## Monday, February 23, 2009

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Peter - thank you for that. Trying to summarise your rather long argument in the form of a short medieval-style quaestio: "Whether objectivism is true or not"

Quod non:

(A) Objectivism implies that every contingent or possible fact is caused by a volitional act.

(B) Some contingent or possible facts (counterfactuals) are not caused by volitional acts.

Ergo &c.

Probatio minoris: "(CF) If I were strong enough, I would lift a 2,000 lb rock" is a true counterfactual proposition whose consequent never was, nor will be caused by a volitional act

Ad minorem: (CF) really has the form “If I exert a force equivalent to 70 pounds on a rock, then such a force will (or will not) move each rock to a certain point in space.” This does not have the form of a counterfactual.

Contra: My belief in the conditional prediction is based upon a prior belief in the kind of counterfactual propositions expressed by (CF).

It must be said, therefore, that Objectivism is false.

These discussions have made been very enlightening to me, Peter, and I'd like to thank you for your very clear presentations. You obviously have put a lot of work into them.

One thing I've been wondering though, isn't causality itself a modal concept? That is, doesn't "A caused B" logically presuppose "if A had not happened then B would not have happened"? If so, then it seems that not only does the Randian concept of volition imply modal concepts, but so does their contrasting concept of causal determinism. To use the example of a Randian on this thread: there is a crater on the moon because the moon was struck by a huge rock sometime in the past. But this implies that if the moon had not been struck by that huge rock at that time, then it would not have this crater. And this is a counterfactual --that is, a modal-- proposition.

Dave Gudeman's point above is a good one.

>>That is, doesn't "A caused B" logically presuppose "if A had not happened then B would not have happened"?

This seems open to counterexamples. Suppose that had the rock failed to strike the moon, another rock would have done so, giving rise to a crater of identical dimensions. This supposition doesn't prevent its being true in the actual world that the particular rock that struck the moon caused the crater.

Dave Gudeman,

There is vast, a pelagic, literature on causation and a number of different theories. There are regularity theories and counterfactual theories, to mention just two. As David Lewis has pointed out, David Hume runs them together in this passage: “We may define a cause to be an object followed by another, and where all the objects, similar to the first, are followed by objects similar to the second. Or, in other words, where, if the first object had not been, the second never had existed.” (1748, Section VII).

You are alluding to a counterfactual analysis of causation. There is quite a lot to be said for it, so Ocham is right. But it faces various objections. (See David Gordon's comment.) It is a big topic.

But if counterfactuals enter into the analysis of causation, then, given that there is causation beyond the sphere of human volition, there is modality beyond the sphere of human volition, and this is yet another thorn in the side of the Objectivists. Peter, here is another article for you to write!

Gudeman
>>That is, doesn't "A caused B" logically presuppose "if A had not happened then B would not have happened"?
Gordon
>>>This seems open to counterexamples. Suppose that had the rock failed to strike the moon, another rock would have done so, giving rise to a crater of identical dimensions. This supposition doesn't prevent its being true in the actual world that the particular rock that struck the moon caused the crater.

Is that a counterexample? If 'B' has as a reference not a type of event (crater being formed) but a particular crater-formation, happening at a specific time, then if the rock had not struck the moon, then this act of crater-formation would not have happened - which does not rule out another, but different crater-formation happening a short time later.

For example, the speaking clock says 'the third stroke'. The three beeps are identical in type, but different in token, different particulars. So "if A had not happened then B would not have happened" is true if interpreted of particulars.

Ocham,

Yes, that's the obvious reply. But then what rules out the possibility that if the rock that in the actual world strcuk the moon had not done so, another rock would have created the numerically same crater at exactly the same time? One can then try to build into the identity criteria of the rock that it has a particular cause. After this, the discussion gets too complicated for me. The online Stanford Encyclopedia of Philosophy has a good discussion of some of the details: http://plato.stanford.edu/entries/causation-counterfactual/

A causal theory of individuation would be interesting. Another thought-experiment: you are offered the chance of £1m but on the condition that, using a powerful matter destructor and re-creator, all the atoms in my body will be annhilated, then replaced with identical atoms and DNA and so on. So a being would be created with exactly the same molecular structure, DNA, memories, and so forth, absolutely indistinguishable from myself. Plus £1m. Would you agree? I'm not sure I would, because of the suspicion that this being, because is existence would have a different cause from my continuous existence, would be no more than a mere identical twin. Thus, individuation by causation.

Bill,

Thanks for posting this post.

And thanks ocham, DaveG, and others for your kind words.

It might be a couple of days before I can respond to some of these comments. I have a couple of urgent projects that need immediate attention.

peter

Peter,

You're welcome. Take your time. According to LW, Culture and Value, that's how philosophers should greet one another. Lass Dir Zeit! Take your time!

And thanks to the Commenter Corps for their constructive contributions.

