Author: Bill Vallicella

On Falsely Locating the Difference Between Deduction and Induction

One commonly hears it said that the difference between deductive and inductive inference is that the former moves from the universal to the singular, while the latter proceeds from the singular to the universal. (For a recent and somewhat surprising example, see David Bloor, "Wittgenstein as a Conservative Thinker" in The Sociology of Philosophical Knowledge, ed. Kusch (Kluwer, 2000), p. 4.) No doubt, some deductive inferences fit the universal-to-singular pattern, while some inductive inferences fit the singular-to-universal pattern.

But it does not require a lot of thought to see that this cannot be what the difference between deduction and induction consists in. An argument of the form, All As are Bs; All Bs are Cs; ergo, All As are Cs is clearly deductive, but is composed of three universal propositions. The argument does not move from the universal to the singular. So the first half of the widely-bruited claim is false.

Indeed, some deductive arguments proceed from singular premises to a universal conclusion. Consider this (admittedly artificial) example: John is a fat chess player; John is not a fat chess player; ergo, All chess players are fat. This is a deductive argument, indeed it is a valid deductive argument: it is impossible to find an argument of this form that has true premises and a false conclusion. Paradoxically, any proposition follows deductively from a contradiction. So here we have a deductive argument that takes us from singular premises to a universal conclusion.

There are also deductive arguments that move from a singular premise to an existentially general, or particular, conclusion. ‘Someone is sitting’ is a particular proposition: it is neither universal nor singular. ‘I am sitting’ is singular. The first follows deductively from the second.

As for the second half of the claim, suppose that every F I have encountered thus far is a G, and that I conclude that the next F I will encounter will also be a G. That is clearly an inductive inference, but it is one that moves from a universal statement to a statement about an individual. So it is simply not the case that every inductive inference proceeds from singular cases to a universal conclusion.

What then is the difference between deduction and induction if it does not depend on the logical quantity (whether universal, particular, or singular) of premises and conclusions? The difference consists in the nature of the inferential connection asserted to obtain between premises and conclusion. Roughly speaking, a deductive argument is one in which the premises are supposed to ‘necessitate’ the conclusion, making it rationally inescapable for anyone who accepts the premises, while an inductive argument is one in which the premises are supposed merely to ‘probabilify’ the conclusion.

To be a bit more precise, a deductive argument is one that embodies the following claim: Necessarily, if all the premises are true, then the conclusion is true. The claim is that the premises ‘necessitate’ the conclusion, as opposed to rendering the conclusion probable, where the necessity attaches to the inferential link between premises and conclusion, and not to the conclusion itself. (A valid deductive argument can, but need not, have a necessary conclusion: ‘I am sitting’ necessitates ‘Someone is sitting,’ even though the latter proposition is only contingently true.)

Equivalently, a deductive argument embodies the claim that it is impossible for all the premises to be true and the conclusion false. I say ‘embodies the claim’ because the claim might not be correct. If the claim is correct, then the argument is valid, and invalid otherwise. Since validity pertains to the form of deductive arguments as opposed to their content, we can define a valid (invalid) deductive argument as one whose form is such that it is impossible (possible) for any (some) argument of that form to have true premises and a false conclusion. Since the purport of inductive arguments is merely to probabilify, not necessitate, their conclusions, they are not rightly described as valid or invalid, but as more or less strong or weak, depending on the degree to which they render their conclusions probable.

‘Broken’ and Other Examples of First-Grade English

It is annoying when a senator says that such-and-such is a 'no-no.' Baby talk!   Closely related is the phenomenon of what might be called 'first grade English.' George Bush and others have spoken of  'growing the economy.' One grows tomatoes, not economies. But perhaps I am being peevish and pedantic.

