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Monday, March 02, 2009

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Standard contrary-to-fact conditionals are canonically expressed “If X had occurred, Y would/could have occurred also.” Many variants of this form exist in ordinary speech, including an emphatic, though clearly redundant formulation, which bothers to assert that the counterfactual consequent did not in fact occur: “ Y did not occur, but it could have if X had.” Where the context of the conversation makes clear what the counterfactual supposition X is, an ordinary speaker routinely favors an even economical (elliptical) form: “Y didn’t occur, but it could have [if…].”

This seems to be the construction that is being dubbed an “antifactual”. I don’t in principle object to neologisms, but for several reasons beyond the obvious, this seems an unhelpful coinage. We are dealing with a standard elliptical contrary-to-fact conditional.

Bill is right to be puzzled when an utterance like “Y didn’t occur, but it could have” has no context to indicate what counterfactual supposition the speaker intends. It is as a speaker had asserted “This argument is unsound” or “He lied to me” when the context affords no referent for "this" or "he". Though syntactical well-formed, those utterances clearly make no claims whose truth value can be adjudicated.

Phil O. Ponus,

Didn't you want to say that Dave is the puzzled one? You are right that there is no need for Dave's neologism. 'Elliptical counterfactual conditional' will do.

It is not entirely clear that (A) above is an elliptical CC, though it could of course be construed as one. Consider

B. Though the universe exists, its nonexistence is possible.

(B) could be elliptical for something like

B* Though the universe exists, it would not have, had God not created it.

But (B) could also be construed unconditionally as expressing just the modal contingency of the universe.

What say you, Peter?

Bill I appreciate the detailed response, but I'm afraid that I was arguing something different than what you understood. It seems that no matter how much effort I put in, I still have trouble making myself clear. But maybe if I respond directly to your understanding of my points, it will help.

You say: “Dave's thesis is that proposition (A) above and relevantly similar propositions are "incoherent." I think we can safely ignore Dave's qualification, "when used in a philosophical sense as Peter, Bill, et al. use them." For Peter and I are using formulations like (A) in the same way any person would. There is nothing particularly 'philosophical' about a sentence like (A);”

If you leave out the qualification “when used in a philosophical sense” then you miss my entire point. As I said in the part that you left out, in normal use, an antifactual is really just a counterfactual with the condition left implicit. What I tried to explain is that the way that you and Peter use antifactuals in your discussions of modal propositions does not lend itself to any sort of implicit condition to turn it into a counterfactual. This is what I meant when I said that you use it in a philosophical sense. As far as I can tell, when you say (in discussions of modal propositions) “I am blogging but I could have been running.” there is no implicit “if ...” to add to that sentence. You seem to intend it as an isolated and complete proposition. It is in this sense that I suspect that it is incoherent. If you do intend some implicit condition, I do not know what it is.

You continue: “Although it is not likely that an ordinary hombre would assert (A), one can easily imagine an ordinary guy saying to his wife, 'It would have been nice had the stream crossed our property.' Or, 'What a beautiful shade tree! Had it grown up closer to the house, it would have provided us with more blessed shade in this infernal desert!'”
But those are not antifactuals and I have no quarrel with them. I'll reiterate that the only issue I was discussing was the coherence of bare antifactuals --those with no context providing an implicit condition to turn them into a counterfactual.

You continue: “But Dave says that (A) is "incoherent." Dave is using this term idiosyncratically to mean that the truth-conditions of (A) cannot be known to obtain. “

When I say that (A) is incoherent, I don't mean that it is impossible to know whether (A) is true or false but that I don't know what it would mean for (A) to be true or false. Consider

(B) There are other actual universes inaccessible from our universe.

There is no way to know if (B) is true or false, but it is not incoherent. By contrast

(C) The power of a man to excel is greater than the power of the sun.

is incoherent. The words all seem to go together, but I really don't know what it would mean for this to be true or false.

Maybe I should have used the word “ambiguous” rather than “incoherent”. I can think of several different ways to interpret (A) (my candidates (1)-(4) indicate some of them) and if I thought that one of these were correct (even if I didn't know which one), then (A) would merely be ambiguous. But I don't think any of these techniques to make (A) unambiguous are really what is intended by Peter and you. That is why I used “incoherent” rather than merely “ambiguous”.

