Author: Bill Vallicella

Does Potential Infinity Presuppose Actual Infinity?

Returning to a discussion we were having back in August of 2010, I want to see if I can get Peter Lupu to agree with me on one point:  It is not obvious or compellingly arguable (arguable in a 'knock-down' way) that there are infinite sets.  Given my aporetic concerns, which Peter thoroughly understands, I will be satisfied if I can convince him that the italicized sentence is true, and therefore that the thesis that the infinite in mathematics is potential only is respectable and defensible and has never been shown definitively to be false. Let us start with a datanic claim that no one can reasonably deny:

1. There are infinitely many natural numbers.

If anyone were to deny (1) I would show him the door.  For anyone who denied (1) would show by his denial that he did not grasp the sense of 'natural number.'  The question, however, is whether from (1) we can validly infer

2. There is a set of natural numbers.

If there is such a set, then of course it is an infinite set, an actually infinite set.  (Talk of potentially infinite sets is nonsense as I have argued in previous posts.)  So, if the inference from (1) to (2) is valid, we have a knock-down proof of actual infinity.  For if there are infinite sets then there are actual infinities, completed infinities. 

Now I claim that it is obvious that (2) does not follow from (1).  For it might be that the naturals do not form a set.  A set is a one-over-many, a definite single object distinct from each of its members and from all of them.  It should be obvious, then, that from the fact that there ARE many Fs it does not straightaway follow that there IS a single thing comprising these many Fs.  This is especially clear in the case of infinitely many Fs.

But from Logic 101 we know that an invalid argument can have a true conclusion.  So, despite the fact that (2) does not follow from (1), it might still be the case that (2) is true.  I might be challenged to say what (1) could mean if it does not entail (2).  Well, I can say that  however many numbers we have counted, we can count more.  If we have counted up to n, we can add 1 and arrive at n + 1.  The procedure is obviously indefinitely iterable.  That means: there is no definite n such one can perform the procedure only n times.  One can perform it indefinitely many times.  Accordingly, 'infinitely many' behaves differently than 'finitely many.'  If something can be done only finitely many times, then there is some finite n such that n is the number of times the thing can be done.  But 'infinitely many' does not require us to say that that there is some definite transfinite cardinal which is the number of times a thing that can be done infinitely many times can be done.  For 'infinitely many' can be construed to mean: indefinitely many.

On this approach, the naturals do not form a single complete object, the set N, but are such that their infinity is an endless task.  The German language allows a cute way of putting this:  Die Zahlen sind nicht gegeben, sondern aufgegeben.  In Aristotelian terms, the infinity of the naturals is potential not actual.  But if you find these words confusing, as Peter does, they can be avoided.  A wise man never gets hung up on words.

Now if I understood him aright, one of Peter's objections is that the approach I am sketching implies that there is a last number, one than which there is no greater.  But it has no such implication.  For the very sense of 'natural number' rules out there being a last number, and this sense is  understood by all parties to the dispute. There cannot be a last number precisely because of the very meaning of 'number.'  Every natural number is such that it has an immediate successor.  But from this it does not follow that there is a set of natural numbers.  For 'has an immediate successor' needn't be taken to mean that each number has now a successor; it can be taken to mean that each number at which we have arrived by computation is such that an immediate successor can be computed by adding 1.

But Peter has a stronger objection, one that I admit  has force.  His objection in nuce is that potential infinity presupposes actual infinity.  Peter points out that my explanation of what it means to say that the naturals are potentially infinite makes use of words like 'can.'  Thus above I said, "however many numbers we have counted, we can count more."  This 'can' refers either to the abilities of men or machines or else it refers to abstract possibilities of counting not tied to the powers of men or machines.

Consider the second idea, the more challenging of the two.  Suppose the universe ceases to exist at a time t right after some huge but finite n has been computed.  Now n cannot be the last number for the simple reason that there cannot be a last number.  This 'cannot' is grounded in the very sense of 'natural number.'  So it must be possible that 1 be added to n to generate its successor.  And it must be possible that 1 be added to n + 1 to generate its successor, and so on.  So Peter could say to me, "Look, you have gotten rid of an actual infinity of numbers but at the expense of introducing an actual infinity of unrealized possibilities of adding 1: the possibility P1 of adding 1 to n; the possibility P2 of adding 1 to n + 1, etc."

The objection is not compelling.  For I can maintain that the unrealized possibilities P1, P2, . . . Pn, . . . all 'telescope,' i.e., collapse into one generic possibility of adding 1.  P1 is the possibility of adding 1 to n and P2 is the possibility of adding 1 to the last number computed just before the universe ceases to exist.

What I'm proposing is that  'Every natural number has an immediate successor'  is true solely in virtue of the sense or meaning of  'natural number.'  Its being true does not require that there be, stored up in Plato's Heaven, a completed actual infinity of naturals, a set of same.  Since I have decidedly Platonic sympathies, I would welcome a refutation of this proposal.

The Christian ‘Anatta Doctrine’ of Lorenzo Scupoli

Buddhism and Christianity both enjoin self-denial. But Buddhism is more radical in that it connects self-denial with denial of the very existence of the self, whereas Christianity in its orthodox versions   presupposes the existence of the self: Christian self-purification falls short of self-elimination. Nevertheless, there are points of comparison between the 'No Self' doctrine of Buddhism and the   Christian doctrine of the self.