I've been wondering if all of these arguments about modal propositions are not misdirected. It's not clear to me that the Randians in this discussion would deny the truth of propositions such as "if no outside force had acted on that mass then it would have continued in a straight line". From the discussion, I suspect that their real position is something like this:

1. In the absence of human volition, nature is deterministic.

2. Certain modal propositions are incoherent, specifically those that suggest that a state of affairs arrived at by a deterministic process might have been different.

Frankly, I'm sympathetic to 2 (and if it weren't for quantum mechanics I might be sympathetic to 1). I suspect that sentences such as "I am blogging now but I might have been running" should be construed as an implicit counterfactual claim, something like "I am blogging now, but if certain other facts had been different an hour ago then I would be running instead.

In any case, it might be worthwhile to try to explore the actual commitments that the Randians in this discussion have with regards to modal propositions.

Dave Gudeman,

1) "it might be worthwhile to try to explore the actual commitments that the Randians in this discussion have with regards to modal propositions."

I think I have stated the actual commitments of Objectivists about modal concepts fairly accurately in Theses A, B, and C. They deny that the modal notion of possible/contingent coherently apply to or that they have a meaning outside the sphere of human volitional facts. However, perhaps HB could comment on this question. Moreover, we can still ask whether my argument would work if their position on this matter would have been as stated.

2) Suppose determinism is true about the physical world. Do you think that it is *incoherent* to maintain that while the tree in my yard boasts 17,243 leaves at time t, it could have boasted 17,244 leaves at time t? Or that the rock could have been moved by a wind equal to 70 pounds? Or that the laws of physics could have been different than what they actually are?

3) I think anyone who holds that claims such as these are *incoherent*, not merely false, will have to show how such a view is compatible with the view that volitional facts are possible, since the later involve essentially beliefs such as that the rock *can* be moved with a force equal to such-and-such pounds. In the absence of such modal beliefs, what point is there to form a plan of action designed to move the rock? Does it make sense to call the following scenario a volitional action: while I know that I cannot exert sufficient force to move the rock and I desire to move it and I do not expect any miracles or divine intervention on my behalf on this matter, nevertheless I will set out to move the rock and shall now do it? I do not think that this scenario describes a volitional act.

4) Volitional acts exploit the independent and prior existence of the very (modal) possibilities the existence of which Objectivists deny. If the Objectivists were right and everything that actually occurs in the natural world outside the sphere of human volition were indeed necessary, then volitional facts would have been impossible.

5) Consider this. Suppose that a rock stands in some desolate place in the universe. Suppose up to time t no human set an eye on it or came close to even knowing its existence. Does it have the property: *a force equal to x pounds can move this rock* or not? Suppose you say: it does not. Now suppose at a time later than t, some humans encounter this rock; they want to move it. They wonder whether it can be moved by a force equal to x pounds? Are we to say that by so wondering the rock suddenly acquired the (Cambridge) property: *a force equal to x pounds can move this rock*? I think such a view is going to be extremely problematical.

peter

Peter, I'm expect that you are properly representing the "official" Randian position. It's just that in trying to make sense of the arguments I've seen here, I've developed a rather different view of the position that the Randians on this list are defending. Of course, I could be being misled by charity since the arguments on the other side are far from clear.

Also, I didn't intend to question the coherence of all modal propositions, only that of a particular subcategory of modal statement --those of the bare form "X could have been Y" where X describes an actual state of affairs and Y does not. Since I suggested reducing statements of this type to other modal statements, I am obviously not suggesting getting rid of modal propositions entirely.

Peter,
Are there two uses of 'possible' in play here, one of which Randians would accept, and one that they would deny? Imagine the deterministic billiard ball world of classical mechanics. In such a world the laws of physics allow a less massy ball travelling sufficiently fast to impact a more massy ball and reverse its motion. Such a reversal can thus be said to be *possible*. But the state of motion in this world could be such that an event of this kind will never occur: perhaps the balls are on such trajectories that such an impact never happens. In this sense a reversal is *impossible*. Like Dave G I suspect that the Rs hold to a strict determinism outside human volition which leaves no room for the possible. Anything other than what has happened/will happen is impossible. There is only one possible world, namely the actual one. But this leaves room for the first sense of 'possible', meaning 'allowed by the laws of physics'. So by their lights, if conditions in the spring were such that by the summer your tree would bear 17243 leaves, then it doesn't make sense that it might bear 17244. On the other hand, they would accept that if a wind of sufficient force were to arise then the rock would move, since that's allowed by the laws of physics. Your argument seems to be about nomological 'possibilities' of this kind, but I don't at the moment see their essentially modal nature, counterfactual or otherwise. I'm clearly missing something here. Could you expand a bit on this?

Dave Gudeman,

I am afraid you are not following the discussion. No one here ever said that -- to use a variant of Peter's example -- the tree in his backyard that has n leaves could have had n + 1 leaves had nothing else been different!

