Category: Logica Docens

Excluded Middle and Future-Tensed Sentences: An Aporetic Triad

Do you remember the prediction, made in 1999, that the DOW would reach 36,000 in a few years?  Since that didn't happen, I am inclined to say that Glassman and Hasset's prediction was wrong and was wrong at the time the prediction was made.  I take that to mean that the content of their prediction was false at the time the prediction was made.  Subsequent events merely made it evident that the content of the prediction was false; said events did not first bring it about that the content of the prediction have a truth-value.

And so I am not inclined to say that the content of their irrationally exuberant prediction was neither true nor false at the time of the prediction. It had a truth-value at the time of the prediction; it was simply not evident at that time what that truth-value was.  By 'the content of the prediction' I mean the proposition expressed by 'The DOW will reach 36,000 in a few years.' 

I am also inclined to say that the contents of some predictions are true at the time the predictions are made, and thus true in advance of the events predicted.  I am not inclined to say that these predictions were neither true nor false at the time they were made.  Suppose I predict some event E and E comes to pass.  You might say to me, "You were right to predict the occurrence of E."  You would not say to me, "Although the content of your prediction was neither true nor false at the time of your prediction, said content has now acquired the truth-value, true."

It is worth noting that the expression 'come true' is ambiguous.  It could mean 'come to be known to be true' or it could mean 'come to have the truth-value, true.'  I am inclined to read it the first way.  Accordingly, when a prediction 'comes true,' what that means is that the prediction which all along was true, and thus true in advance of the contingent event predicted, is now known to be true.

So far, then, I am inclined to say that the Law of Excluded Middle applies to future-tensed sentences. If we assume Bivalence (that there are exactly two truth-values), then the Law of Excluded Middle (LEM)can be formulated as follows. For any proposition p, either p is true or p is false. Now consider a future-tensed sentence that refers to some event that is neither impossible nor necessary. An example is the DOW sentence above or  'Tom will get tenure in 2014.'  Someone who assertively utters a sentence such as this makes a prediction.  What I am currently puzzling over is whether any predictions, at the time that they are made, have a truth-value, i.e., (assuming Bivalence), are either true or false.

Why should I be puzzling over this?  Well, despite the strong linguistic inclinations recorded above, there is something strange in regarding a contingent proposition about a future event as either true or false in advance of the event's occurrence or nonoccurrence.  How could a contingent proposition be true before the event occurs that alone could make it true? 

Our problem can be set forth as an antilogism or aporetic triad:

1. U-LEM:  LEM applies unrestrictedly to all declarative sentences, whatever their tense.
2. Presentism:  Only what exists at present exists.
3. Truth-Maker Principle: Every contingent truth has a truth-maker.

Each limb of the triad is plausible.  But they can't all be true.  The conjunction of any two entails the negation of the third.  Corresponding to our (inconsistent) antilogism there are three (valid) syllogisms each of which is an argument to the negation of one of the limbs from the other two limbs.

If there is no compelling reason to adopt one ofthese syllogisms over the other two, then I would say that the problem is a genuine aporia, an insoluble problem.

People don't like to admit that there are insolubilia.  That may merely reflect their dogmatism and overpowering need for doxastic security.  Man is a proud critter loathe to confess the infirmity of reason.

Atomic Sentences and Syncategorematic Elements

According to Fred Sommers (The Logic of Natural Language, p. 166), ". . . one way of saying what an atomic sentence is is to say that it is the kind of sentence that contains only categorematic expressions." Earlier in the same book, Sommers says this:

In Frege, the distinction between subjects and predicates is not due to any difference of syncategorematic elements since the basic subject-predicate propositions are devoid of such elements.  In Frege, the difference between subject and predicate is a primitive difference between two kinds of categorematic expressions. (p. 17)

Examples of categorematic (non-logical) expressions are 'Socrates' and 'mammal.'  Examples of syncategorematic (logical) expressions are 'not,' 'every,' and  'and.'  As 'syn' suggests, the latter expressions are not semantic stand-alones, but have their meaning only together with categorematic expressions.  Sommers puts it this way: "Categorematic expressions apply to things and states of affairs; syncategorematic expressions do not." (164) 

At first I found it perfectly obvious that atomic sentences have only categorematic elements, but now I have doubts.  Consider the atomic sentence  'Al is fat.' It is symbolized thusly: Fa.  'F' is a predicate expression the reference (Bedeutung) of which is a Fregean concept (Begriff) while 'a' is a subject-expression or name the reference of which is a Fregean object (Gegenstand).  Both expressions are categorematic or 'non-logical.'  Neither is syncategorematic.  And there are supposed to be no syncategorematic elements in the sentence:  there is just 'F' and 'a.'