In his Combattimento Spirituale (1589), Lorenzo Scupoli writes:

     You my mind, are not mine: you were given me by God. Neither are
     the powers active within me — will, with its energy – mine. Nor
     does my feeling, my ability to enjoy life and all my surroundings
     belong to me. My body with all its functions and requirements,
     which determine our physical well-being, is not mine either….And
     I myself belong not to me, but to God. (Unseen Warfare, St. Vladimir's Seminary Press, 1995, p.   172)

Apart from the references to God, this meditation of Scupoli, of which the above is merely an excerpt, bears a striking resemblance to the one contained in the Anattalakkhana Sutta. Buddha there examines each of the khandas, body, feeling, perception, etc., and concludes with respect to each of them that "This is not mine. This is not my self. This is not what I am." In Scupoli we encounter virtually the   same litany: body, feeling, mind . . . of all of which it is true that "This is not mine, etc." Of course, nothing depends on the exact taxonomy of personality-constituents. The point is that however one classifies the constituents of personality, no one of them, nor any combination of them, is veridically identifiable as one's very self. I say 'veridically,' since we do as a matter of fact (falsely) identify   ourselves with all manner of item both within us (feelings, memories, etc.) and without us (property, progeny, etc.) But these false self-identifications are part of what our ignorance/sinfullness consists in.

Thus Scupoli (who I take to be a representative Christian, and who is of interest here only as such) and Buddha agree with respect to the (negative) thesis that nothing in one's experience is veridically identifiable as one's very self. Thus nothing that we ordinarily take to be ourselves (our bodies, our thoughts, feelings, memories, etc.)  can in truth be one's self. But there is also similarity in their reasoning. One way Buddha reasons is as follows. If x (body, feeling, perception, etc.) were my very self, or were something that belonged to me, then I would have complete control over x. But it is evident that no x is such that I have complete control over x. Therefore, no x is either my self or anything that belongs to me. This could be called the 'complete control' argument. Scupoli has something similar:
     Let us remember that we can boast only of something which is a
     direct result of our own will and is done by us independently of
     anything else. But look how our actions proceed. How do they begin?
     Certain circumstances come together and lead to one action or
     another; or a thought comes to our mind to do something, and we do
     it. But the concurrence of circumstances does not come from us;
     nor, obviously, is the thought to do something our own; somebody
     suggests it. Thus, in such cases, the origin or birth of the
     thought to do something cannot or should not be an object of
     self-praise. Yet how many actions are of this kind? If we examine
     them conscientiously, we shall find that they almost all start in
     this way. So we have nothing to boast of. (174)

This passage suggests the following argument: One cannot justifiably take pride in anything (an action, a physical or mental attribute, etc.) unless one originates it 'independently of anything else.' But   nothing is such that one originates it in sublime independence of all else. Therefore, one cannot justifiably take pride in anything.

But does this amount to an argument against the self? It does, given the Buddhist assumption, crucial to the reasoning in the Anattalakkhana Sutta, that a self is an entity that has complete control over itself. Such a self could justifiably take pride in its actions and attributes. For it would be their fons et origo. So if one cannot justifiably take pride in any of one's actions or attributes, then one is not a self. Pride is one of the seven deadly sins  precisely because the proud person arrogates to himself a status he lacks, namely, the status of being a self in the sense in which this term is employed in the Anattalakkhana Sutta.

In sum, both Buddha and Scupoli are claiming that no one of us is a self for the reason than no one of us is in complete control of any of his actions or attributes. No one of the things which one normally takes to be oneself or to belong to oneself (e.g., one's body, habits, brave decisions, brilliant insights, etc.) is such that one has originated it autonomously and independently.

The main difference between Buddha and Scupoli, of course, is that the latter maintains that God gives us what we do not have under our control. Thus for Scupoli, what we do not have from ourselves, we have from another, and so have. But for Buddha, what we do not have from ourselves, we do not have at all.

“I Swear, If You Existed, I’d Divorce You.”

If the recipient of this insult had been a philosophy professor instead of a mere history  professor, he might have responded as follows.  "Darling, by the Existence Symmetry of Relations, if a relation R holds, then either all of its relata exist or none of them do. Now one cannot divorce a person to whom one is not married.  So you and I stand in the marital relation.  It follows that if I don't exist, then you don't either."

‘Celebrating’ the First Anniversary of ObamaCare

There is a caucus of GOP physicians in the House of Representatives.  Here they reflect on ObamaCare's first year.  It's good that there are M.D.s in the Congress.  Negatively, physicians are not lawyers.  Positively, they are scientifically trained without being mere theoreticians: they diagnose, they cut, they sew.  They are the plumbers and the auto mechanics of the human body.  They grapple at close quarters with recalcitrant matter.  They don't just talk, write, and argue.  Not that the latter aren't important; they are.  But balance is also important.

We need more doctors, engineers, and businessmen in government — and fewer lawyers.  And a few working stiffs, too.  There are truck drivers and pipe fitters who could do the job.  How can a government top-heavy with lawyers be representative of the folks?

Overextended Abroad, Collapsing Within

I fear for my country.  Will it go the way of the Roman Empire?  With a 14 trillion dollar national debt, we are in dire fiscal straits.  So what does Obama the Irresponsible do?  He works to socialize medicine here while expending more blood and treasure over there.  The man is a disaster.  His domestic and foreign policies are incoherent.  Here.