David B writes " In this sense a reversal is *impossible*" Why? Seems like you are confusing temporal and modal notions, something I've warned against many times. If x never happens, or has not ever happened, it does not follow that it can't happen!

Bill,

I may well be confusing temporal and modal notions---I do find the topic of modality difficult. But consider this: Well before the launch of the Cassini mission to Jupiter and Saturn in 1997 scientists at NASA would have performed some celestial mechanics calculations and reached the conclusion that within the next ten years, say, the motion of the planets would be such that it would indeed be *possible* to launch a spacecraft of a suitable size and adequate fuel capacity, slingshot it around the inner planets and Jupiter, and eventually reach Saturn. This conclusion would have been based on the known laws of physics and the known orbital state of the planets. Surely this sense of 'possible' is the one I'm using in my previous comment and the one that Peter is referring to in his post, namely, the sense of the possible that's needed in order to plan our actions?

What Peter has successfully shown I think, is that we need to have an understanding of 'how the world works', ie, some grasp of the patterns in nature, before we can act successfully. What I'm not clear about is to what extent this is incompatible with the rigid determinism to which the Rs appear to adhere, and in particular, with their resulting severely impoverished sense of modality. I'd like to ask Peter to try to make this step of his argument clearer.

Peter, I've just looked again at your para 12:

12) Thesis C basically says that every contingent or possible fact is caused by a volitional act. But, if that were so, then there could not be contingent facts that are independent or volitional acts. But we have seen above that there are plenty of true counterfactual propositions about objects that were not, are not currently, and never will be causally connected to any volitional acts. Therefore, the extension of modal notions is wider than the extension of volitional notions. Hence, Thesis C is false.
I think you have shown that there are such true counterfactuals. But might not an R claim that they are *necessary* rather than *contingent*? This would seem to be consistent with an impoverished sense of modality.

DavidB,

"I think you have shown that there are such true counterfactuals. But might not an R claim that they are *necessary* rather than *contingent*? This would seem to be consistent with an impoverished sense of modality."

I don't think they can claim that because these counterfactuals state that certain state of affairs are *possible*. What I have shown is that in order to devise a plan of action one must believe that a certain state of affairs *can* happen, not that it *must* happen.

peter

Peter,

I apologise if I'm not up to speed on counterfactuals. I couldn't see any connection between counterfactuals and modality. Would I be right in thinking that the implicit step in your argument that's causing me difficulty is that counterfactuals are inherently modal? That in order to make any sense at all of a counterfactual we have to have the 'possible worlds' machinery in mind, a counterfactual being true iff there is no possible world in which its antecedent is true and its consequent false? Perhaps you or Bill could say a little more on this.

Cause and Contingency:
Objectivism and the Origins of Modal Distinctions

In “One Fallacy of Objectivism” and “Volition and Modality” I have argued that volitional facts entail counterfactuals and, therefore, logically presuppose an independent modal distinction. If my argument is correct, then the Objectivists stand of accepting volitional facts but rejecting an independent modal distinction is untenable. However, this argument, even if it is correct, does not address the underlying rationale which leads Objectivists to adhere to these twin theses. Now, some sympathetic commentators such as David Brightly and others have raised questions which I think navigate the discussion toward exploring this issue. So the question of the present post is this: What is the underlying rationale that leads Objectivists to reject an independent modal distinction yet accept that volitional facts exist and that all facts beyond volitional facts are necessary?

1) Imagine a time in the history of the universe when no mortal volitional agents exist. Suppose two rocks, A and B, glide in space on a collision course. Let us ignore for the moment the possibility that the universe is governed by indeterministic laws. Now imagine freezing the universe a fraction of a second before rocks A and B collide. Given the laws of nature and the initial conditions that determine the path of the two rocks, what could prevent their collision? Well, one possibility is that the laws of nature suddenly change so that two rocks that are on a collision course are instantaneously transported into opposite locations in the universe just before they collide. The second possibility is that while the laws of nature remain constant, divine intervention prevents the collision of rocks A and B in this case. The third possibility is that one of the rocks or both opt out of the collision. (The case where some other rock or force steers one of the rocks away from the collision path is not relevant here)

2) Objectivists hold that the above possibilities that could prevent the collision of rocks A and B either make no sense or confirm their claim that the origin of contingency is volition. First, it makes no sense to think that the laws of nature suddenly change abruptly so as to prevent the collision. If there is a law of nature that would transport the two rocks to opposite sides of the universe, then such a law would dictate from the outset that the two rocks cannot collide, contrary to the assumption of the present example. What makes no sense is to suppose that no such law exists only to abruptly come into existence just before the two rocks collide. Divine intervention is not an option because (i) divine intervention would require a divinity and Objectivists reject the existence of such; and (ii) even if we were to accept divinity, then it is the volitional act of a divine being that realizes the possibility that the rocks do not collide. The third possibility that the rocks opt out of the collision either makes no sense at all because rocks do not have the qualities required to make free choices or, if we are willing to entertain such a possibility, then we are forced to admit that free choice is the grounds or origin of possibility in the physical universe.

