The following argument parallels the Slingshot Argument expressed here.

(P1) *If* X is explicable (can be explained), and X is logically equivalent to Y, then Y is explicable (for any X and Y).

(P2) *If* X is explicable, and X is semantically equivalent to Y, then Y is explicable (for any X and Y), where semantically equivalent facts are ones that are expressible by syntactically identical sentences whose referring terms refer to the same thing: for example, ‘the fact that Socrates is happy’ is semantically identical to ‘the fact that the person who is identical to Socrates is happy’, since ‘the person who is identical to Socrates’ refers to the same thing as ‘Socrates’ (and everything else about the sentences are the same).

[Edit. P2 may be more plausible if stated this way: *If* X is explicable, and X and Y both say the same thing about the same things (and say nothing else about any other things), then Y is explicable (for any X and Y). Then the deduction below will need a premise to the effect that the cumbersome facts considered there ultimately say the same thing about the same things (and say nothing else about any other things)*.]

(P3) At least one fact is explicable.

From (P1) – (P3), we deduce the principle that every fact has an explanation has follows. First, there is an explicable fact F (by P3). Second, F is logically equivalent to this fact Q: the x, such that [x is identical to Socrates, and F obtains] is identical to the x, such that [x is identical to Socrates]. Third, for any fact, F*, Q is semantically equivalent to this fact R: the x, such that [x is identical to Socrates, and F* obtains] is identical to the x, such that [x is identical to Socrates]. This is because where F and F* are both facts (and so both obtain), ‘the x, such that [x is identical to Socrates, and F obtains]’ and ‘the x, such that [x is identical to Socrates, and F* obtains]’ both refer to one and the same thing: Socrates (if they refer at all). Finally, R is logically equivalent to F*. It then follows from P1 and P2 that F* is explicable (for any F*), since F is explicable. Therefore, every fact is explicable. To get to PSR, we add the premise that if a fact f has no explanation, then the fact that (f obtains and f has no explanation) is inexplicable.

Replies to the Slingshot Argument may (or may not) carry over.

* I think we would normally say that ‘Mark’s favorite cat is happy’ is about a certain cat but is not also *about* the description (“Mark’s favorite cat”) used to pick out that cat. Keeping this in mind, consider the following “semantically equivalent” sentences:

1. Mark’s favorite cat, Spot, is happy.

2. the cat C [such that C is Mark’s favorite cat, Spot] is happy.

3. the cat C [such that C is Mark’s favorite cat, Spot, and C is in the White House] is happy.

4. the cat C [such that C is Mark’s favorite cat, Spot, and C is in a house that is white] is happy.

5. the cat C [such that C is Mark’s favorite cat, Spot, and C is on a planet in which someone is a president] is happy.

6. the cat C [such that C is Mark’s favorite cat, Spot, and C is in a universe in which the fact that someone is a president obtains] is happy.

7. the cat C [such that C is Mark’s favorite cat, Spot, and C is in a universe in which F* obtains] is happy. (given any F* that obtains)

Do these all say the same thing about the same cat (and say nothing about anything else)? If not, at which point does the aboutness condition break down?

More to the point: if (1) expresses an explicable fact, do all the rest (thereby) do, too? If not, at which point does the explicability inference break down?

Angra,

Yes, they are semantically equivalent. Someone might view them as two different (cumbersome) ways of saying that Socrates is self-identical. The question of why believe the premise is a good one, and I don’t claim to have an answer.

One idea that might appeal to some people is that a fact is explained if there is an explanation of why the things that fact is about are the way the fact says they are, and semantically equivalent facts are ultimately about the same things (because the sentences that express them refer to the same things) and say the same things about those things (for example, in the case above, the facts say, in different ways, that Socrates is identical to Socrates). I don’t think one must already accept PSR to find that appealing. I also don’t think one must reject PSR to find that unappealing (for whatever reasons).

Joshua,

The reason I get the impression that one would have to accept the PSR already is that in order to explain Q, it seems to me one needs to explain why the x such that [x is identical to Socrates, and the fact humans evolved from fish obtains] is identical to the x, such that [x is identical to Socrates].

But in order to explain that, one needs to explain why humans evolved from fish (assuming Socrates existed, but he did).

The same for R and Barack Obama.

So, it seems to me that if one suspects that there might be a fact F* such that F* has no explanation, and accepts that there is a fact F such that F has an explanation, plausibly one would suspect (at least, if one agrees with my assessment above) that Q(F) has an explanation (because F does), but Q(F*) does not, because F* does not.