You continue: “Consider candidate (1). If the history of the tree had been different, if, for example, a certain bird hadn't bit off a certain leaf that it did bite off, then the tree would have had one more leaf than it it actually has. The italicized sentence strikes me as obviously true. If Dave denies that it is true, then we don't have a basis for further discussion; for then he is denying what I take to be a DATUM, a given, something obviously the case.”

I agree that your example is coherent and true. In fact, candidates (3) and (4) were such that they could be used to extend (A) to form (A'), such that (A') would be coherent and either true or false --that is, I would know what it means for (A') to be true or false whether or not I had any way to obtain the answer.

You continue: “For surely (A) is true. Dave admits as much when he asks for the truth-conditions of (A). (One cannot ask for the truth conditions of a proposition that is not true; so Dave's asking for truth-conditions presupposes the sentence's being true.)”

I'm afraid that I don't understand this section. Maybe there is a technical meaning of “truth conditions” that I don't know. I simply meant the conditions under which the proposition would be true. I was asking what would have to obtain in order for (A) to be true or false.

You continue: “Now is Dave saying that no one knows that propositions like (A) are true? Or is he saying that no one knows HOW propositions like (A) are known to be true?”

Neither one. I'm saying that (A) is fundamentally ambiguous; that Bill can say it is true and Peter can say it is true, and they might be saying two entirely different things. And poor Dave doesn't know which of the many things that they might be saying they actually are saying.

DaveG

Here is (A):

(A)While the tree in my yard boasts 17,243 leaves at time t, it could have boasted 17,244 leaves at time t.

Here are roughly its truth conditions. Let w designate the actual world, and let w* designate an accessible possible world in which my yard exists, it has a particular tree in it. Call this tree 'Suma':

TC for A:
(A) is true just in case in w Suma is in my yard and it has 17,243 leaves at t and there is a possible world w* accessible to w such that Suma is in my yard at w* and Suma has 17,244 leaves at t.

Which part of TC you fail o understand or think is ambiguous?

peter

Dave,

I think pursuing this any further with you would be a waste of my time especially if you use 'incoherent' to mean ambiguous!

AMBIGUOUS: A word, phrase, or sentence is said to be ambiguous iff it admits of two or more definite meanings.

Bill, I'm sorry you feel that way. Although I did suspect that your patience for this topic was limited when you simply skipped over the explanations I gave of what I meant by "used philosophically" and "incoherent". And now again. As I said, that the reason that I don't think "ambiguous" is adequate to describe the character of antifactuals is because, although there are various definite meanings that could be attributed to an antifactual, I don't think any of those meanings is what is intended.

There is a wonderful scene in “On the Waterfront” between Brandon and Steiger. Brando plays a boxer whose career was ruined by his brother pressuring him to take dives. Brando laments his lost career with the line “I coulda been a contender.”

Is this an elliptical counterfactual? Let’s concede there is no simple implicit antecedent here. We can’t imagine Steiger asking his brother “If?” But the context of their conversation makes clear what Brando means by “I coulda been”: I had the skills at that time to fight at the level of a heavyweight contender, I had fought my way up to a contender shot, but you asked me to take a dive in the critical fight and I did, ending my chance.” These are the well-known facts, and these facts are what make us concede the truth of Brando’s claim.

In general, this paradigm suggests, it is well-understood contextual facts about the past, about how things were, that decide the truth or falsity of contrary-to-fact conditionals in ordinary speech. Paradoxical it may seem, but it is facts that decide the true value of “counterfacts”.

Now imagine that Brando had said “I also could have been the Pope.” Most people would have heard this as a (bad) joke, because the context for such a claim was completely lacking. What basis could Brando possibly have for claiming a lost ecclesiastical career? “I could have been the Pope” isn’t so much ambiguous, with a plurality of possible & competing interpretations, as lacking any clear sense, undefined, if you wish, by the context and the background information we have. Just as “this argument is unsound” is undefined when we have no referent for “this”.

Now if Brando and Steiger had also been philosophers--God forbid--the context would have been different, and perhaps "ambiguous" would be the right word for the problem with "I coulda been the Pope."