What about the current overuse of 'broken'?  Are you as sick of it as I am?  The El Lay Times  (20 December 2010) opines that California Isn't Broken.  No?  One hears that the Social Security admininstration and the Immigration and Nauralization Service are 'broken.' One breaks things like guitar strings, bicycle chains, and glasses. That which is broken no longer functions as it was intended to. A broken X is not a suboptimally functioning X but a nonfunctioning X.  Social Security checks are mailed to millions of recipients reliably month after month.Clearly, neither the SSA nor the INS are 'broken' strictly speaking. They just don't function very well and are in dire need of reform.

So why call them 'broken'? Is your vocabulary so impoverished that no better word comes to mind?

 
 "President Obama has said plainly that America's health care system is broken." That from Peter Singer in "Why We Must Ration Health Care" (NYT Magazine, July 19, 2009, p. 40.)  I guess that is why Canadians and others come to the USA for medical treatment they cannot get under a socialized system.

Why are people such linguistic lemmings? If some clown uses 'broken' inappropriately, why ape him? One has to be quite a lemming to ape a clown. (How's that for a triple mixed metaphor?) 

 
People who employ baby talk and first grade English in contexts that demand careful thought demonstrate their thoughtlessness and unseriousness.  Precision in the use of language may not be sufficient for clear and productive thinking, but it is necessary. 
 
Language matters.

What Is Intentionality?

He now calls himself 'Edward Ockham.'  I was pleased to receive an e-mail from him this morning in which he directs me to his latest post, Is There a Problem of Intentionality?, and suggests a crossblogging effort.  So I perused his post.  He opens:

Is there a problem of intentionality? That depends what intentionality is. Let's accept the following definition, for the sake of argument.

(1) Intentionality: the existence of some thoughts depends on the existence of external objects

Is that a problem? Yes, and for two reasons.

As far as I can see, the definition on offer bears little resemblance to anything called 'intentionality' in the discussions of this topic since the time of Brentano.  So before  discussion of any problem of intentionality, we need to come to some agreement as to what intentionality is.  Here is how I characterized it in an earlier post:

The influential Austrian philosopher Franz Brentano took intentionality to be the mark of the mental, the criterion whereby physical and mental phenomena are distinguished. For Brentano, (i) all mental phenomena are intentional, (ii) all intentional phenomena are mental, and (iii) no mental phenomenon is physical. (Franz Brentano, Psychologie vom empirischen Standpunkt (1874), Bk. II, Ch. 1.)

What is intentionality? ‘Intentionality’ is Brentano's term of art (borrowed from the Medievals) for that property of (some) mental states whereby they are (non-derivatively) of, or about, or directed to, an object. Such states are intrinsically such that they 'take an accusative.'  The state of perceiving, for example, is necessarily object-directed. One cannot just perceive; if one perceives, then one perceives something. The idea is not merely that when one perceives one perceives something or other; the idea is that when one perceives, one perceives  some  specific object, the very object of that very act.  The same goes for intending (in the narrow sense), believing, imagining, recollecting, wishing, willing, desiring, loving, hating, judging, knowing, etc. Such mental states — thoughts or thinkings, cogitationes, in the broad Cartesian sense of the term —  refer beyond themselves to objects that may or may not exist, or may or may not be true in the case of propositional objects. Reference to an object is thus an intrinsic feature of mental states and not a feature they have in virtue of a relation to an existing object. This is why Brentano speaks of the "intentional in-existence of an object." It is also why Husserl can 'bracket' the existence of the object for phenomenological purposes. Intentionality is not a relation, strictly speaking, though it is relation-like.  This is an important point that many contemporaries seem incapable of wrapping their heads around. 

This is nearly the opposite of what 'Ockham' is saying above.  He seems to be saying that intentional thoughts are all and only those thoughts whose existence depends on the existence of an external object.  Accordingly, the intentionality of a thought is its existential dependence on an existing external object.

But this misses the crucial point that  the directedness of a cogitatio to a cogitatum qua cogitatum — which is the essence of intentionality standardly  understood — does not at all depend on the external existence of the cogitatum. So I find the above definition of 'Ockham' wildly  idiosyncratic.  He goes on to argue against it, but that's like rolling a drunk or beating up a cripple.  Too easy, a 'slap job.'