*But in order to explain [why the x such that [x is identical to Socrates, and the fact humans evolved from fish obtains] is identical to the x, such that [x is identical to Socrates]], one needs to explain why humans evolved from fish (assuming Socrates existed, but he did).*

Maybe so, but it’s not perfectly clear to me. Is the following true?

In order to explain why that guy who is over there exists, one needs to explain why that guy is over there.

Intuitively it seems not, though I suppose it would depend on how you’re using ‘the guy who is over there’.

On the other hand, in the case of Q (Q: the x, such that [x is identical to Socrates, and the fact humans evolved from fish obtains] is identical to the x, such that [x is identical to Socrates]), it seems to me that Q is not explained by F.

In other words, it seems to me that to say that (the x, such that [x is identical to Socrates, and the fact humans evolved from fish obtains] is identical to the x, such that [x is identical to Socrates]) because (humans evolved from fish) does not cut it as an explanation.

But if saying that (the x, such that [x is identical to Socrates, and the fact humans evolved from fish obtains] is identical to the x, such that [x is identical to Socrates]) because (humans evolved from fish) does not cut it as an explanation of Q, it seems to me that an explanation of the fact that humans evolved from fish would be required.

On the other hand, if I’m mistaken and an adequate explanation of Q is F, then, then the problem is (P1), for the following reason:

Q and F are logically equivalent, and (we assume) F explains Q, but if F explains Q, it seems that Q does not explain F (infinite conjunctions may be a different issue, but in this case it seems clear cut that F and Q don’t explain each other).

But unless one already accepts the PSR, I’m not sure why one would be inclined to accept (P1), since a person who suspects that there *might* be a fact P without an explanation will probably conclude that P explains Q(P) (i.e., why the x is identical, etc.), but P might still not be explained, and an explanation of Q(P) does not give us an explanation of P, just as in my example, an explanation of Q does not give us an explanation of F, under the assumption that F explains Q.

The premises are true, but create triviality by removing all content except truth value itself.

I can prove all numbers are logically and semantically the same: multiply them by 0 and they all give the same result.

SO, if we say all facts and true statements are = “T”, the logical truth value, we have a sort of multiply by 0 transform happening. The net effect is to collapse all useful distinctions from our meaning.

Angra,

I agree that F doesn’t seem like a good explanation of Q, though I’m not presently seeing why F thereby needs an explanation (apart from premises in the psr slingshot argument itself). I may be misunderstanding.

I was thinking that “the guy who is over there” functions the same way as “the x such that F” — to pick out the items the fact in question is about. (And so an explanation of the Q is not thereby an explanation of the F.)

Incidentally, the advocates of the original Slingshot Argument would deny P3, since P3 is inconsistent with the conclusion of *their* argument. So one can accept P2 (as would the advocates of the original argument) without accepting PSR, if one denies P3 (or P1).

Joshua,

Okay, so we agree that F is not a good explanation of Q.

If we have an explanation L of Q, plus a trivial explanation E of the fact that Q and F are not logically equivalent, would L and E not explain F?

If so, I’m not sure how one would go about explaining Q without giving an explanation of F.

If not, then I’m not sure why one would be willing to accept P1.

In any case, it seems to me that we have the following:

If an explanation of Q requires one of F, then unless one already accepts the PSR, it seems one would not be willing to accept P2.

If an explanation of Q does not require one of F, then I’m not sure one who doesn’t already accept the PSR would be inclined to accept P1, because F and Q are logically equivalent but an explanation of Q fails to explain F.

Regarding P3, that’s an interesting point, though I’m inclined to accept that premise.

Good observations, Angra.

It seems the situation comes down to this (if I understand you): given P3 and given that F is explained if Q is explained (which follows from P1), P2 is true if and only if PSR is true…

In other words, the most vulnerable premise P2 is true if and only if the conclusion is true, assuming the other premises are true. (A sign of a valid argument!) Someone with your depth of insight into the argument might then resist P2 by seeing that it’s true if and only if the conclusion is true. Fair enough.

Still, someone else might find all three premises evidently true (or have various reasons to accept them). I don’t want to rule that out, a priori.

And I confess that it’s hard for me to see why a fact X should be explicable while a fact Y that ultimately says the same thing about the same things is not (see the * in the original post). At any rate, if PSR is equivalent to P1&P2&P2, then that itself could be of interest, since then we’ve transformed a conjecture into three sub-conjectures, any or all of which may (or may not be) easier to confirm or disconfirm.