That is approaching the source of my confusion, Philoponus --on the one hand, Peter, Bill, et al seem to be saying that "I coulda been the pope" would be false in this case. But they have also said that "the laws of physics could have been different". If you think of possibilities on a scale of "how possible" something is, it seems much more possible for Brando to be the pope than for the laws of physics to be different.

Peter, what is ambiguous is "accessible possible world". Just for the sake of my examples, lets instead use the sentence:

(B) the tree could have lost a leaf.

Which of the following constitutes an accessible possible world?

(1) a world in which a man had plucked a leaf off of the tree in order to make a philosophical point.

(2) a world in which a genetically-improved chimp had plucked a leaf off the tree in order to make a philosophical point.

(3) a world in which a perfectly normal chicken had picked a leaf off of the tree in order to make a philosophical point.

(4) a world in which the Tree Fairy had come from the land of Faerie to pluck a leaf off of the tree in order to make the number of leaves in the universe a prime number.

(5) a world in which at some previous time the laws of nature had been such that for a few brief moments, it was physically impossible for any tree to have exactly 17,244 leaves, and so the extra leaf just vanished.

(6) a world in which the number 17,244 does not exist, so although all of the physical process were the same, the last leaf just could not exist.

I'm not being deliberately obtuse here. I genuinely think that you are using “possiblity” in an inconsistent way.

From previous discussions of possible worlds, I expect that you would say 1, 2, 3, an 5 are possible but 6 is not. I don't know what you would say about 4. But if you say that all of those are possible, how can you say that it is not possible that you could suddenly turn into a ball? If the laws of physics could be different, then how can any geometrically-conceivable physical event be ruled out?

And once again, let me reiterate that I'm not talking about counterfactuals here. I'm willing to concede that some modal propositions are meaningful. It is only the bare antifactuals that seem to have no meaning.

By the way, I came up with another possible meaning for (A)

(5) there exists a proposition P such that P is false but "if P then (A) would have been” is true.

This interpretation has the virtue that in many cases you could actually know it to be true. But I doubt that this is true in all cases.

Phil O. Ponus,

Excellent example, though what the Brandon character actually said was, "I could been a contendah." [grin]

You seem to be saying that there is a CFC into which to embed 'I could have been a contender,' perhaps this:

1. If you, brother, had not asked me to take a dive, then I would be a contender.

>>In general, this paradigm suggests, it is well-understood contextual facts about the past, about how things were, that decide the truth or falsity of contrary-to-fact conditionals in ordinary speech.<< No, these facts, though relevant to understanding Brando's statement and the tacit conterfactual, do not decide the latter's truth or falsity. They merely determine the latter's sense.

In any case, I don't know what you are contending (forgive the pun) with these examples. What exactly is your thesis? Is it your thesis that modal sentences like 'I could have been a contender' must be construed as elliptical for CFCs in which they figure as parts? See my latest post.

DaveG
In a previous response I have stated (roughly) the truth-conditions of (A) according to the standard semantics for modal logic.

1) You complained above that “what is ambiguous is "accessible possible world".” It is not! There is a precise and clear formal characterization of this relation among possible worlds (sometimes the notion of ‘alternative world’ is used instead of ‘accessible’; but the concepts are exactly the same). The basic idea is that R (the standard designation of accessibility among possible worlds) formally codifies the intuition that the distribution of truth values of propositions in various possible worlds represents the conditions under which modalized sentences are true or false in a given world. So <>P is true in w just in case there is a w* (within a frame [F] of possible worlds) such that Rw*w and valuation v; v(P,w*)=T (v assigns T to ‘P’ in w*). A Frame is a collection of possible worlds that depends upon the interpretation of R: the frame [F] will be a collection of successive time slices in tense logic, for instance, etc. v is the standard valuation that assigns truth values to atomic propositions, complex ones, and quantified ones in each member of [F]. v assigns truth values to modal propositions utilizing R over the frame [F]. The truth-conditions then are stated in terms of {[F], R, v} depending upon the interpretation of R (tense logic, Deontic logic, aletic logic, etc.)
So ‘accessible possible world’ has a precise formal characterization and it is not ambiguous except insofar as it can be interpreted as a temporal relationship among worlds or as a deontic relationship or as an epistemic relationship or as an aletic relationship.

