Category: Modal Matters

Volition and Modality (Peter Lupu)

 This is a guest post by Peter Lupu. Minor editing by BV.

1) In One Fallacy of Objectivism (henceforth, OFO) I gave an argument that a distinction Objectivists insist upon between “metaphysical” or natural-facts vs. volitional-facts logically presupposes the traditional modal distinction between contingent vs. necessary – a logical presupposition they vehemently deny. Three kinds of objections were presented against my argument. The first kind challenged my argument by questioning the sense in which the distinction between natural vs. volitional facts logically presupposes the modal distinction. The second kind of objection alleges that since the contingent and the possible are the offspring of human volitional action, they cannot possibly exist antecedently to and independently from the sphere of human volition. The third kind of objection maintains that a certain Objectivist theory about concept acquisition and concept formation refutes my argument. I shall ignore here objections that belong to this last category because they deserve a separate treatment. So I shall focus exclusively on the first two objections.


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Further Modal Concepts: Consistency, Inconsistency, Contradictoriness, and Entailment

I argued earlier that the validity of argument forms is a modal concept.  But the same goes for consistency, inconsistency, contradictoriness, and entailment.  Here are some definitions. 'Poss' abbreviates 'It is broadly-logically possible that ___.' 'Nec' abbreviates 'It is broadly-logically necessary that ___.' '~' and '&' are the familiar truth-functional connectives. 'BL' abbreviates 'broadly logically.'

D1. A pair of propositions p, q is BL-consistent =df Poss(p & q).

Clearly, any two true propositions are consistent. (By 'consistent' I mean consistent with each other.  If I mean self-consistent, I'll say that.)   But there is more to consistency that this.  It is a modal notion.  Consistency cannot be defined in terms of what is actually the case.  One must also consider what could have been the case.  As long as p, q are contingent, they are consistent regardless of their truth-values. If both are true, they are consistent.  If both are false, they are consistent.  If one is true and the other false, or vice versa, they are consistent.

D2. A pair of propositions, p, q, are BL-inconsistent =df ~Poss(p & q).

D3. A pair of propositions p, q are BL-contradictory =df ~Poss(p & q) & ~Poss (~p & ~q).

Note the difference between inconsistency and the stronger notion of contradictoriness.  If two propositions are inconsistent, then they logically cannot both be true.  If two propositions are contradictory, then they are inconsistent but also such that their negations logically cannot be true.

Example. All men are rich and No men are rich are inconsistent in that they cannot both be true.  But they are not contradictory since their negations (Some men are not rich, Some men are rich) are both true.  All men are rich and Some men are not rich are contradictory.  Some men are rich, Some men are not rich are neither inconsistent nor contradictory.

D4. P entails q =df ~Poss(p & ~q).

Entailment, also called strict implication,  is the necessitation of material implication.  If '–>' stands for the material conditional, then the right hand side of (D4) can be put as follows: Nec (p –> q).

(Alethic) modal logic's task is to provide criteria for the evaluation of arguments whose validity or lack thereof depends crucially on such words as 'possibly' and 'necessarily.'  But if I am right, many indispensable concepts of nonmodal logic (e.g., standard first-order predicate logic with identity) are modal concepts. 

 

 

The Difference Between Possibility and Contingency

Over lunch yesterday, Peter Lupu questioned my assertion that possibility and contingency are not the same.  What chutzpah! So let me now try to prove to him that they are indeed not the same, though they are of course related.  To put the point as simply and directly as I can, possibility and contingency are not the same because every necessary proposition is possible, but no necessary proposition is contingent.  Perhaps this requires a bit of explanation.

We first divide all propositions into two mutually exclusive and jointly exhaustive groups, the noncontingent and the contingent.  The first group subdivides into two mutually exclusive and jointly exhaustive subgroups, the necessary and the impossible.  A proposition is necessary (impossible) just in case it is true in every (no) possible world.  A proposition is possible just in case it is true in some possible worlds.  It follows that if proposition p is necessary, then p is possible, but not conversely.

Since we know that there are necessary propositions, and since we know that every necessary proposition is a possible proposition, we know that there are necessary propositions which are possible.  But we also know that no necessary proposition is contingent.  It follows that we know that there are possible propositions that are not contingent.  It follows that the extension of 'possible proposition' is different from the extension of 'contingent proposition.'  This suffices to show that possibility and contingency are not the same.  Here are some definitions.  I have included definitions not fomulated  in the imagery of possible worlds for those who are 'spooked' by his imagery.

A proposition p is possible =df there is a possible world in which p is true.

A proposition p is possible  =df it is not necessary that p be false.

A proposition p is contingent =df there is a possible world in which p is true and there is a possible world in which p is false.

A proposition p is contingent =df p is both possibly true and possibly false.