Joshua,

Good observations you too, and thanks.

Regarding premise 2, I wouldn’t be inclined to say that Q and R say the same thing about the same thing, in a colloquial sense, even if they do in some technical sense (there may be more than one sense in which two statements may be about something).

For instance, let’s say that Alice and Bob are high school students in the US, who have never heard of Pol Pot, or of JosÃ© Gervasio Artigas, but both know that Socrates existed, and we know that they know (we check by asking them).

Let’s say that we tell Alice the following:

Q(PP): The x, such that [x is identical to Socrates, and the fact that Pol Pot was the leader of the Khmer Rouge obtains] is identical to the x, such that [x is identical to Socrates].

Then, we tell Bob the following:

Q(JGA): The x, such that [x is identical to Socrates, and the fact JosÃ© Gervasio Artigas was born in Montevideo obtains] is identical to the x, such that [x is identical to Socrates].

Did we tell them the same thing about the same thing?

Intuitively, I would say that we didn’t, and I suspect that they probably would agree.

It seems to me that in a usual sense, we told Alice, in a very convoluted and *implicit* way, that Pol Pot was the leader of the Khmer Rouge, and we told Bob, also in a very convoluted and implicit way, that Artigas was born in Montevideo, but we did not tell Bob that Pol Pot was the leader of the Khmer Rouge, and we did not tell Alice that Artigas was born in Montevideo, implicitly or otherwise.

But if Q and R are facts (side note: or propositions? statements? I think that that might require clarification) that say the same thing about the same thing, I would say that I do not see any relation between the fact that two facts say the same thing about the same thing and whether the two of them are explicable.

Moreover, in that case, it seems clear to me that the fact that two facts say the same thing about the same thing does not imply that their explanations are in any way related.

For instance, in order to explain Q(PP), I may well offer a causal account of the fact PP (i.e., the fact that Pol Pot was the leader of the Khmer Rouge), and also an easy explanation of the fact that Q(PP) is logically equivalent to Q(PP), and it seems to me that that explains Q(PP).

But that does not explain Q(JGA), and it seems to me that it’s totally unrelated to any explanation of Q(JGA).

Regarding the *, I would tentatively say that whether some of the sentences say the same thing about the same thing may depend on context (I think ‘identical to’ works better than ‘happy’ as an example, though this isn’t required).

For instance, let’s consider the following sentences (I use ‘sentences’ to follow the cat example):

S0: The Morning Star is identical to the Evening Star.

S1: The C such that [C is the Morning Star] is identical to the C such that [C is Evening Star].

S2: The C such that [C is the Evening Star] is identical to the C such that [C is the Evening Star].

S3: The Evening Star is identical to the Evening Star.

Do all of those sentences say the same thing about the same thing?

Even assuming a common language throughout, that depends of what the speaker intends to say, but in most cases, I would say that no, they do not say the same thing about the same thing (the problem is between S1 and S2), at least in a common sense of the expression ‘saying the same thing about the same thing’, for the following reason:

We define ‘the Morning Star’ by pointing at an object in the morning and say ‘that thing that is over there all mornings’, and similarly we define ‘the Evening Star’ by pointing at an object and saying ‘that thing that is over there all evenings’.

If we assert S0, (probably) we’re saying that the object that is over there all mornings is also the thing that is over there all evenings.

But if we assert S3, we’re not saying that. We’re just saying that the object that is over there all evenings is identical to itself.

Yes, “aboutness” considerations may constitute a promising objection.

Consider the phrase, ‘the x, such that F’. If we give it a Russellian expansion, then the Q isn’t equivalent to F. But without the expansion, Q might be thought to say something about other things (such as *being the one and only x, such that F*), given a de dicto reading. This is a reply to the original slingshot argument worth thinking about.

It would be interesting to see what advocates of the original slingshot argument think of the psr slingshot argument (where “fact” talk is perhaps replaced with “true proposition” talk).

Josh:

Interesting.

1. P1 by itself implies that if any necessary truth is explicable, they all are. That’s not clear.

2. I feel very little pull to accepting P2, apart from the pull to accept the PSR. <The heads result of the coin toss is heads> is explicable, since it is explanatorily grounded in the facts that there was a toss and the tautology that all heads results are heads, but one shouldn’t be able to conclude *from this* that <The result of the coin toss is heads> is explicable. (I am assuming that “explicable” means *has an explanation* rather than *possibly has an explanation*. If the latter, I need to think a bit more.)

