A failed Deep Thought

I was going to post the following as Deep Thoughts XLIII, in a series of posts meant to be largely tautologous or at least trivial statements:

1. Everyone older than you was once your age.

And then I realized that this is not actually a tautology. It might not even be true.

Suppose time is discrete in an Aristotelian way, so that the intervals between successive times are not always the same. Basically, the idea is that times are aligned with the endpoints of change, and these can happen at all sorts of seemingly random times, rather than at multiples of some interval. But in that case, (1) is likely false. For it is unlikely that the random-length intervals of time in someone else’s life are so coordinated with yours that the exact length of time that you have lived equals the sum of the lengths of intervals from the beginning to some point in the life of a specific other person.

Of course, on any version of the Aristotelian theory that fits with our observations, the intervals between times are very short, and so everyone older than you was once approximately your age.

One might try to replace (1) by:

2. Everyone older than you was once younger than you are now.

But while (2) is nearly certainly true, it is still not a tautology. For if Alice has lived forever, then she’s older than you, but she was never younger than you are now! And while there probably are no individuals who are infinitely old (God is timelessly eternal), this fact is far from trivial.

Deep Thoughts XLII

No one speaks about what cannot be spoken about.

Deep Thoughts XL

The unknown is not very well known.

[My son wrote this on my board while bored in my office.]

Deep Thoughts XXXIX

You cannot leave an empty room.

[The idea behind this lovely tautology is from my daughter Clare.]

Deep Thoughts XXXVIII

If you don't try, you won't fail.

Deep Thoughts XXXVII

Everybody is somebody.

Deep Thoughts XXXVI

The necessary is always possible.

Deep Thoughts XXXV

Meeting the minimum requirements is always good enough.

[This is a variant on XXXIV. There are times when we say things like "The minimum is not good enough." When we do that, what I think happens is that we have a context shift. "The minimum" is understood relative to one set of ends or norms while the "good enough" is understood relative to another. One kind of a case is where you're competing for a job. Meeting the minimum required qualifications is good enough for being hirable in principle (if it's not, the minimum requirements were incorrectly stated), but is not good enough for beating the competition. Another kind of case is where someone is being evaluated in a number of areas (or with respect to a multiplicity of assignments). In each area, there is a minimum requirement. Meeting that requirement is good enough for not failing according to that requirement. But there may be a second, meta requirement to exceed the minimum in most of the areas. (There cannot coherently be a requirement to exceed the minimum in all areas. For if there were such, then the "minimum" in each area would not be a minimum requirement but a maximum disqualifier.) In any case, when we keep the context constant (and as a rule in natural language context in short sentences stays constant), "The minimum is not good enough" is a self-contradiction.]

Deep Thoughts XXXIII

Everything is possible except the impossible.

Deep Thoughts XXXII

"[T]here is no such thing as being too good."[note 1]

[This is a counterpoint to this. Like it, it rests on ensuring a consistent context of evaluation.]

Deep Thoughts XXXI

The adequate is good enough.

[If I wrote in a letter of recommendation that someone was an adequate candidate that would probably the kiss of death. But why? Putative explanation 1: It is a tautology that the adequate is good enough. However, it is only a tautology if the same context is held fixed throughout the sentence. Thus, someone might be adequate as a student, but not good enough for admission to a highly competitive program. Putative explanation 2: Letters of recommendation are overblown.]

Deep Thoughts XXIX

No one has proved the unprovable.

Deep Thoughts XXVIII

Only the impossible is not possible.

Deep Thoughts XXVII

Only the eternal is forever.

[Actually, this is only a necessary truth on some readings of "forever" and "eternal". We need to read "eternal" as compatible with merely futureward eternity, but not pastward eternity. We need to read "forever" as implying infinite futureward temporal extent, so that existing at every time not count as sufficient for existing forever (imagine a world where the timeline has only a finite extent from beginning to end—we don't want to count a being that exists from the beginning to the end of time as existing forever in that world). It's worth noting that the converse of the above Deep Thought might not be a necessary truth. For a timeless being can be eternal, but I am not sure a timeless being counts as existing "forever", except of course in an analogical sense.]

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 XXIII

One cannot succeed without trying.

Deep Thoughts XXII

The inevitable never fails to arrive.

Deep Thoughts XXI

There is nothing quite like something incomparable.

Deep Thoughts XX

There is something to be said for an irrefutable theory: It can't be refuted.

[This isn't quite a tautology, because "There is something to be said for" has a valuative component that does not tautologously follow from irrefutability. Anyway, I am always amused when I see the move made against Intelligent Design in public debate: "It's irrefutable. And besides, the evidence is against it." It seems to be like the case of the man who complained that the food was revolting and the portions too small. (I am assuming that "refutable" means something weaker than "can be apodeictically disproved", since coherent scientific theories tend not to meet that standard of refutability.)]