3) If we arrive at the conclusion that none of the possibilities entertained above presents a reasonable scenario that could prevent rocks A and B from colliding, then once we unfreeze the universe the two rocks *must* collide: it is *necessary* that they collide. For suppose that it is not necessary that the two rocks collide. Then it is possible that they do not collide. “But, then, what is the *source* or *origin* of such a possibility?” an Objectivist would ask. “What would *cause* such a possibility to be a feature of the situation?”; “You got to give me a causal story that explains this possibility” the Objectivist demands “a story that postulates some causal factor that exists at the moment we froze the universe so that it would account for the possibility that the two rocks do not collide once the universe is unfrozen. But we have already seen that no such causal story makes sense.”

4) My imagined Objectivist interlocutor demands that in order to postulate that the above situation does indeed feature the modal property of contingency or possibility of non-collision we must first provide a *causal account* of how this situation acquired this modal property: what could be the *causal origin* of such a modal property? And my Objectivist interlocutor rightly maintains that he has already ruled out the only three viable accounts that could offer such a causal story. Therefore, since no viable causal account of such a possibility remains on the table, the situation of the two rocks does not feature the modal property to the effect that the two rocks could avoid collision.

5) Now fast forward: human agents enter the scene (or any similarly situated creatures). Their appearance in the universe brings with it for the first time consciousness, intentional attitudes, and the ability to choose freely. These properties in turn cause human beings to produce volitional acts. Unlike my rocks A and B, human beings can act in a way that opts out from a collision; they can decide to collide with each other or other objects or not to do so. Now for the first time, the Objectivist maintains, we have a viable causal story that explains the origin of modal properties; i.e., that offers a cogent explanation of how a certain situation acquires its modal property of contingency or possibility. And this story invokes essentially volitional facts. Hence, volitional facts are prior to modal properties, since they are required to explain them.

6) I have tried above to the best of my abilities to explore the underlying rationale Objectivist have for their adherence to the twin theses. The rationale that emerges from the discussion is this. Objectivists demand that the modal properties of a given situation must be given a causal account: i.e., an account that explains the origin or source of the contingency or possibility property a fact is alleged to feature in terms of certain causally antecedent factors. Thus, if a certain situation features the modal property of being contingent or of “possibly being such-and-such”, then we better have an account as to how this situation acquired this modal property in causal terms. A causal account of this kind, an account of origin in causal terms, can be given once human volitional acts are present and are available to cite as the causal origin that introduced modal properties. But in the absence of volitional facts, there is simply nothing in the universe that can serve as an explanation of the origin of modal properties in causal terms.

7) The essential philosophical point that emerges here is that from an Objectivist point of view cause precedes contingency and possibility. And since the Objectivists maintain that the concept of causation is prior to modal concepts (including the concepts of contingency and possibility), they also think that the attribution of modal properties to a situation (i) must be justified; (ii) the justification must explain the origin or source of these properties; and (iii) the explanation of the origin or source of such modal properties must be given in causal terms.

8) Why do objectivists think that cause precedes contingency? I suspect that this thesis derives from a view Objectivists hold about the epistemology of concept formation. Objectivists hold that perception is central to the acquisition and formation of any concepts whatsoever. And the concept of cause is central to perception. Therefore, the concept of cause has epistemological priority over any modal concepts. Moreover, we acquire the concept of cause before we acquire any modal concepts: therefore, the concept of cause has temporal priority over modal concepts. Once we keep these Objectivist canons firmly in mind, it is quite natural that Objectivists find it so puzzling how one can be justified in attributing modal properties to a physical situation without explaining how the situation acquired these modal properties in causal terms. It is inconceivable, from this point of view that a physical situation should feature modal properties and no causal explanation is available as to how it acquired these modal properties. From this point of view, on its own and independently from our conception of it the world embodies only causal properties. Therefore, the origin of every other property we might wish to attribute to it must be explained in causal terms.

9) I think the above articulates the underlying philosophical rationale for the Objectivists’ stand about modal concepts. I, for one, reject every element of this philosophical picture. I also think that it is internally flawed. Objectivists maintain that existence precedes consciousness (at least according to HB) and it is for this reason that they insist that every mental event must be object directed and that there cannot be a free floating consciousness. But if existence precedes consciousness, then the properties of existence, including its modal properties, cannot depend upon any aspect of consciousness including the mechanisms involved in how consciousness acquires its contents or the epistemological or temporal priority of concept acquisition. Thus, whether existence features modal properties is a metaphysical question and cannot depend upon priorities that are fixed by epistemological matters.