3. I worry that the reason we are pulled to accepting P1 and P2, besides of course the plausibility of the PSR, is that we are pulled to accepting the following false claims:

P1a. If p and q are logically equivalent, an explanation of one is an explanation of the other.

P2a. If p and q are semantically equivalent, an explanation of one is an explanation of the other.

That the *conjunction* of P1a and P2a is false follows from a version of your slingshot argument: for if P1a and P2a are true, then any explanation of any fact is an explanation of all facts, so that the fact that I posted this comment (which explains why you’re reading it) explains why World War II started. But it’s pretty clear that P2a is false on its own, say because of the coin toss example. And P1a is false since it is false that any explanation of a necessary truth is an explanation of every necessary truth (that the sky is blue explains why the sky is blue or 2+2=4; but it doesn’t explain why 2+2=4).

4. The Russellian objection seems powerful to me.

Alex:

1. Restrict the argument to contingent facts.

2. By ‘explicable’, I mean possibly has an explanation. (Not sure that helps.)

3. Nice observation. The worry may be less acute given the above point, but I’ll have to think more about that.

4. For what it’s worth, I’m skeptical of the Russellian expansion (in this context), but without the Russellian expansion aboutness considerations seem to cause trouble… On the other hand, it is hard for me to see how a difference in the respective facts should account for a difference with respect to possibly being explained. It’s hard for me to see either way.

Josh:

1. Let p be an explicable necessary truth. Let r be its explanation. Let q be any contingent truth. Then, plausibly, r&q explains p&q (not completely–the q part isn’t explained, but it’s still an explanation). So p&q is explicable. So q is explicable. So P1 is enough for the argument argument without P2 it seems.

2. I missed this: “if a fact f has no explanation, then the fact that (f obtains and f has no explanation) is inexplicable”. I think the argument needs to be more complex. For there is a way in which facts of the form <f obtains and f has no explanation> can be explained: they can be explained by citing f’s inexplicability. To get the premise, you need the claim that that’s the *only* way that such facts can be explained. That’s initially pretty plausible, I guess.

But suppose that comings into existence of fundamental entities can be explained causally or not at all. Suppose (impossibly!) x is a fundamental entity that comes into existence causelessly. Then we can explain why x came into existence inexplicably: x came into existence causelessly and x is the sort of thing whose coming into existence can only be explained causally.

E.J. Lowe gave me permission to post his comment on the psr slingshot argument:

>

Alex,

Your observation about equivalent propositions is interesting. We may put the argument in terms of ‘partial explanation’, where ‘x partially explains y’ means ‘x explains at least part of y’. Then we may deduce that every contingent fact possibly has an explanation from:

1. Some necessary fact is possibly partially explained.

2. If X is a contingent fact that is possibly partially explained, then any fact equivalent to X is possibly partially explained.

I think it’s somewhat surprising that weak psr should follow, even if (2) is not independently justified.

I got to thinking about “Slingshot PSR” arguments because I was thinking about what difference between two facts might, in principle, account for why the one fact is explicable and the other is not. Suppose, for example, that it is explicable why being triangular should be instantiated. Should it not, then, also be explicable why being square should be instantiated, and more generally, for any shape? Why should shape make a difference with respect to explicability? More generally, what sorts of differences between facts might make a difference with respect to explicability? That’s an open question, and I think it’s worth investigating.

Josh:

“More generally, what sorts of differences between facts might make a difference with respect to explicability?”

Here’s a cynical answer: “Those facts can be explained which can in principle have explanations that fit with one’s worldview.”

The premises are true, but create triviality by removing all content except truth value itself.

I can prove all numbers are logically and semantically the same: multiply them by 0 and they all give the same result.

Joshua, I’m not sure I’m getting this right. I have a question:

For instance:

F: the fact that humans evolved from fish.

F*: the fact that Barack Obama is the POTUS.

Q: the x, such that [x is identical to Socrates, and the fact humans evolved from fish obtains] is identical to the x, such that [x is identical to Socrates].

R: the x, such that [x is identical to Socrates, and the fact that Barack Obama is the POTUS obtains] is identical to the x, such that [x is identical to Socrates].

Then, Q is semantically identical to R?

If not, please clarify.

If so, then ‘semantically identical’ looks like a misnomer to me, but in any case, unless one already accepts that every fact has an explanation (or that no fact does, but that would be weird), I’m not sure why one would be inclined to accept (P2).