Scientistic Nonsense in the NYT Sunday Book Review

The review begins:

The universe, the 18th-century mathematician and philosopher Jean Le Rond d’Alembert said, “would only be one fact and one great truth for whoever knew how to embrace it from a single point of view.” James Gleick has such a perspective, and signals it in the first word of the title of his new book, “The Information,” using the definite article we usually reserve for totalities like the universe, the ether — and the Internet. Information, he argues, is more than just the contents of our overflowing libraries and Web servers. It is “the blood and the fuel, the vital principle” of the world. Human consciousness, society, life on earth, the cosmos — it’s bits all the way down.

At his point I stopped reading.  A bit is a binary digit.  So my love for my wife is binary digits all the way down?  That's nonsense, and beneath refutation.  An appropriate response would be, "Get out of here, and take your scientistic Unsinn with you."  A more charitable response: "Please come into my office and lie down on the couch.  We need to talk."  Some need therapy, not refutation.

See the Scientism category for rather more patient unmaskings of this sort of rubbish.

Blackman Versus Butchvarov: Objects, Entities, and Modes of Existence

(UPDATE: 23 March.  Butchvarov sent me some comments via e-mail the main ones of  which I insert in the text in red.)

This post assumes familiarity with Panayot Butchvarov's "protometaphysics," as he calls it.  But I will begin by sketching the distinction between objects and entities.  Then I will present an objection that occurred to me and Larry Lee Blackman independently.  That will be followed by a response that Butchvarov could make to the objection.  Finally, I will try to show that Blackman's objection, despite his disclaimers, commits him to a doctrine of modes of existence, but that this is not the bad thing he thinks it is.  This post ties in with our earlier explorations of the modes-of-existence doctrine which is dogmatically denied by a majority of analytic philosophers.  (These earlier posts are collected in the Existence category.)  There is also an obvious tie-in with earlier posts on Intentionality.

I. Entities and Objects

Entities exist while objects may or may not exist. Some objects exist and some do not. When one imagines Santa Claus or hallucinates a pink rat, an object appears, an object that doesn’t exist. When one perceives his hand, an object appears too, one that exists. The difference between an object that exists and one that does not is explicated by Butchvarov in terms of indefinite identifiability: An object exists if and only if it is indefinitely identifiable with other objects. The domain of objects is logically prior to the domain of entities. The application of the concepts of identity and existence to the domain of objects results in a "conceptual transition" from the domain of objects to the domain of entities or existents. (BQB 39) The concepts of identity and existence sort objects into the existent and the nonexistent. Identity and existence are therefore classificatory concepts.  Of the two concepts, identity is the more basic since existence is explicable in terms of it.  The identity in question is material as opposed to formal identity, the kind affirmed in true, informative identity statements like 'The morning star is the evening star.'  But although identity and existence are genuine concepts, they are only concepts: there is nothing in the world that corresponds to them.

Butchvarov’s Meinongian commitment to nonexistent objects is a direct consequence of his Sartrean view of consciousness as exhausting itself in its objects. For on this view consciousness harbors no representations or other intermediary contents that could serve as surrogate objects when we think about what does not exist. Imagination of a mermaid is not consciousness of a mental image or other content of consciousness but precisely consciousness of a mermaid. Consciousness of a mermaid is just as outer-directed and revelatory of a material item as consciousness of a dolphin. But mermaids do not exist. Therefore, some objects do not exist. To take intentionality at phenomenological face-value, as Butchvarov does, is to accept nonexistent objects. Phenomenologically, consciousness is just the revealing of objects, only some of which are indefinitely identifiable. (THIS SECTION STATES MY VIEWS BETTER THAN I HAVE EVER DONE  MYSELF!)

II. An Objection

There is a strong temptation to suppose that if there are nonexistent objects, as Meinongians maintain, then they must have some ontological status despite their not existing.  After all, they are not nothing.   And so one might suppose that they must have the status of merely intentional objects.  By 'merely intentional object' I mean an accusative of consciousness that does not exist in reality but does exist as, and only as, an accusative of consciousness.  (We will have to ask whether one who accepts merely intentional objects must also accept modes of existence.)  (I AM UNEASY ABOUT YOUR USE OF ‘ACCUSATIVE.’ IT IS A GRAMMATICAL TERM. WHAT YOU MEAN BY IT IS ‘OBJECT,’ BUT THEN YOUR PHRASE “MERELY INTENTIONAL OBJECTS” JUST MEANS “OBJECTS THAT DO NOT EXIST BUT SOMEONE IS CONSCIOUS OF THEM.) But for Butchvarov, the class of nonexistent objects does not have the same extension as that of merely intentional objects.   For he tells us that there is "no contradiction in supposing that there are objects that are not perceived, or imagined, or thought by anyone." (BQB 62, quoted in Larry Lee Blackman, "Mind as Intentionality Alone," Metaphysica, vol. 3, no. 2 December 2002,p. 45)  If there are such nonexistent objects, then of course it cannot be true that x is a nonexistent object iff x is a merely intentional object.

Furthermore, what I am calling merely intentional objects are mind-dependent: they exist as, and only as, accusatives of mind.  No mind, no merely intentional objects.  But Butchvarov's nonexistent objects are neither mind-dependent nor mind-independent, whether logically or causally.  Only what exists is either mind-dependent or mind-independent.  It follows that none of his nonexistent objects are what I am calling merely intentional objects. 