My posts on intentionality are collected here (Intentionality category) and here (Brentano category).

 

December Twilight Zone Schedule

Here.  Marathon starts New Year's Eve morning and runs for two days.  My eyes glued to the set, my wife invariably asks, "Haven't you seen that episode before?"  She doesn't get it.  I've seen 'em all numerous times each.  Hell, I've been watching 'em since 1959 when the series first aired.  But the best are inexhaustibly rich in content, delightful in execution, studded with young actors and actresses who went on to become famous alongside the now forgotten actors of yesteryear, period costumes and lingo, allusions to the politics of the day.  Timeless and yet a nostalgia trip.  A fine way to end one year and begin another.

To see how much philosophical juice can be squeezed out of one of these episodes, see here.

Professor Mondo

Looking for some high-quality conservative culture critique anent the antics of the late Captain Beefheart who died last week, I typed 'New Criterion Captain Beefheart' into the Google engine. I was forthwith conducted to the stoa of Professor Mondo, presumably because he links to New Criterion and recently posted about Beefheart.  Noting that he also links to me, I thought it would be nice to direct some traffic his way.

Mondo's self-description:

I’m a medievalist at a small college in a small college town. I like reading, writing, music, and thinking — practicing any of these individually or in combination. Turnoffs include Brussels sprouts, bad music, and creeping totalitarianism.

As for the Brussels sprouts, de gustibus non est disputandum; but steaming  the hell out of them and drenching them in a good Hollandaise sauce laced with Tabasco works wonders for me.  Ditto for broccoli and other stinkweeds.

UPDATE 12/21:  Apparently my linkage caused a 'Mav-alanche' at Mondo's site.  My pleasure.

 

Death as a Relational Harm?

Here is some Epicurean reasoning:

1. Death is annihilation. (Materialist assumption)
2. A harm is a harm to someone or something: for there to be a harm, there must be a subject of harm. (Conceptual truth)
3. Nothing is a subject of a harm at a time at which it does not exist. (Plausible principle)
Therefore
4. No dead person is a subject of harm.
Therefore
5. Death (being dead) cannot be a harm to one who is dead.

Assuming that (1) is accepted, the only way of resisting this argument is by rejecting (3).  And it must be admitted that (3), though plausible, can be reasonably rejected.  Suppose I promise a dying man that I will take good care of his young and healthy dog.  But I renege on my promise in order  to save myself the hassle by having the dog euthanized.  Epicurus in hand, I reason, "There is no harm to my friend since he doesn't exist, and there is no harm to the dog because its transition to nonexistence will be quick and painless.  Caring for the dog, however, is a harm to me.  Sure, I will break my promise, but on consequentialist grounds, what's wrong with that?"

Thomas Nagel would disagree and call my reneging "an injury to the dead man."  ("Death" in Mortal Questions, Cambridge UP, 1979, p. 6)  For Nagel, "There are goods and evils which are irreducibly relational; they are features of the relations between a person, with spatial and temporal boundaries of the usual sort, and circumstances which may not coincide with him either in space or in time." (p. 6)  Death is such an evil.  Being dead is a circumstance that does not temporally coincide with the decedent.  In other words, a thing can have properties at times at which it does not exist provided it once existed. (Few if any would claim that a thing can have properties at times at which it does not exist if it never existed.  And so it is not an evil for Schopenhauer's never- existent son 'Will' that he never existed.)

A Nagelian rejection of (3) is respectable and plausible as a means of turning aside the Epicurean argument.  But it is scarcely compelling.  For the Epicurean can simply insist that there are no relational harms.  After all, there is something metaphysically murky about maintaining that a person who is nothing is yet the subject of a harm or injury simply on the strength of his having once existed.  If you are now nothing, then you are now nothing: why should your once having been be relevant?