Example.  No color is a sound is possible but not contingent.  There is a possible world in which it is true, but no possible world in which it is false.  Tom's favorite shirt is red is contingent.  There is a possible world in which it is true and a possible world in which it is false.

UPDATE (21 February): David Brightly provides a very useful map of the modal terrain in the Comments.

 

Validity as a Modal Concept and a Modal Argument for the Nonexistence of God

'Modally Challenged' comments:

I've run into this argument on several occasions and while the author(s) insist theists will accept the premises, it's more the validity I'd appreciate your take on.

1) If God is possible, then God is a necessary being.
2) If God is a necessary being, then unjustified evil is impossible.
3) Unjustified evil is possible.
Therefore, God is not possible.

In this post I explain the distinction between validity and soundness, explain why validity is a modal concept, and then use this fact to show that the modal distinction between the necessary and the contingent applies outside the sphere of human volition, contrary to what followers of Ayn Rand maintain.  Finally, I demonstrate the validity of the above atheist argument.

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Necessity and Contingency Within the Sphere Not Affected by Human Volition

Harry Binswanger asks: ". . . within the sphere not affected by human volition (the "metaphysically given") what are the grounds for asserting a difference between necessity and contingency? Aren't all the events that proceed in accordance with physical law in the same boat?"

This is large topic with several aspects.  This post concentrates just one of them.

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Putting My Contingency Into English: Are There Legitimate Non-Epistemic Uses of ‘Might’?

I exist now.  But my nonexistence now is possible. ('Now' picks out the same time in both of its occurrences.) 'Possible' in my second sentence is not intended epistemically.  Surely it would be absurd were I to say, 'My nonexistence now is possible for all I know' or 'My nonexistence now is not ruled out by what I now know or believe.'  If I am certain of anything, I am certain that I exist, and that rules out my present nonexistence. So in the second sentence above 'possible' is to be taken non-epistemically.  The metaphysical point is that I am a contingent being.  But how put this into ordinary English?

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One Fallacy of Objectivism

The following comment is by Peter Lupu. It deserves to be brought up from the nether reaches of the ComBox to the top of the page. Minor editing and highlighting in red by BV.

One Fallacy of Objectivism

1) Objectivists seem to hold two theses:

Thesis A: There is a fundamental conceptual distinction everyone does or ought to accept between “metaphysical facts” vs. “volitional or man-made facts”; for the sake of brevity of exposition I shall occasionally refer to this distinction as the ‘Randian distinction’.

Thesis B: The content of the traditional philosophical distinction between contingent vs. necessary facts is either reducible to the Randian distinction or to the extent it is not so reducible it is conceptually incoherent, superfluous, or cannot be clearly demarcated; for the sake of brevity I shall occasionally refer to the distinction between contingent (and possible) vs. necessary facts as the ‘Modal distinction’.

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Modalities of Sin

Horace Jeffery Hodges asked me to comment on his post Divine Sovereignty and Human Freedom.  Inasmuch as such commentary would require exegetical skills I do not possess, not to mention time I do not have — I am under the gun to finish an article for The Monist — I shall have to beg off.  Perhaps others can join in the discussion at Jeff's place.  But given my longstanding interest in matters modal, I was intrigued by the following quotation from Thomas Boston, courtesy of David C. Innes:

State of Innocence – posse peccare (able to sin)
State of Sin – non posse non peccare (not able not to sin)
State of Grace – posse non peccare (able not to sin)
State of Glory – non posse peccare (not able to sin)

Imaginable, Conceivable, Possible: How Justify Modal Beliefs?

Crumb_selfportrait As I use them, 'imaginable' and 'conceivable'  mean the following. Bear in mind that there is an element of stipulation and regimentation in what I am about to say.  Bear in mind also that the following thoughts are tentative and exploratory, not to mention fragmentary.  The topics are difficult and in any case this is only a weblog, a sort of online notebook.

To imagine X is to form a mental image of X.   To imagine a two-headed cat is to form a mental image of (more cautiously: as of) a two-headed cat.  To say that X is imaginable is to say that someone has the ability to imagine it. To envisage is to visually imagine. Not all imagining is visual.

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Back to Parmenides: Binswanger’s Defense of Rand’s Block Universe

In response to Harry Binswanger, I wrote:

My diagnosis of our disagreement is as follows. You think that what is causally necessitated (e.g. the lunar craters) is broadly-logically necessary (BL-necessary) whereas I think that what is causally necessitated is broadly-logically contingent. Because you think that what is causally necessitated is BL-necessary, you naturally think that my having my hat on is not causally necessitated. If I've understood you correctly, you do not deny that there are BL-contingent events, an example being my freely choosing to put on my hat. What you deny is that there are any BL-contingent events in nature (the realm of the non-man-made).