10) I have briefly hinted at how the conversation might proceed from here on. The principal goal of this post, however, was to uncover the underlying rationale for the Objectivists’ adherence to the two theses noted above. A thorough critique of this rationale deserves a separate conversation.

peter

Bill: please forgive me for once again breaching your stricture on being pithy.

Bill, you said, "I am afraid you are not following the discussion. No one here ever said that -- to use a variant of Peter's example -- the tree in his backyard that has n leaves could have had n + 1 leaves had nothing else been different!"

I never thought so. I was talking about the meaning of certain kinds of statements, not the implications of those statements. From what you, Peter, and some others have said about modal statements, I just can't figure out how you are using some of them. I think in normal language (which you and Peter have both appealed to as part of your defense of these statements), there is always some implicit extra clause. But in your term-of-art usage, I can't figure out what that implicit extra clause should be. Any candidates that I can come up with seem to be disallowed by something else that you or Peter has said. I'll try to write up a critique this weekend to explain what I mean.

Response to David Brightly

In several posts DavidB and DaveG raised a concern about my argument in OFO and the present post (Volition and Modality) and challenged me to address this concern. In this post I shall take up his challenge.

1) I shall quote from one of DavidB’s posts because it clearly states this challenge. DavidB writes:

“Are there two uses of 'possible' in play here, one of which Randians would accept, and one that they would deny? …Like Dave G I suspect that the Rs hold to a strict determinism outside human volition which leaves no room for the possible. Anything other than what has happened/will happen is impossible. There is only one possible world, namely the actual one. But this leaves room for the first sense of 'possible', meaning 'allowed by the laws of physics'. So by their lights, if conditions in the spring were such that by the summer your tree would bear 17243 leaves, then it doesn't make sense that it might bear 17244. On the other hand, they would accept that if a wind of sufficient force were to arise then the rock would move, since that's allowed by the laws of physics. Your argument seems to be about nomological 'possibilities' of this kind, but I don't at the moment see their essentially modal nature, counterfactual or otherwise. I'm clearly missing something here. Could you expand a bit on this?”

1.1) DavidB’s concern is this. In OFO and the current post “Volition and Modality” I argued that the distinction Objectivists accept between natural vs. volitional facts logically presupposes the modal distinction between necessary vs. possible. Therefore, Objectivists cannot consistently deny the modal distinction while adhering to the existence of natural vs. volitional facts. DavidB raises the possibility that my argument here proves only that the existence of volitional and natural facts presupposes a version of the modal distinction Objectivists already accept. But, DavidB wonders whether my argument proves that the existence of natural vs. volitional facts presupposes the modal distinction the Objectivists reject. If it does not do so, then my argument fails to show that Objectivists are inconsistent.

1.2) In order to adequately answer DavidB’s concerns, it is best to carefully distinguish two pairs of notions of necessity and possibility. One pair is the distinction between *causally-necessary* vs. *causally possible*; these are the concepts Objectivists countenance. Suppose there is a unique set of physical laws L that governs every actual event in the universe. In addition, let us assume that for every given time t and event e, there is a unique set of initial conditions N such that L+N causally determine e uniquely. Call this causal determination *causal-necessity*: so L+N causally necessitate whether e occurs or does not occur and in this sense e (or its non-occurrence) is said to be causally-necessary. The occurrence of an event e is *causally-possible* just in case the non-occurrence of e is not causally-necessary. I shall refer to these two notions collectively as ‘Causal-Modalities’. Objectivists deny that the concept of causal-possibility applies outside the realm of the volitional.

1.3) The second pair of notions of necessary and possible are the modal notions Bill, myself, and a few others defended as indispensible. In order to distinguish these modal notions from the Causal-Modalities I shall follow a variant of Bill’s usage in several of his posts and designate them as ‘BL-necessary’ vs. ‘BL-possible’. We may define them as follows: a proposition is BL-necessary just in case it is true in every possible world; it is BL-possible just in case it is true in some possible worlds. For present purposes we may think of a *possible world* as a maximally consistent set of propositions. I shall refer to these two notions collectively as BL-Modalities. Objectivists reject BL-Modalities. They think that BL-Modalities are either reducible to the Causal-Modalities or that they are meaningless or that they are extensionally equivalent to the Causal-Modalities they countenance.

2) Now it is relatively easy to show that BL-Modalities are indispensible. Bill has shown that BL-Modalities are required outside the volitional realm in order to characterize the notions of validity of an argument, consistency, inconsistency, and other so-called logical concepts. Taking into account Bill’s arguments, we may also consider the following examples. It is *impossible* to build a table with a round and square surface simultaneously or to prove that 2 +2 = 5 or to prove the proposition “Snow is white and it is not the case that snow is white” (where the pertinent words mean what they usually mean). Now, what kind of modality is involved in these claims? We certainly do not mean to say simply that it is *causally-impossible* to build a table with a round and square surface or that it is *causally-impossible* to prove that 2 + 2=5 or to prove that “Snow is white and it is not the case that snow is white”. If I were to say that the alchemists’ goal to produce gold by mixing up various substances is *impossible* because gold is a fundamental element, then the pertinent notion of ‘impossibility’ is indeed a causal one. But in my examples above, we do not merely say that building a table that features a round and square surface is causally-impossible because such a thing is not “allowed by the laws of physics” (or chemistry). Rather, we are saying something much stronger. We are saying that regardless of what the laws of physics or chemistry are, it is logically or mathematically impossible to build a table that has a round and square surface or prove that 2+2=5 or that snow is white and it is not the case that snow is white. And what we mean here is that doing these things is BL-impossible. So BL-Modalities are indispensible and they are required in order to identify the logical boundaries of volitional acts.