Blackman's worry, and mine too, is expressed by Blackman when he writes, "He [Butchvarov] denies that nonexistent objects are mind-dependent, but in an obvious sense they are, since, in a world without minds, there would be no perceivings of golden mountains, no imaginings of centaurs, etc." (Blackman, 55)  Now Butchvarov denies on phenomenological grounds that there are individual mental subjects and mental acts as well.  So Butchvarov might respond that of course there are no imaginings of centaurs, if imaginings are mental acts.  So we need to put Blackman's objection more precisely.  The objection needn't presuppose that there are individual minds or mental acts.  The essence of the objection is that in a world without mind (consciousness)  there are no perceptual or imaginal objects.  (THIS IS AMBIGUOUS, THOUGH THE FAULT IS MINE BECAUSE I USE ‘PERCEPTUAL’ AND ‘IMAGINAL’ FOR THE NONRELATIONAL PROPERTIES IN QUESTION. BUT THEY ARE EXPLICITLY INTENDED TO EXCLUDE REFERENCE TO A CONSCIOUSNESS.) Denying as he does that there are minds and mental acts,  Butchvarov must deny that imagining, perceiving, remembering, etc. are types of mental acts or properties of mental acts.  Act-differences are displaced onto the object as monadic (nonrelational) properties of objects. Thus it is a nonrelational, and hence intrinsic, property of centaurs that they are imaginal objects.  This being understood, Blackman's objection can be put by saying that in a world without consciousness there would be no perceptual or imaginal or memorial objects, and that therefore, in a world without consciousness, there would be no such nonexistent objects.  Blackman is of course assuming that there could be a world without consciousness.  If Butchvarov were to claim that there could not be, then his theory of objects would have idealism as a consequence.

The problem can be set forth as an aporetic triad:

1. Only what exists is either mind-dependent or mind-independent. (MY POINT IS THAT CAUSAL RELATIONS HOLD ONLY BETWEEN EXISTENT OBJECTS. IF THERE IS AN EXISTENT SUCH AS MIND, THEN DEPENDENCE ON IT WOULD BE SUCH A RELATION.)

2. There are objects that do not exist.
3. Both the distinction between objects and entities, and the related distinction between existent and nonexistent objects, are  mind-involving in the sense that in a world without mind these distinctions would not obtain. (THE TERM ‘MIND’ HERE IS AMBIGUOUS. IF IT MEANS ‘CONSCIOUSNESS’ THEN MIND IS NOT THE SORT OF THING ON WHICH ANYTHING CAN DEPEND OR NOT DEPEND.)

The limbs of this triad are individually plausible but jointly inconsistent.  For example, (1) and (2) taken together entail the negation of (3).  Indeed, any two limbs, taken together, entail the negation of the remaining one.  Since Butch is committed to both (1) and (2), he will solve the problem by denying (3).  Unfortunately, (3) is at least as plausible as (1) and (2).  Blackman, if I have understood him, will go further and say that (3) is more plausible than (1).  Accordingly, Blackman will solve the problem by denying (1). 

There is of course the possibility that the inconsistent triad is a genuine aporia, a conceptual impasse, and thus insoluble on the plane of the discursive intellect, which of course is where philosophy must operate.  I can't prove that it is a genuine aporia, but all three limbs, though jointly inconsistent, make a strong claim on our acceptance.  It is therefore not unreasonable to hold that we have no rational ground to prefer the rejection of one limb rather than another.  Of course, there is no way to stop people from being dogmatic.  Thus some will quickly reject (2) while ignoring the phenomenological and dialectical considerations Butch adduces in support of it.

My point, then is that Butchvarov's position, which requires the acceptance of (1) and (2), and the rejection of (3), is not compelling and is rationally rejectable.   

III.  A Possible Butchvarov Response

Suppose we reject (1) as I am inclined to do.  We would then be maintaining that an item can be mind-dependent without existing in reality. ('Exist' when used without qualification just means 'exist in reality.')  An imagined centaur would then exist-in consciousness without existing in reality.  And so we would have to distinguish between two distinct modes of existence, existence simpliciter (existence in reality) and intentional existence (existence in consciousness as a mere intentional object).  A scholastic philosopher would speak of esse reale and esse intentionale.  At this point Butch would probably object by saying that talk of modes of existence involves an intolerable equivocation on 'exists.'  If one adheres strictly to the univocity of 'exists' and cognates, then one cannot sensibly speak of modes of existence (as opposed to categories of existent).  So one can imagine Butchvarov arguing:  (a) To reject (1) is to embrace a doctrine of modes of existence which entails the  thesis that 'exist(s)' is equivocal.  (b) But this equivocity thesis is unacceptable.  So (c) (1) ought to be accepted.  (d) Given the phenomenological evidence for nonexistent objects, (3) ought to be rejected.  On the equivocity of 'exist(s)' see the work by the Butchvarov student, Dennis E. Bradford, The Concept of Existence: A Study of Nonexistent Particulars (University Press of America, 1980), pp. 37 ff.

IV.  Blackman's Attempt to Avoid Equivocity

Blackman agrees with me that in a world without mind there are no nonexistent objects.  But Blackman doesn't agree with me that holding this commits him to modes of existence:  ". . . to assert that gargoyles exist as the objects of our awarenesses is not to employ the term 'exists' equivocally, as Butchvarov might allege." (Blackman, 55)  Why not?