2) I am going to stick to (A) instead of your (B). Regarding the TC for (A) which I have offered in my previous post, here it is again:

TC for (A): A is true just in case in w Suma is in my yard and it has 17,243 leaves at t and there is a possible world w* accessible to w such that Suma is in my yard at w* and Suma has 17,244 leaves at t.

You ask: “Which of the following constitutes an accessible possible world?” and then you list six conditions that characterize worlds. I will only consider conditions (1), (2), (3), and (5) because your number (6) does not characterize a possible world in my view. I believe that if numbers exist at all, then they exist necessarily and that includes the number 17,244. Therefore, there is no possible world in which the number 17, 244 does not exist and as a result of this reason Suma is deprived of that extra leaf. Regarding (4), it raises complicated issues about fictional entities that are not directly pertinent to the fundamental issues under consideration here.

3) What are your (1), (2), (3), and (5)? They are all ways of giving the causal antecedents for there being only 17,243 leafs on Suma. Therefore, they all, I repeat ALL, characterize alternative possible worlds in which Suma has only 17,243 leafs. (There are plenty of others). They differ with respect to the causal antecedent; i.e., what *caused* Suma to have only 17,243 leafs rather than 17,244. Thus, in one possible world the cause for Suma’s leaf-deficiency is that a passerby plucked a leaf; in another a bird did it, in another a chimp did and so on.

4) Your objection, thus, confuses giving truth-conditions for a given propositions vs. giving a causal-explanation why the conditions so given obtain. These are two different enterprises not to be confused.

5) Consider an example not involving modal operators: C= “There are two books on the desk”. What are the truth conditions for proposition C? They are roughly as follows:

TC for (C): C is true just in case there is an x and there is a y such that x is a book and y is a book and x is on the table and y is on the table and x is not identical to y.

TC for (C) tells us the conditions under which (C) is true or false. But notice that these truth conditions do not tell us WHY the two books are on the table. That belongs to a causal-explanation not to truth-conditions. If a truth-conditional semantics for *any* sentences had to include causal accounts, no truth conditions could be given. Therefore, if the truth-conditions of unmodalized propositions do not have to include the antecedent causal conditions that caused the state of affairs that makes that propositions true, there is no reason to demand this from giving the truth-conditions for modalized propositions. Regarding this matter, both are treated in the same way.

6) I anticipated that one source for your objections was confusing giving truth-conditions (semantics) with giving a causal-explanation (empirical investigation). Once this confusion is removed, then the project of giving truth conditions to modalized propositions is not a problem. My Suma-sentence then raises no special problems: it’s truth-conditions are clear.

peter

Phil-O-Ponus,

Great example. Pertinent!

I assume here some of the material I posted as a response to DaveG.

Suppose Brandon had a lifelong secret desire to be a Pope. Suppose he was a bit tipsy when that scene was shot and uttered: “I coulda been a Pope”. Suppose the editors (for reasons that are still shrouded in mystery) cut the movie in a way that left this utterance by Brandon. As you note, this utterance by Brandon in that movie would have been totally out of context, unclear, and inscrutable. However, it does not follow from such examples that there is something fundamentally wrong with counterfactual assertions or with modal logic.

How we handle such examples?
The fundamental idea is to force the relation of accessibility R to be sensitive to such contextual elements. While the details of such logical machinery may be very complicated, the basic ideas should be clear. Force R to select from the frame of possible worlds [F] only those worlds that contextually make sense. There are at least two ways I can think of how to do this.

(a) The brute force way is to place a contextual condition upon R so that it selects only those worlds from [F] that satisfy these conditions. E.g., we can tell R to select only those worlds in which Brandon was a boxer and exclude those worlds in which Brandon has a career in the Catholic Church. Thus R* will select only a subset of possible worlds such that in each of them Brandon has a career as a boxer rather than a career in the Catholic Church. V* (i.e., the restriction of v to a valuation function that assigns truth conditions to the sunset of worlds chosen by R*) assigns F to the proposition “I could have been a Pope” in all of those worlds R* selects: i.e., in which Brandon is a boxer. The disadvantage here so far as I can see is that we are going to have an indefinite number of relations of accessibility for each contextual element. There may be a general way of solving this problem, but I have no idea how to do this.