So it looks like a stand-off, an aporetic impasse.  The considerations for and against (3) seem to cancel each other.

One consideration in favor of (3) is presentism, the doctrine that the present time and its contents alone exist.  If the present alone exists, then past individuals do not exist at all.  If so, they cannot be subject to harms.  A consideration contrary to (3) is our strong intuition that harms and injuries can indeed be inflicted upon the dead.  The dead may not have desires, but we are strongly inclined to say that they have interests, interests subject to violation.  (The literary executor who burns the manuscripts entrusted to him; the agent of Stalin who deletes references to Trotsky from historical documents, etc.)

 

Evil As it Appears to Atheists and Theists

In the preface to his magnum opus, F. H. Bradley observes that "Metaphysics is the finding of bad reasons for what we believe upon instinct, but to find these reasons is no less an instinct." (Appearance and Reality, Oxford 1893, p. x) The qualifier 'bad' is out of place and curiously off-putting at the outset of a 570 page metaphysical tome, so  if, per impossibile, I had had  the philosopher's ear I would have suggested 'good but not rationally compelling.'  Be that as it may, the point is that our basic sense of things comes first, and only later, if at all, do we take up the task of the orderly discursive articulation of that basic sense.

Thus atheism is bred in the bone before it is born in the brain.  The atheist feels it in his bones and guts that the universe is godless and that theistic conceptions are so many fairy tales dreamt up for false consolation.  This world is just too horrifying to be a divine creation: meaningless unredeemed suffering; ignorance and delusion; the way nature, its claws dripping with blood, feasts on itself; moral evil and injustice — all bespeak godlessness.   There can't be a God of love behind all this horror!  For most atheists, theism is not a Jamesian live option.  What point, then, in debating them?

This deep intuition of the godlessness of the world  is prior to and the force behind arguments from evil.  The arguments merely articulate and rationalize the intuition.  The counterarguments of theists don't stand a chance in the face of the fundamental, gut-grounded, atheist attitude.  No one who strongly  FEELS that things are a certain way is likely to be moved by what he will dismiss as so much verbiage, hairsplitting, and intellectualizing.

But for the theist it is precisely the horror of this world that motivates the quest for a solution, or rather, the horror of this world together with the conviction that we cannot provide the solution for ourselves whether individually or collectively. Evil is taken by the theist, not as a 'proof' of the nonexistence of God, but as a reason, a motive, to seek God.  'Without God, life is horror.' 

Addendum 12/21:  I should add that it would be pointless to seek God if any of the atheist arguments were compelling.  But none are. 

Saturday Night at the Oldies: Captain Beefheart and Buck Owens

Don Van Vliet, better known as Captain Beefheart, has died of complications of multiple sclerosis at age 69.  Obituary  here.  Apparently, hanging out in the Mojave desert can do strange things to your head.  Here is a taste from the 1969 Trout Mask Replica album.  Far out, man.  Here is something rather more accessible from the 1967 debut Safe as Milk album.  And I think I remember Abba Zabba from that same album.  (Which reminds of the saying, 'If you remember the '60s, you weren't there.')

From Mojave to Bakersfield.  I once had a girlfriend, half Italian, half Irish.  Volatile combo, not recommended.  I had me a Tiger by the Tail.  My wife's half Italian, but the phlegmaticity of her Polish half mitigates, moderates, and modulates her latent Italianate volcanicity, which remains blessedly latent.

Truck Drivin' Man.  Act Naturally.

Divine Simplicity and Whether Existence is a First-Level Property

A London reader, Rob Hoveman, kindly sent me Howard Robinson's "Can We Make Sense of the Idea that God's Existence is Identical to His Essence" (in Reason, Faith and History: Philosophical Essays for Paul Helm, ed. M. W. F. Stone, Ashgate 2008, pp. 127-143).  This post will comment on the gist of section 4 of Robinson's article, entitled 'Existence is Not a Property.'