To say that gargoyles exist as the objects of my imaginings and that penguins exist as the the objects of my (veridical) perceptions is no more to use the term 'exists' equivocally than it is to to claim that the word 'exists' is used equivocally in the locutions, 'I exist as a father' and 'I exist as a husband.'  In neither case are we supposing different 'modes' of existence. (Ibid.)

The comparison is faulty.  I grant that there is no equivocation on 'exists' as between 'I exist as a father' and 'I exist as a husband.'  The first is equivalent to 'I exist and I am a father' while the second is equivalent to 'I exist and I am a husband.'   No equivocation!  But then  'Gargoyles exist as the objects of my imaginings' is equivalent to 'Gargoyles exist and gargoyles are objects of my imaginings' and 'Penguins exist as the objects of my (veridical) perceptions' is equivalent to 'Penguins exist and penguins are the objects of my (veridical) perceptions.'  Here there is equivocation! From this one can see that the comparison is flawed.  For while it is true that penguins exist and are the objects of my (veridical) perceptions, it is false that gargoyles exist and are the objects of my imaginings when 'exists' is employed univocally.  Penguins exist but gargoyles do not.

Blackman is trying to have it both ways: he is trying avoid the doctrine of modes of existence (modes of being) while maintaining that nonexistent objects are mind-dependent.  But this is impossible.  If nonexistent objects are mind-dependent, then they must exist in some way or mode.  This is because ontological dependence/independence obtains only between items that have some mode of existence.  An item that has no being or existence whatsoever cannot be said to be independent or dependent on mind or on anything else.  This is the core insight embodied in (1).  On the other hand, if there are no modes of being or existence,  then nonexistent objects cannot be said to be mind-dependent.

Although Blackman is on very solid ground in claiming that nonexistent objects are mind-dependent, he falls into incoherence because of his adherence to the analytic dogma that there cannot be modes of existence.  Further proof of the incoherence is in evidence when Blackman states that  "We might say that nonexistent objects, like the existent ones, belong to something larger called 'reality,' but the claim that nonexistent objects are in a sense 'real' is innocuous, as long as it understood that their 'reality' consists merely in their being the (strictly mental) intentions of certain awarenesses. (55-56)  It seems to me that the first independent clause in this sentence contradicts the second.  If reality is common to existent and nonexistent objects, then surely the reality of an object (whether existent or nonexistent) cannot consist in its being the strictly mental intention (i.e., intentum, intentional object) of certain awarenesses.

I claim that the widespread analytic view that there cannot be modes of existence is but a dogma.  In earlier posts collected in the Existence category I try to show that typical arguments against the doctrine fail and that there is a way between the horns of univocity and sheer equivocity of the river bank/financial bank sort (which I grant is intolerable).  If I am right about this, the insights of both Blackman and Butchvarov can be accommodated.  Blackman is right to insist that nonexistent objects are mind-dependent.  And Butchvarov is right to think that only what exists can stand in relations of dependence or independence.  But Butchvarov is wrong to think that only what exists in reality exists.  What exists in the mode of esse intentionale also exists but not in reality, only in consciousness.

Knowledge as Absolute Impossibility of Mistake

I incline towards Panayot Butchvarov's notion of knowledge as involving the absolute impossibility of mistake. In The Concept of Knowledge (Northwestern  UP, 1970), Butchvarov writes that "an epistemic judgment of the form 'I know that p' can be regarded as having the same content as one of the form 'It is absolutely impossible that I am mistaken in believing that p'." (p. 51)

One way to motivate this view is by seeing it as the solution to a certain lottery puzzle.

Suppose Socrates Jones has just secured a teaching job at Whatsamatta U. for the 2011-2012 academic year. Suppose you ask Jones, "Do you know what you will be doing next year?" He replies, "Yes I know; I'll be teaching philosophy." But Jones doesn't like teaching; he prefers the life of the independent scholar. So he plays the lottery, hoping to win big. If you ask Jones whether he knows he isn't going to win, he of course answers in the negative. He doesn't know that he will win, but he doesn't know that won't either. Jones also knows that if he wins the lottery, then he won't work next year at a job he does not  like.

On the one hand, Jones claims to know what he will be doing next year, but on the other he also claims to know that if he wins the lottery, then he won't be doing what he claims to know he will be
doing. But there is a contradiction here, which can be set forth as follows.

Let 'K' abbreviate 'knows,' 'a' the name of a person, and 'p' and 'q' propositions. We then have:

   1. Kap: Jones knows that he will be teaching philosophy next year.
   2. Ka(q –>~p): Jones knows that if he wins the lottery, then he will
   not be teaching philosophy next year.
   3. ~Ka~q: Jones does not know that he does not win the lottery.
   Therefore
   4. Ka~q: Jones knows that he does not win the lottery. (From 1 and 2)
   But
   5. (3) and (4) are contradictories.
   Therefore
   6. Either (1) or (2) or (3) is false.

Now surely (3) is true, so this leaves (1) and (2). One of these must be rejected to relieve the logical   tension. Isn't it obvious that (1) is the stinker, or that it is more of a stinker that (2)? The inference from (1) and (2) to (4) is an instance of the principle that knowledge is closed under known implication: if you know a proposition and you know that it entails some other proposition, then you know that other proposition. This seems right, doesn't it? So why not make the obvious move of rejecting (1)?

