Marriage issue) gives an account of the "companion love" in marriage as centered on the argumentative forging of shared reasons.

While there is some argumentative forging of shared reasons in marriage, it seems to me that any account of marriage that makes the production of shared reasons be central is a conceit of affluent Western culture (bet you never expected that phrase from me!). I imagine two peasants. They fall in love, marry, pray together, raise children together, work the fields with the children, are taken care of in their old age by some of the children, and go to their eternal reward (not all necessarily in this order—in particular, falling in love may follow marrying, and the praying together hopefully happens all through the process).

The couple's joint life follows a pattern set by religious and secular tradition, the cycles of nature, and economic necessities. In the ideal case, they do indeed share ends—they jointly pursue food, drink, shelter, clothing, eternal salvation, reproduction and various joys, all for and with one another and their children. Many of their shared reasons are a function of what they individually have antecedent reason to pursue (e.g., clothing and eternal salvation) and which become a joint end when they come together in love. But in those cases there is no need for a production of reasons—they have the shared reasons in virtue of their shared humanity and their shared circumstances, as well as, perhaps, their love. (I am suspicious of the idea of love giving rather than recognizing much in the way of reasons. One could try to argue that love takes individual reasons and transforms them into joint ones.)

There is, of course, a dialogical struggle to recognize the reasons they already have—they are not perfect phronimoi who automatically are cognizant of all the reasons present for them. And there will likely be much argument over means, but that is not what Westlund is talking about.

Still there will be aspects of their relationship where they do have significant freedom. On long winter evenings, do they play dice, tell stories and jokes, sing, dance, sew and/or carve? Which non-required religious devotions do they embrace as a family? Which of their needy neighbors will they support and in what way? But in the case of devotion and charitable activity, this is merely the working out of a shared plan for particularizing and pursuing imperfect duties which they have, independently of any forging of theirs, a reason to fulfill. If the couple is lucky enough not to be too exhausted from the day's work, there may be some time for evening recreational activities, and there there will be a need to choose shared ends—but that simply does not seem to be of the essence to the marriage. It would be unfortunate if the couple were unable to do this, but their companion love does not depend on the availability of this.

Tevye: ... But do you love me?
Golde: Do I love you?
For twenty-five years, I've washed your clothes,
Cooked your meals, cleaned your house,
Given you children, milked the cow.
After twenty-five years, why talk about love right now?
...
Tevye: Do you love me?
Golde: I'm your wife!
Tevye: I know. But do you love me?
Golde: Do I love him?
For twenty-five years, I've lived with him,
Fought with him, starved with him.
For twenty-five years, my bed is his.
If that's not love, what is? (The Fiddler on the Roof)

Some liar paradoxes without truth

Let "@" be the name of the actual world.

1. The proposition expressed by (1) in English is not entailed by the proposition that @ is actual.
2. The proposition expressed by (2) in English is not compossible with the proposition that @ is actual.
3. The proposition expressed by (3) in English is not necessary.
4. The proposition expressed by (4) in English is not known by anybody.
5. The proposition expressed by (5) in English cannot be known by anybody.

That (1) and (2) are paradoxical is obvious. That (3) is paradoxical is easy to see. For if (3) is false, then (3) is necessarily true. If (3) is true, then then it is only contingently true. But the argument that if (3) is false, then (3) is necessarily true works in all worlds. So in no world is (3) false. So (3) cannot be contingently true.

The paradoxicality of (4) is a bit more fun, though I am less sure of it. If (4) is false, then (4) is known by somebody and hence true. So, (4) cannot be false. But now that we have a logically sound argument for (4), we know (4)—or at least we could, and then we can consider the argument in the possible world where we do know it. But if we know (4), then (4) is false.

What about (5)? Well, if (5) can be known by anybody, it can be true and known. But it cannot be both true and known. So, (5) cannot be known by anybody. But this is a good argument for the truth of (5), so even if we don't know (5), somebody can know it on the basis of this argument. But then (5) is false.

Is pollution bad for the earth?

A curious thought hit me today: What could it mean for something, say pollution, to be bad for the earth? We have, I think, a fairly good idea of what it is for something to be good or bad for a human, a dog, a wasp, a tree and maybe even a bacterium. But for a planet? For humans, dogs, etc., there are roughly three accounts of well-being: (a) the hedonist account that well-being is pleasure and absence of pain, (b) the desire account that well-being is (roughly) fulfillment of desires and lack of frustration of desires, and (c) the flourishing account. Now, (a) requires consciousness and (b) requires mind, so neither is applicable to a tree, a baceterium or the earth.