One major implication of the doctrine of divine simplicity (DDS) is that in God essence and existence are the same.  My Stanford Encyclopedia article on DDS will fill you in on some of the details.  A number of objections can be brought against DDS.  Here only one will be considered, namely, the objection that existence cannot be a first-level property, a property of individuals.

The objection might go like this.  If in God, an individual, essence and existence are identical, then existence must be a first-level property of God.  But existence cannot be a first-level property.  Therefore, essence and existence cannot be identical in God.

This objection is only as good as the Fregean theory according to which existence is a property of concepts only.  Without explaining why distinguished thinkers have been persuaded of its truth, let me give just one reason why it cannot be right.  The theory says that existence is the property of being instantiated. An affirmative general existential such as  'Horses exist,' then, does not predicate existence of individual horses; it predicates instantiation of the concept horse.  And a negative general existential such as  'Mermaids do not exist'  does not predicate anything of individual mermaids — after all, there aren't any — it denies that the concept mermaid has any instances.

To see what is wrong with the theory, note first that instantiation is a relation, a dyadic asymmetrical relation.  We can of course speak of the property of being instantiated but only so long as it is understood that this is a relational property, one parasitic upon the relation of instantiation.  Therefore, if a first-level concept C is instantiated, then there is some individual x such that  x instantiates C.  It would be nonsense to say that C is instantiated while adding that there is nothing that instantiates it.  That would be like saying that Tom is married but there is no one to whom he is married.  Just as 'Tom is married' is elliptical for 'Tom is married to someone,' 'C is instantiated' is elliptiucal for 'C is instaniated by some individual.'

Now either x exists or it does not. 

Suppose it does not.  Then we have instantiation without existence.  If so, then existence cannot be instantiation.   For example, let C be the concept winged horse and let x be Pegasus.  The latter instantiates the former since Pegasus is a winged horse.   But Pegasus does not exist.  So existence cannot be the second-level property of instantiation if we allow nonexistent objects to serve as instances of concepts. 

Now suppose that x exists.  Then the theory is circular: it presupposes and does not eliminate first-level existence. The concept blogging philosopher is instantiated by me, but only because I possess first-level existence.  One cannot coherently maintain that my existence consists in my instantiating that concept or any concept for the simple reason that (first-level) existence is what makes it possible for me to instantiate any concept in the first place.

If what we are after is a  metaphysical theory of what it is for an individual to exist, then Frege's theory in  all its variants (the Russellian variant, the Quinean variant, . . .)  is wholly untenable.  I demonstrate this in painful detail in A Paradigm Theory of Existence, Kluwer, 2002, Chapter 4.  Robinson, p. 133, is on to the problem, and makes the following intriguing suggestion: "But there is a way of taking the second order analysis which is not incompatible with regarding 'exists' as a first order predicate, and that can be approached by treating existence as a monadic property of concepts." (133)

The idea is that, rather than being a relational property of concepts, as on the Fregean theory, existence is a nonrelational property of concepts.  If this could be made to work, it would defuse the circularity objection I just sketched.  For the objection exploits the fact that instantiation is a dyadic  relation. 

But if existence is to be construed as a monadic (nonrelational) property of concepts, then concepts cannot be understood as Frege understands them.  For Frege, concepts are functions and no function is an ontological constituent of its value for a given argument or an ontological constituent of any argument.  For example, the propositional function expressed by the the predicate '___is wise' has True as its value for Socrates as argument.  But this function is not a constituent of the True.  Nor is it a constituent of Socrates.  And for Frege there are no truthmaking concrete states of affairs having ontological constituents.