Surely Jones does not KNOW that he will be teaching philosophy next year. How could he KNOW such a thing? The poor guy doesn't even KNOW that he will be alive tomorrow let alone have his wits sufficiently about him to conduct philosophy classes. He doesn't KNOW these things since, if we are serious, knowledge implies the impossibility of mistake, and our man can easily be mistaken about what will happen in the future.

Of course, I realize that there is much more to be said on this topic.  
  

Saturday Night at the Oldies: The Implements of Sewing

Wanda Jackson, Silver Threads and Golden Needles (1956).  With less of a country flavor, and more of a folk-rock sound, The Springfields' version is the best to my taste.  Features Dusty Springfield before she went solo and a great guitar solo.  Here's Dusty with her first and main solo hit.  And here's a 1969 Linda Ronstadt version of Silver Threads.

Jackie De Shannon, another '60s cutie, here gives forth with Needles and Pins.  The British group The Searchers provide a competent cover. 

The Notion of a Cumulative Case

 In a comment thread Tony Hanson asked me if I had written a post on cumulative-case arguments.  After some digging, I located one that I had written 24 August 2004.  Here it is for what its worth. 

……………
 
Suppose you have a good reason R1 to do X. Then along comes a second good reason R2 to do X. Does R2 remove the justificatory force of R1? Obviously not. Does R2 leave the justificatory force of R1 unchanged? No again. Clearly, R2 augments the force of R1. Any additional good reasons R3, R4, . . . Rn, would of course only add to the justification for doing X. What we have here is a cumulative case for doing X, a case in which the justificatory force of the good reasons is additive.
 
A thorough discussion would have to distinguish between cumulative case arguments in which each reason is sufficient to justify the action envisaged, and cumulative case arguments in which one or more or all of the reasons are individually insufficient to justify the action envisaged.
 
Suppose each reason in a cumulative case argument is individually sufficient to justify the action envisaged. Then in what sense are the reasons additive? They are additive in that each additional sufficient reason provides an additional fail-safe mechanism. If an agent has many reasons each of which is both good and sufficient for doing X, then, if one of the reasons should turn out to be either bad or insufficient, then the other reasons are available to shoulder the justificatory burden.
 
Apply this to the Iraq war. One reason for going to war was the widely shared belief that Saddam had WMDs. Another was that he was a known sponsor of Palestinian Arab terrorists and a reasonably surmised sponsor of other terrorists. (On the second point, see Stephen F. Hayes, The Connection: How al-Qaeda's Collaboration with Saddam Hussein Has Endangered America, Harper Collins, 2004) A third was humanitarian: the liberation of the Iraqi people from a brutal dictator and his sons. A fourth was to enforce unanimous U.N. resolutions that this august body did not have the cojones to enforce itself. A fifth was to end the ongoing hostilities, e.g., Iraqi attacks on coalition warplanes. Even if no one of these reasons is sufficient to justify the invasion, the five taken together arguably provide good and sufficient reason for the action.
 
The strategy of ‘Divide and Conquer’ cannot be used against a cumulative case argument. Suppose Jack has several reasons for marrying Jill: she’s nubile and pretty, moneyed and witty; they are physically and psychologically compatible; they share the same values; she has beautiful eyes, and there is beauty at the opposite pole of her being as well. So Jack has nine good reasons. It simply won’t do to point out that each of them, taken singly, is insufficient to justify the marriage. A good reason is not the same as a sufficient reason. A good reason can be either sufficient or insufficient. What then are examples of bad reasons? A bad reason would be her having a police record, or her having a doctorate in biology when her doctorate is in mathematics.
 
The point is that several good, but individually insufficient, reasons can add up to a good and sufficient reason. If so, then ‘Divide and Conquer’ is a fallacious form of refutation. But that is what many leftists do when they oppose the Iraq war. Suppose that the cumulative case consists of R1, R2, and R3, each of which is insufficient by itself to justify doing X. The ‘Divide and Conquer’ objector wrongly infers ‘no reason’ from ‘insufficient reason.’ Thus he thinks that if R1 is insufficient, then R1 is no reason, and similarly for R2 and R3. He then concludes: no reason + no reason + no reason = no reason. He fails to appreciate the additivity of individually insufficient but good reasons, just as the typical poor person fails to appreciate the additivity of the small amounts of money he throws away on cigarettes, lottery tickets, and overpriced convenience store items.
For example, if a conservative gives liberation of the Iraqi people as a reason for the invasion, the leftie is likely to object: "But then why don’t we liberate the North Koreans?" This is an asinine response since it it is based on a failure to appreciate that the liberation reason is only one part of a cumulative case, not to mention the fact that an attempted liberation of the North Koreans could easily lead to nuclear war. Granting that liberating the Iraqi people is an insufficient reason for the war, it does not follow that it is no reason at all. It is a good reason which, though insufficient taken by itself, is part of a cumulative case which amounts to a good and sufficient reason for the war.
Another mistake that leftists make is to confuse a reason with a motive. They do this when they say that a proffered reason is not the real reason. A reason is a motive when it plays a motivating role within the psychic economy of an agent. Suppose Jack has available to him an objectively good reason R for marrying Jill. But Jack is not consciously or subconsciously aware of R. Obviously, R can play no role in the etiology of his envisaged action. Yet R remains an objectively good reason for performing the act in question. A good reason need not be a motivating reason, and a motivating reason need not be a good reason. The expression ‘real reason’ should be avoided because it is ambiguous as between good reason and motivating reason.
 