Your scheme makes sense if (i) time is [metrically] infinite in the past direction; (ii) nature always existed; (iii) nature exists of BL-necessity (also known in the trade as metaphysical necessity) and nothing about nature is BL-contingent. On these assumptions, every event is BL-necessary. Add to that the assumption that every event in nature is causally determined, and we get the extensional equivalence of the causally necessitated and the BL-necessary. Man-made facts, which you grant are BL-contingent, are not causally necessitated because, for you, X is causally necessitated if and only if X is BL-necessary.

If the foregoing expresses your view, then I think I have isolated the source of our disagreement: we disagree over (iii). I see no reason to accept it. Do you have an argument?

Binswanger responded:

Your "diagnosis" is correct in spirit. I have quarrels over formulation, but there's no need to discuss them here. So we disagree about (iii): the existence of nature is logically necessary and nothing about nature is logically contingent.

You ask for an argument for that. Well, the first part is axiomatic: "existence exists." What makes that logically necessary? The fact that "existence doesn't exist" is a contradiction. "What is, is; what is not, is not" Parmenides wisely said.

The second part is non-axiomatic, and derives from causality. Objectivism holds that causality is the application of the law of identity to action. Things do what they do because they are what they are. For the fragile to act as non-fragile would be the same kind of contradiction as for glass to be not glass. This view of causality rejects the Humean event-to-event idea of causation (which actually originated with Telesio, I believe). We go back to the pre-Renaissance (broadly Greek) view of causation as a relation between entities and their actions.


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Epistemic/Doxastic Possibility

Recent forays into the metaphysics and epistemology of modality require us to be quite clear about the senses  of 'possible,'  necessary,'  and the other modal words in play.  In the contexts mentioned, these words are not being used epistemically or doxastically. 

Is Joan in her office? If I ask you, you might reply, "It's possible." Or if I ask you, "Is Zorn's Lemma logically independent of the Axiom of Choice" you might reply, "It's possible." We need to clarify these uses of 'possible.'

From Possibilities to Possible Worlds

1. One cannot do modal logic, let alone modal metaphysics, without both modal concepts and  'modal intuitions.' One has to start from a pre-thematic understanding of modal concepts such as possibility and necessity and how they are interrelated and also from certain prior convictions about what counts as possible and  necessary. (The same is true in other disciplines such as ethics: if you don't grasp the distinctions and interconnections among the permissible, the impermissible, the obligatory, and the supererogatory, and have some reasonably firm intuitions about what particular actions and ommissions fall under these categories, then there is no point in doing ethics.)

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Is the Existence of God Entailed by Alternative Ways Natural Things Might Have Been?

This post is a sequel to Ayn Rand on Necessity, Contingency, and Dispositions.  There we were examining this quotation:

What do you mean by "necessity"? By "necessity," we mean that things are a certain way and had to be.  I would maintain that the statement "Things are," when referring to non-man-made occurrences, is the synonym of "They had to be."  Because unless we start with the premise of an arbitrary God who creates nature, what is had to be. (IOE, 2nd ed., p. 299)

Rand's argument may be set forth as follows:

1. If there are alternative ways non-man-made things might have been, then an arbitrary (free) God exists.

2. It is not the case that an arbitrary (free) God exists. Ergo,

3. There are no alternative ways non-man-made things might have been.

I rigged the argument so that it is valid in point of logical form: the conclusion follows from the premises.  But are the premises true?  A more tractable question: Do we have good reason to accept them?

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Notes on Van Inwagen on Modal Epistemology

Herewith, some interpretive notes and critical comments on Peter van Inwagen's paper, "Modal Epistemology" (Philosopical Studies 92 (1998), pp. 67-84; reprinted in van Inwagen, Ontology, Identity, and Modality, Cambridge UP, 2001, pp. 243-258.)

1. Van Inwagen describes his position as "modal scepticism" (245) but a better name for it would be 'mitigated modal scepticism' since he does admit that we have modal knowledge: "I think we do know a lot of modal propositions . . . ." (245)

Harry Binswanger Defends Rand

I thank Dr. Binswanger for commenting on the post, Modal Confusion in Rand/Peikoff.  His  stimulating comments deserve to be brought to the top of the page.  I have reproduced them verbatim below.  I have intercalated my responses  in blue.  The ComBox is open, but the usual rules apply: be civil, address what is actually said, argue your points, etc. 

…………………..

As an actual Objectivist philosopher, let me attempt to address Bill's critique of Peikoff's article.

First, there's a significant typo in the first line of his reproduction of Peikoff's last paragraph. Peikoff did *not* write: "Truth is the identification of a fact WITH reality." (As someone pointed out, that is nonsensical.) The actual sentence is: "Truth is identification of a fact OF reality." (emphasis added by me)

(For the merely connotative difference between "fact" and "fact of reality," see _Introduction to Objectivist Epistemology_, p. 243).

BV: Guilty as charged. I apologize for the unintentional typographical error.

Now on to the main point. The Objectivist position is twofold:

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