That leaves the flourishing account. But while I have some idea about canine and waspish flourishing, I have very little idea about planetary flourishing. For instance, does hosting life make a planet flourish, or to the contrary, do planets flourish more when they are devoid of life? After all, if the average member of a natural kind is likely to have a normal degree of flourishing, it appears that lifeless planets have a normal degree of flourishing. So as long as we don't literally blow the earth into pieces, it seems that whatever pollution we inflict on it, we won't push it below the normal level of well-being.

But perhaps we need to distinguish different kinds of planets, and different kinds of planets have different kinds of flourishing. Thus, maybe, a planet in a "habitable zone" in a stellar system has the support of organic life as part of its flourishing. But what kind of organic life is needed for flourishing? Is the planet better off for hosting more complex life-forms? (Is a house better off for having people rather than geckos in it?) Or for a greater diversity of life-forms? (Is a house better off for having people and cockroaches rather than just people?) It seems plausible that unless we have a metaphysical teleology, either of the Aristotelian or the theistic sort, for planets in the habitable zone, these questions have no answer. And even if we have such a teleology, the epistemology of that teleology will be difficult, because the earth is the only habitable planet we know of, and typically we learn about the teleological properties of a natural kind by observing multiple instances.

But perhaps it is a mistake to think of the earth as rocks, water and atmosphere. Rather, the suggestion goes, the ecosystem is not just hosted by the earth, but is a part of the earth. I am not sure we should buy that. While parthood might not in general be transitive, it seems plausible that since we are parts of the ecosystem, then if the ecosystem were a part of the earth, we would be parts of the earth. But surely we are not parts of the earth. We live on earth, but we are not parts of it any more than we are parts of the galaxy (though the earth is a part of the galaxy).

But let us grant that the ecosystem is a part of the earth—or maybe that "the earth" is sometimes a metonymy for the ecosystem. In that case, pollution that causes destruction of a part of the ecosystem without a compensating growth elsewhere do seem to be contrary to the flourishing of the earth. But more detailed study of flourishing still seems mired in epistemic problems. It is very hard to figure out the teleology of the ecosystem as a whole, unless we accept revelation and say that the teleology is the support of humanity.

Tarski's definition of truth-in-L

Tarski's definition is often noted—typically critically—as being applicable only to the languages he gave it in. Thus, he defined truth-in-L, or more generally satisfaction-in-L, for several cases of L. However, I think this misses something that goes on in the reader when she understands Tarski's account: the reader, upon reading Tarski, gains the skill to generate the definition of truth-in-L for other languages L (at least ones that are sufficiently formalized). One just gets it (I think Max Black makes this point). A standard way of defining A in C (where C is a context and A is a context-sensitive concept to be define) is to give some "direct definition" of the form

1. x is a case of A in C iff F(x,C).

However, Tarski's case exemplifies a different way of defining "A in C": one teaches (perhaps by example) a procedure (perhaps specified ostensively) which, for every admissible C, will generate a definition of A-in-C. Call this "procedural definition". A direct definition has an obvious advantage with respect to comprehensibility. However, a procedural P definition does advance the understanding. For instance, suppose that instead of giving a definition of a heart that applies to all species, I teach you a method which, when properly exercised upon Ks, gives you a definition of the heart-of-a-K.

Now, in ordinary cases, one can move from a procedural definition to a direct definition as follows:

2. x is a case of A in C iff x satisfies the definition of A-in-C that P would produce given C.

However, in the Tarskian case, we cannot do this for the simple reason that (2) would end up being circular if A is satisfaction! To understand what it is to satisfy a definition one needs to know that which one is trying to define. So in Tarski's case—and pretty much in Tarski's case alone—procedural definition is not the same as direct definition.

Nonetheless, a procedural definition, even when it does not give rise to a direct definition, is valuable—as long as the grasp of the procedure does not depend on the concept to be defined. And here, I think, is the real failure of Tarski's definition: one's grasp of the concept of a predicate—which is central to the method—is dependent on one's grasp of the concept of satisfaction.