3) What about my argument that the existence of volitional acts logically presupposes BL-modalities? DavidB suggests that perhaps my argument presupposes only Causal-Modalities. Could that be the case? I don’t think so.
3.1) DavidB invites us to accept on behalf of the Objectivists a deterministic conception of the world. Let us do that. Then he makes the following claims, again on behalf of the Objectivists, which I shall reproduce here:

(a) “Anything other than what has happened/will happen is impossible.” i.e., outside the volitional realm.

(b) “There is only one possible world, namely the actual one. But this leaves room for the first sense of 'possible', meaning 'allowed by the laws of physics'.”

(c) The Objectivists “would accept that if a wind of sufficient force were to arise then the rock would move, since that's allowed by the laws of physics.”

(d) My argument in OFO and in the current post “Volition and Modality”, “seems to be about nomological 'possibilities' of this kind, but I don't at the moment see their essentially modal nature, counterfactual or otherwise.”

3.2) Every one of DavidB’s claims (a)-(d) is seriously problematical upon careful inspection or turns out to be inconsistent with the other claims.

4) Consider (a): How should we interpret the modal term ‘impossible’ in (a)? Well, there are two possibilities.

4.1) DavidB might intend the term ‘impossible’ to belong to the category distinguished above as the Causal-Modality. In this case (a) means something like this: every event that actually happened/will happen is *causally-necessary* and an event that did not happen/will not happen is *causally-impossible*. But such an interpretation is compatible with the claim that even though an event e actually happened and, hence, it is causally-necessary, still the non-occurrence of e is BL-possible. Unless the Objectivists prove that BL-Modality is either reducible to Causal-Modality or incoherent or extensionally equivalent to the later, they cannot simply rule this possibility out. Moreover, as we have seen in the examples given in # (2) above: e.g., the table with a round and square surface and the other cases, we already need BL-Modality in order to say that making such a table is BL-impossible. So this interpretation of the term ‘impossible’ is not going to work here.

4.2) DavidB might intend the term ‘impossible’ in (a) to belong to the category of BL-Modality. Of course, such an interpretation is going to countenance BL-Modality, contrary to the Objectivists position which DavidB attempts to defend. Moreover, so interpreted (a) is clearly false. Therefore, DavidB’s claim (a) fails to support the Objectivist position. In fact, upon careful scrutiny it most likely refutes it.

5) Consider claim (b). The first sentence of (b) simply stipulates that there is only one possible world; namely, the actual one. Now, perhaps there is only one possible world and that world is the actual one. But, whether this is so requires an argument; such a claim cannot be established by means of a stipulation. And one way to offer an argument is to show that BL-modality is either reducible to Causal-Modality or that it is incoherent or that it is extensionally equivalent to the later. But DavidB and the Objectivists have not proven any of these things as yet and as argued in # (2) above, there is overwhelming evidence against dispensing with BL-Modality in any of these ways. Therefore, the first sentence of (b) is not established. But suppose we grant it for the moment so we can examine the second sentence of (b).

5.1) So we grant for the moment that there is only one possible world and that world is the actual world. The second sentence of (b) says something like this: the fact that there is only one possible world and that is the actual world “leaves room” for the “first sense of ‘possible’”; i.e., the sense clarified by the notion of “allowed by the laws of physics.” The notion of “allowed by the laws of physics” appears also in DavidB’s claim (c) in connection with my rock example. Now, my question is this: What does DavidB mean by the phrase ‘allowed by the laws of physics’? Surely the term ‘allowed’ is not equivalent here to ‘permissible’ in the moral or legal sense. What does it mean then? There are two possibilities to consider

5.1.2) First, one might entertain the thought that the term ‘allowed’ in the phrase ‘allowed by the laws of physics’ means that while an event e did not actually occur, its occurrence is nonetheless possible in the sense that it is *causally-possible*. But, now, how can that be? According to (a), if e did not actually happen, then it is *causally-impossible*. How can something be both causally-possible and causally-impossible at the same time? I don’t think DavidB intends to accept this result. So clearly the category of Causal-Modality is not the right category to be used in order to interpret the notion of ‘allowed by the laws of physics’.