(b) The better and gentler way is to substitute for R an accessibility relation RR that is sensitive to a relation of relevance among conditions. This will marry relevance logic with modal logic. Then RR will again exclude worlds in which Brandon has an ecumenical career rather than a boxing career. V then will follow RR in truth value assignments for Brandon’s assertion “I coulda been a Pope” and assign it F. The technical details of this are complicated and I have no idea how this is going to work, but at least the general principle should be clear.

These ways are available to make sense of the kind of contextually sensitive examples Phil-O-Ponus raised. I am sure that someone more knowledgeable about the technical apparatus of modal logic could describe these matters much better. My point however is to point out that these examples do not show that there is something fundamentally wrong with the conceptual foundation of modal logic. They show how complicated ordinary discourse can be and how imaginative some of us can be.

peter


Peter,

I think the problem with Dave lies deeper. He just doesn't understand the notion of an unrealized possibility, let alone the notion of a non-actual possible world. Your beloved tree Suma has n leaves at t. Now to you and me it is clear that Suma could have had n + 1 leaves (or n + 2 or n - 1, etc.) at time t. Apparently, for Dave sentences like 'Suma could have had one more leaf than it actually has' are meaningless. We, by contrast, maintain that such sentences are not only meaningful, but true.

As for your explanation of accessibility, I didn't find your explanation very clear. You say, "(sometimes the notion of ‘alternative world’ is used instead of ‘accessible’; but the concepts are exactly the same)." Say what?

There is no need to bring in the notion of accessibility if we are employing, as I assumed all along, the S5 system of modal logic. For on S5 every possible world is accessible to every other one.
The characteristic S5 axiom states that Poss p --> Nec Poss p. In other words, what is possible does not vary from world to world. As you know, S5 subsumes S4 the characteristic axiom of which states that Nec p --> Nec Nec p. In other words, what is necessary does not vary from world to world. Putting the two together, on S5 modalized propositions do not vary in modal status from world to world.

Accessibility can be explained in terms of relative possibility: W is accessible to W* iff any proposition true in W* is possible in W.
But, granting S5, we don't need to worry about which worlds are accessible to which worlds.

Peter,

The problem with Dave is not that he doesn't understand accessibility, but that he doesn't understand the notion of a BL-possible world. And he doesn't understand the latter because he doesn't understand the notion of an unrealized possibility. Could he be a closet Randian? Or a Randian 'plant'? Just kidding.

Bill,

I think you are letting DaveG of the hook too easy. It is easy to pretend as if one is modally blind and simply does not understand certain kind of propositions. Then there is not much to say. But DaveG gave certain considerations and I think those considerations simply confuse truth-conditions with causal-explanation. So once this is made clear and it is also made clear that the two projects are distinct, then he must find another argument or considerations against modal propositions like the one we are considering.

As for "accessibility". In S5 R is universal. But there are two reasons to still keep it in the semantic background. In other modal systems it is needed. In other interpretations of the modal operators it is needed (e.g., temporal interpretation of the modal operators R will be needed). In addition, it does indeed represents the formal counterpart to the intuition that what is possible in one world, is true in some worlds that are related to it. And as I responded to Phil-O-onus, it is useful to have it so that we can express needed restrictions on it.

So all in all, while you are right that in the specific cases we are considering, R is not essential (we can state everything without it in S5), it offers the kind of flexibility I need to respond to DaveG and others when things get somewhat fussy.

peter

Peter,

I now see why it may be useful to appeal to accessibility for the handling of certain cases. I liked your typo above, 'Phil-O-onus.' That puts the onus probandi right where it belongs.

I agree with your point that Dave may be confusing causal conditions with truth-conditions. But I still think that the root of his difficulties is an inability to attach sense to the notion of broadly logical possibility/necessity.

Bill,

I suspect that you are right about this. If so let it emerge as a diagnosis from the debate. Then the summation is going to be that some people are modally blind (to use your apt phrase) while others are not. You can't make a modally blind person see the tint of the possible and necessary.

'Phil-O-onus' a typo? I intended it all along!

peter

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