For Robinson's suggestion to have a chance, concepts must be understood as ontological constituents of individuals like Socrates.  Accordingly,

Existence is not simply a property of the individual, in the ordinary sense; it is more a metaphysical component of it, along with form or essence. So the monadic property of the concept — its instantiation — is the same as the existence of the individual. (134)

Essence and existence are thus ontological constituents or metaphysical components of contingent individuals.  This is definitely an improvement over the Fregean view inasmuch as it preserves the strong intuition, or rather datum,  that existence belongs to individuals.  But this Thomistic view has its own problems.  It is difficult to understand how existence could be a proper part of an existing thing as the Thomistic analysis implies.   After all, it is the whole of Socrates that exists, Socrates together with all his spatial parts, temporal parts (if any), and ontological 'parts.'    As pertaining to the whole of the existing thing, its existence cannot be identified with one part to the exclusion of others.  For this  reason, in my book I took the line that the existence of an individual is not one of its constituents, but the unity of all its constituents.

Validity, Invalidity, and Contravalidity

If a deductive argument is valid, that does not say much about it: it might still be probatively worthless. Nevertheless, validity is a necessary condition of a deductive argument's being probative. So it is important to have a clear understanding of the notion of validity.  An argument is valid if and only if one of its logical forms is such that no argument of that form has true premises and a false conclusion.

Continue reading “Validity, Invalidity, and Contravalidity”

No Labels? Label We Must!

This is silly.  "Not Right. Not Left. Forward."  There are are real differences between Right and Left that cannot be ignored.  The positions must be carefully defined — and appropriately labeled.  'No labels' is itself a label — an inept one.  Label we must.  So we ought to do it carefully and thoughtfully.

I now hand off to Jonah Goldberg.

 

God, Evil, Matter and Mind: How Both Theists and Materialists Stand Pat in the Face of Objections

It is a simple point of logic that if propositions p and q are both true, then they are logically consistent, though not conversely. So if God exists and Evil exists are both true, then they are logically consistent, whence it follows that it is possible that they be consistent. This is so whether or not anyone is in a position to explain how it is possible that they be consistent. If something is the case, then, by the time-honored principle ab esse ad posse valet illatio, it is possible that it be the case, and one's inability to explain how it is possible that it be the case cannot count as a good reason for thinking that it is not the case.

Example.  No one has successfully answered Zeno's Paradoxes of motion.  (No, kiddies, Wesley Salmon did not successfully rebut them; the 'calculus solution'  is a joke.) But from the fact, if it is a fact, that no one has ever shown HOW motion is possible, it does not follow that motion is not possible. 

So if it is the case that God exists and Evil exists are logically consistent, then this is possibly the case, and a theist's inability to explain how God and evil can coexist is not a good reason for him to abandon his theism — or his belief in the existence of objective evil.

The theist is rationally entitled to stand pat in the face of the 'problem of evil' and point to his array of arguments for the existence of God whose cumulative force renders rational his belief that God exists. Of course, he should try to answer the atheist who urges the inconsistency of God exists and Evil exists; but his failure to provide a satisfactory answer is not a reason for him to abandon his theism. A defensible attitude would be: "This is something we theists need to work on."

Atheists and naturalists ought not object to this standing pat since they do the same. What materialist about the mind abandons his materialism in the face of the various arguments (from intentionality, from qualia, from the unity of consciousness, from the psychological relevance of logical laws, etc.) that we anti-materialists marshall?

Does the materialist give in? Hell no, he stands pat, pointing to his array of arguments and considerations in favor of materialism, and when you try to budge him with the irreconcilability of intentionality and materialism, or qualia and materialism, or reason and materialism, or whatever, he replies, "This is something we materialists need to work on."  He is liable to start talking, pompously, of his 'research program.'  He may even wax quasi-religious with talk of "pinning his hopes on future science"  as if — quite absurdly — knowing more and more about the meat within our skulls will finally resolve the outstanding questions.  And what does science have to do with hope?  There is also something exceedingly curious about hoping that one turns out to be just a material system, a bit of dust in the wind.

"I was so hoping to be proved to be nothing more than a clever land mammal slated for destruction, but, dammit all, there are reasons to think that we are more than animals and have a higher destiny.  That sucks!"