5.1.3) Fortunately, another interpretation is available: X is *allowed* by the laws of physics means that the occurrence of x is *consistent* with the laws of physics alone (i.e., without the initial conditions). Now we can make sense of what DavidB intends to say in his claim (b). The fact that there is only one possible world and everything that occurs in it is causally-necessary “leaves room” for (read “is consistent”) with the thought that some non-occurring event is nonetheless *possible* because we can recast this thought by saying that despite the fact that an event e did not actually occur, it’s occurrence nonetheless is *consistent* with the laws of physics that govern the actual world (minus the initial conditions). Splendid!

5.1.4) Except that now we must ask the following question: In what sense is the non-occurrence of an event in the only world that exists is said to be *consistent* with the laws of physics in that world? Surely the sense of ‘consistent’ here cannot mean “causally-possible* because since the event in question did not actually occur, by the Objectivists lights its non-occurrence is causally-necessary and, hence, it is not *causally-possible*. The only other sense that we can give to this notion is that despite the fact that the event in question did not actually occur and, therefore, its non-occurrence is causally-necessary, the proposition that such an event occurs is *logically consistent* with the laws of physics (alone, minus initial conditions). But, such an interpretation, the only one that makes sense of DavidB’s claim (b), must face Bill’s argument that the notion of logical consistency belongs to the category of BL-Modality. Therefore, if Bill is right, then DavidB’s claim (b) presupposes the category of BL-Modality and with it the notions of BL-possibility and BL-necessity.

6) I think the above considerations apply to claims (c) and (d) as well. However, I do wish to expound a bit on claim (d). As noted above, the notion of ‘nomological possibility’ presupposes the notion of BL-possibility and, therefore, the notions of BL-Modality. The overall picture is this. Assuming determinism, the laws of physics together with a complete specification of initial conditions causally-necessitate natural events. Nevertheless, we frequently want to, and occasionally must, acknowledge that certain events could have been otherwise. What do we mean when we acknowledge this fact? Well, the above analysis suggests that what we mean is that if some of the relevant initial conditions were different, then the following situation is consistent with the laws of physics and some alternative initial conditions; namely, the event that actually occurred would not have occurred and some other event would have occurred instead. And this complicated statement can be rephrased by saying that something other than what actually occurred could have occurred because there is a possible world other than the actual world in which the actual laws of physics are true, some of the initial conditions are altered, and the event that did not occur in the actual world occurs in this possible world. I maintain that something like this is logically entailed by the existence of volitional facts and I have argued this in OFO and in “Volition and Modality”. The above discussion shows, I think, that DavidB’s objections did not refute this argument. If anything, they reinforced it as well as Bill’s corresponding arguments regarding validity, consistency, etc.

peter

Good work, Peter. I wonder if it will convince David B.

Bill,

Thanks.

I wonder first whether he will be able to read all of it before the end of the year.

peter

OK, a couple of preliminary points: my issue over “types of modal propositions” is not at all the same as the one Peter addresses above in his response to David B. I was not concerned about “types of necessity” but about differing syntactic forms of modal propositions. Specifically, the only form of modal proposition that I've seen Randians object to in this discussion is those of a form similar to “x might have been p” where p is a predicate that did not (at the time under consideration) apply to x. I have yet to see a Randian object to a proper counterfactual, by which I mean a proposition of a form similar to “if P had been true then Q” where P was false at the time under consideration (I believe that this is the normal definition of “counterfactual” in philosophy, please correct me if I'm wrong). Peter says that Rand rejects all modal propositions, and I'll take his word for it, but this could just mean that the Randians in this discussion are not defending Rand's position --the position that Peter is opposing-- and so the discussion is at cross purposes.

However, the larger issue is that I'm having a hard time getting a coherent sense from the way that Peter, Bill and a few others are using propositions of the form “x might have been p” where p did not apply to x at the time under discussion. For brevity, I refer to such propositions as antifactuals. Since my confusion stems from a gestalt of statements involving modal propositions and antifactuals by Peter, Bill, et al, it's possible that the real issue is just that Peter, Bill, et al have slightly contrasting views of these issues and so the gestalt that I have picked up is inconsistent even though each of their positions taken alone would be consistent.

In normal speech when someone utters an antifactual like “I am blogging right now but I could have been running”, there is an implicit condition such as “if I could find my running shoes” or “if it were not raining” which depends on the context. In other words, they mean “I had a choice”. This is not what Peter, Bill, et al mean in their use of “possible”; they mean something more fundamental than the existence of human volition. I have been trying to figure out what their implicit condition is.

Peter has, I believe, said explicitly that he means that it was logically or mathematically possible. But this conflicts with some examples that Peter, Bill, et al. have given such as “... it is possible for me to kick the ball, given certain facts etc. By contrast, it is not possible for me to turn myself into a ball or a bullet or fly without any mechanical devices like birds can.” (from Peter's guest post, “One Fallacy of Objectivism”). Clearly, there is no logical or mathematical barrier to Peter turning himself into a ball --the only thing that stands in his way is physics (but Peter, Bill, et al. have also said that physical laws could possibly have been different, which makes examples of this sort even more confusing).