Suppose Bush II’s sole motive for invading Iraq was to avenge Saddam’s assasination attempt on his father, Bush I. Even on this wildly counterfactual assumption, there were good reasons for the invasion. For an action to be justified, all that is required is that there be objectively good reasons for the action; it is not necessary that the agent’s motives be objectively good reasons. Even if an agent is not justified in doing X – because he is either not aware of or motivated by the good reasons for doing X – the act itself (the act-type itself) can have justification. Our man Jack, for example, may be driven to marry Jill by his lust and nothing besides; but this does not entail that his marrying her lacks justification. Jack’s father might say to him: "Son, you made the right decision, but for the wrong reason." The rightness of the decision is due to the availability of good reasons even if horny Jack did not avail himself of them.

At this point an objector might maintain that what I am calling good reasons are simply ex post facto rationalizations.But a rationalization after the fact is not the same as a good reason that plays no motivating role in bringing about the fact. For a rationalization is a bad reason. Suppose Ali physically assaults Benjamin because Benjamin is a Jew and Ali believes that Jews are the "sons of pigs and monkeys." After the fact, A explains his behavior by saying that B insulted him. Suppose B did insult A. A is rationalizing after the fact as opposed to giving a good reason after the fact. B’s insulting of A did not give A a good reason for initiating physical violence against B.

Now let us suppose that Bush II’s sole motive for ordering the Iraq invasion was his desire to deprive Saddam of the WMDs that he, Bush, believed Saddam to possess. Suppose, plausibly, that the belief is false. In that case, Bush II’s motivating reason was not an objectively good reason – based as it was on a false belief – but it could still count as a subjectively good reason in this sense: he had a reason that was a good reason based on the information he had available to him at the time of the decision. I would then argue that the other reasons, which are objectively good, bear the justificatory burden.

An astonishing number of people, some of them intelligent, believe that the motivating reason for the Iraq invasion was the desire to secure access to Iraqi oil. But if that was the motivating reason, it is was a very bad reason since (i) the oil was flowing; (ii) starting a war with an opponent believed to have WMDs and known to have ignited oil wells in the past is clearly a stupid way to secure access to Iraqi oil; (iii) the projected cost of the war would be scarcely offset by the value of the oil secured; and (iv) deposing Saddam and his sons was not at all necessary to insure the flow of oil. I would argue that since this oil reason is so obviously bad, it is not reasonable to impute it to Bush and his advisers as the motivating reason for the invasion.

To sum up. The case for invading Iraq was a cumulative case. A cumulative case cannot be refuted by ‘Divide and Conquer.’ A good reason need not be a sufficient reason. A reason is not the same as a motive: there can be objectively good reasons for an action even if the agent of the action is not motivated by any of these reasons. To find good reasons after the fact is not to engage in ex post facto rationalization. This is because a rationalization is the providing of a bad reason.  But of course, liberals and leftists are so blinded by their passionate hatred of Bush II, that patient analysis of the foregoing sort will be lost on them.

 

The Bigger the Government, the More to Fight Over: The NPR Case

An excellent illustration of this truth is the current brouhaha over the defunding of National Public Radio (NPR).  Why is time and money being wasted debating this?  The short answer is that government has assumed a function that is obviously inessential to it and arguably illegitimate.  If government stuck to its essential tasks, one of which is obviously not public broadcasting, then we wouldn't be having this debate which is not only unproductive,  but also distractive from truly pressing issues such as 'entitlement' reform.  (A curious coinage, wouldn't you say?  As if prosperous oldsters who, having had a lifetime to accumulate substantial net worth in a relatively stable political and economic environment, are entitled to  intergenerational wealth transfer payments even in excess of what they have contributed  plus a reasonable return.)

The quality of the NPR debate in the House of Representatives was truly depressing.  (I have watched a good portion of it on C-SPAN — which is not supported by Federal dollars and is as objective as an media outlet  gets.)  It's as if the participants live on different planets.  One expects liberals and their opponents (both conservatives and libertarians) to disagree about the  role of government.  But they can't even agree on the 'green eyeshade' issue.  A sensible Republican gets upon and explains how the defunding of NPR will save taxpayers' dollars.  Then a Dem rises to flatly deny that there will be any savings. 

Liberals and conservatives  will argue until doomsday about the size, scope, and legitimate functions of government.  Those arguments are unavoidable and intractable due to profound axiological and philosophical differences.  But one would have thought that agreement could be reached about simple economic facts.  A husband and a wife might argue over whether the tax rebate should be spent on upgraded carpeting or on security doors.  That would be par for the course.  But if they argue about the size of the rebate or about whether or not cancelling their subscription to cable TV will save them x dollars per month,then they are in deep trouble and headed for divorce court.

The Dems are either lying or engaging in some other less blatant form of prevarication when they claim that defunding NPR will not affect the Federal budget deficit.

The liberal case is exceedingly weak, an indication being the rhetorical tricks and distortions liberals sink to.  For example, Representative Louise Slaughter claimed that the Republicans are out to "destroy" NPR.  See here at :34.  That's an outright lie. Or is she so stupid as not to know that defunding a program which its own officers admit does not need Federal funding is not to destroy it?  Contemptible.  Another Dem claimed that the Republicans are ought to"silence" NPR.  Another outright lie.