Another reason that I can't believe Peter, Bill, et al really intend the “logical and mathematical possibility” interpretation is that it doesn't seem to add anything interesting to philosophy once you already have “a priori”. Why not just say that “the fact that I would be blogging now rather than running was not true a priori?”

Yet another reason to reject this interpretation is that Bill has several times asserted that if God exists, then he exists necessarily. But I don't think that Bill means that if God exists, then it can be proven logically or mathematically.

So, what are the truth conditions of an antifactual such as

(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 some candidates:

(1) if the history of the tree had been different then ...
(2) if the laws of physics had been different then ...
(3) there exists a set of propositions S that were true at times before t such that, had each member of S been false, then given the truth of the various laws of physics and biology, an omniscient being could infer that the number of leaves would be 17,244 at time t.
(4) there exists a set of propositions S that were true at times before t such that, had each member of S been false, then given the truth of the various laws of physics and biology, I can infer by my normal power of reasoning and prediction that the number of leaves would be 17,244 at time t.

The problem with all of these candidates is that I don't think you can really know that any of them is true, but Peter, Bill et al. seem to be committed to the proposition that humans can know the truth of antifactuals. I can't come up with anything that humans could know the truth of short of the fact that (A) is not ruled out by mathematics or logic. But I've already discussed the problems with that interpretation. So that's what I mean when I say that I suspect that antifactuals, when used in a philosophical sense as Peter, Bill, et al use them are incoherent. I cannot figure out what the truth conditions of such propositions are. I can come up with several candidates, but none of them seems to be consistent with the usage and with what Peter, Bill, et al have said about modal propositions.

Sorry about the "Doc Rampage" signature above. When I type the first "D" in the box, Firefox gives me a list of choices and I selected "Doc Rampage" instead of my name by accident.

"I wonder first whether he will be able to read all of it before the end of the year."

Possibly not. We have the electricians in...

Sorry DavidB,

I was inspired by all of this grim argument about the non-existence of the set of all truths; so I was trying to prove the contrary by enumeration... until I realized that it is best to let Grim state his conclusion to the effect that for every set x, it is not the case that x = ?.

peter

Hello Peter,

Thank you for making sense of my vaguely worded reservations. Much appreciated. The critical paragraphs are 5.1.3 and 5.1.4, I think, where you introduce the notion of an event being 'consistent with the laws of physics' as exegesis of my 'allowed by the laws of physics'. Let me expand a little on how I understand this.

First, what I think we mean here by an 'event' is a transition from one state to another, perhaps relatively close together in time. For example, the event of a flying brick breaking a window is a transition from a state with brick moving towards window, window intact (S1 at t1, say) to a state with brick on far side of window frame, glass in shards on ground (S2 at t2, say). In classical mechanics, the laws of physics take the form of a set of differential equations L relating the positions and momenta of material particles and their time derivatives. For a wide class of equations it can be shown that there is a unique solution S(t) expressing the particle positions and momenta as functions of time which satisfies the equations L and is such that S(t1)=S1. Usually there is a whole family of solutions each of which satisfies the equations L. The requirement that S(t1)=S1 then picks out a unique member of this family, S. Only if there is a solution S such that S(t1)=S1 and S(t2)=S2 would we say that the specific event E is consistent with the laws of physics. There is no commitment as to whether states S1 and S2 ever arise. Consistency of an event with the laws of physics thus translates into an existence assertion over some domain of differentiable functions.

My quibble with para 5.1.4 is that we seem to move from 'event consistent with the laws of physics' to 'event *logically consistent* with the laws of physics.' At present I'm content with the above explication and see no need further to translate it into a consistency assertion over some set of propositions. Also, I have no idea how this might be done!

Could I also comment on something you say in para 6?

"Well, the above analysis suggests that what we mean is that if some of the relevant initial conditions were different, then the following situation is consistent with the laws of physics and some alternative initial conditions; namely, the event that actually occurred would not have occurred and some other event would have occurred instead. And this complicated statement can be rephrased by saying that something other than what actually occurred could have occurred because ***there is a possible world other than the actual world in which the actual laws of physics are true, some of the initial conditions are altered, and the event that did not occur in the actual world occurs in this possible world. ***" [my emphasis]

The words following 'because' seem to be an explanation of what we mean by 'possible event'. My feeling is that this explanation fails because it merely transfers 'possible' from 'event' to world'; it doesn't explicate 'possible' in any more fundamental way, preferring to rely on our intuitive understanding.

I'm in a similar position with 'possible event' as I am with validity of argument form. I think (and hope to have shown) that there is an adequate account of each concept that stops a long way short of full-blown modality. But this is not to say that an account in modal terms can't be given.

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