By the way, here is where civility meets a limit. One is under no obligation to be polite to a liar.

But Rep. Sheila Jackson Lee takes the cake.  She claimed that defunding NPR is an affront to the First Amendment.  How stupid can a liberal be?  Apparently she thinks that the First Amendment protects a government-funded propaganda arm of the Left from the people when it is the other way around:  the First Amendment protects the speech rights of the people against the government.

Of course, no liberal will admit his bias, either out of mendacity, or more likely, because he is simply incapable of seeing it. For a typical liberal, his view of the world is the world.  Hence liberals are mostly incapable of  seeing that NPR pushes a liberal-left point of view.  The problem, again, is not that they have that point of view, but that they feel justified in using taxpayers' dollars to promote it.  Part of the problem is that they do not understand how anyone could reasonably disagree with them. 

The bigger the government, the more to fight over.  Do you like pointless bickering?  Then support an ever-expanding state.

For more on NPR, see here  and here. 

Can the Chariot Take Us to the Land of No Self?

An abbreviated version of the following paper was published under the same title in The Proceedings of the Twenty-First World Congress of Philosophy, vol. 9, ed. Stephen Voss (Ankara, Turkey), 2006, pp. 29-33.

……………….

According to Buddhist ontology, every (samsaric) being  is impermanent, unsatisfactory, and devoid of self-nature.  Anicca, dukkha,  anatta: these are the famous three marks (tilakkhana) upon which the whole of Buddhism rests.  I would like to consider a well-known Buddhist argument for the third of these marks, that of anatta, an argument one could call ‘The Chariot.’  The argument aims to show that no (samsaric) being is a self, or has self-nature, or is a substance.  My thesis will be that, successful as this argument may be when applied to things other than ourselves, it fails when applied to ourselves.

Continue reading “Can the Chariot Take Us to the Land of No Self?”

God, Probability, and Noncontingent Propositions

Matt Hart comments:

. . . most of what we conceive is possible. So if we say that

1) In 80% of the cases, if 'Conceivably, p' then 'Possibly, p'
2) Conceivably, God exists
Ergo,
3) Pr(Possibly, God exists) = 80%
4) If 'Possibly, God exists' then 'necessarily, God exists'
Ergo,
5) Pr(Necessarily, God exists) = 80%,

we seem to get by.

I had made the point that conceivability does not entail possibility.  Hart agrees with that, but seems to think that conceivability is nondemonstrative evidence of possibility.  Accordingly, our ability to conceive (without contradiction) that p gives us good reason to believe that p is possible.

What is puzzling to me is how a noncontingent proposition can be assigned a probability less than 1.  A noncontingent proposition is one that is either necessary or impossible.  Now all of the following are noncontingent: 

God exists
Necessarily, God exists
Possibly, God exists
God does not exist
Necessarily, God does not exist
Possibly, God does not exist.

I am making the Anselmian assumption that God (the ens perfectissimum, that than which no greater can be conceived, etc.) is a noncontingent being.  I am also assuming that our modal logic is S5.  The characteristic S5 axiom states that Poss p –> Nec Poss p.  S5 includes S4, the characteristic axiom of which is Nec p –> Nec Nec p.  What these axioms say, taken together, is that what's possible and necessary does not vary from possible world to possible world. 

Now Possibly, God exists, if true, is necessarily true, and if false, necessarily false.  (By the characteristic S5 axiom.)  So what could it mean that the probability of Possibly, God exists is .8?  I would have thought that the probability is either 1 or 0.  the same goes for Necessarily, God exists. How  can this proposition have a probability of .8?  Must it not be either 1 or 0?

Now I am a fair and balanced guy, as everyone knows.  So I will deploy the same reasoning against the atheist who cites the evils of our world as nondemonstrative evidence of the nonexistence of God.  I don't know what it means to say that it is unlikely that God exists given the kinds and quantities of evil in our world.  Either God exists necessarily or he is impossible (necessarily nonexistent).  How can you raise the probability  of a necessary truth?  Suppose some hitherto unknown genocide comes to light, thereby adding to the catalog of known evils.  Would that strengthen the case against the existence of God?  How could it?

To see my point consider the noncontingent propositions of mathematics.  They are all of them necessarily true if true.  So *7 + 5 = 12* is necessarily true and *7 + 5 = 11* is necessarily false.  Empirical evidence is irrelevant here.  I cannot raise the probability of the first proposition by adding 7 knives and 5 forks to come up with 12 utensils.  I do not come to know the truth of the first proposition by induction from empirical cases of adding.  It would also be folly to attempt to disconfirm the second proposition by empirical means.

If I can't know that 7 + 5 = 12 by induction from empirical cases, how can I know that possibly, God exists by induction from empirical cases of conceiving?  The problem concerns not only induction, but how one can know by induction a necessary proposition.  Similarly, how can I know that God does not exist by induction from empirical cases of evil?

Of course, *God exists* is not a mathematical proposition.  But it is a noncontingent proposition, which is all I need for my argument.

Finally, consider this.  I can conceive the existence of God but I can also conceive the nonexistence of God.  So plug 'God does not exist' into Matt's argument above.  The result is that probability of the necessary nonexistence of God is .8!

My conclusion:  (a) Conceivability does not entail possibility; (b) in the case of noncontingent propositions, conceivability does not count as nondemonstrative evidence of possibility.