But wait a minute!  What about the immediate juxtaposition of 'F' and 'a' in that order? That juxtaposition is not nothing.  It conveys something.  It conveys that the referent of 'a' falls under the referent of 'F'.  It conveys that the object a instantiates the concept F. I suggest that the juxtaposition of the two signs is a syncategorematic element.  If this is right, then it is false that atomic sentence lack all syncategorematic elements.

Of course, there is no special sign for the immediate juxtaposition of 'F' and 'a' in 'Fa.'  So I grant that there is no syncategorematic element if such an element must have its own separate and isolable sign. But there is no need for a separate sign; the immediate juxtaposition does the trick.  The syncategorematic element is precisely the juxtaposition.

Please note that if there were no syncategorematic element in 'Fa' there would not be any sentence at all.  A sentence is not a list.  The sentence 'Fa' is not the list 'F, a.'  A (declarative) sentence expresses a thought (Gedanke) which is its sense (Sinn).  And its has a reference (Bedeutung), namely a truth value (Wahrheitswert).  No list of words (or of anything else) expresses a thought or has a truth value.  So a sentence is not a list of its constituent words.  A sentence depends on its constituent words, but it is more than them.  It is their unity. 

So I say there must be a syncategorematic element in 'Fa' if it is to be a sentence.  There is need of a copulative element to tie together subject and predicate.  It follows that, pace Sommers, it is false that atomic sentences are devoid of syntagorematic elements.

Note what I am NOT saying.  I am not saying that the copulative element in a sentence must be a separate sign such as 'is.'  There is no need for the copulative  'is.'  In standard English we say 'The sea is blue' not 'The sea blue.' But in Turkish one can say Deniz mavi and it is correct and intelligible.  My point is not that we need the copulative 'is' as a separate sign but that we need a copulative element which, though it does not refer to anything, yet ties together subject and predicate.  There must be some feature of the atomic sentence that functions as the copulative element, if not immediate juxtaposition then something else such as a font difference or color difference.

At his point I will be reminded that Frege's concepts (Begriffe) are unsaturated (ungesaettigt).  They are 'gappy' or incomplete unlike objects.  The incompleteness of concepts is reflected in the incompleteness of predicate expressions.  Thus '. . . is fat' has a gap in it, a gap fit to accept a name such as 'Al' which has no gap.  We can thus say that for Frege the copula is imported into the predicate.  It might be thought that the gappiness of concepts and predicate expressions obviates the need for a copulative element in the sentence and in the corresponding Thought (Gedanke) or proposition.

But this would be a mistake.  For even if predicate expressions and concepts are unsaturated, there is still a difference between a list and a sentence.  The unsaturatedness of a concept merely means that it combines with an object without the need of a tertium quid.  (If there were a third thing, then Bradley's regress would be up and running.)  But to express that a concept is in fact instantiated by an object requires more than a listing of a concept-word (Begriffswort) and a name.  There is need of a syncategorical element in the sentence.

So I conclude that if there are any atomic sentences, then they cannot contain only categorematic expressions.

The Aporetics of Singular Sentences

I should issue a partial retraction.  I wrote earlier,"The TFL representation of singular sentences as quantified sentences does not capture their logical form, and this is an inadequacy of TFL, and a point in favor of MPL."  ('TFL' is short for 'traditional formal logic'; 'MPL' for 'modern predicate logic with identity.' )

The animadversions of Edward the Nominalist have made me see that my assertion is by no means obvious, and may in the end be just a dogma of analytic philosophy which has prevailed because endlessly repeated and rarely questioned.  Consider again this obviously valid argument:

1. Pittacus is a good man
2. Pittacus is a wise man
—–
3. Some wise man is a good man.

The traditional syllogistic renders the argument as follows: 

Every Pittacus is a wise man
Some Pittacus is a good man
—–
Some wise man is a good man.

This has the form:

Every P is a W
Some P is a G
—–
Some W is a G.

This form is easily shown to be valid by the application of the syllogistic rules. 

In my earlier post I then repeated a stock objection which I got from Peter Geach:

But is it logically acceptable to attach a quantifier to a singular term? How could a proper name have a sign of logical quantity prefixed to it? 'Pittacus' denotes or names exactly one individual. 'Every Pittacus' denotes the very same individual. So we should expect 'Every Pittacus is wise' and 'Pittacus is wise' to exhibit the same logical behavior. But they behave differently under negation.

The negation of 'Pittacus is wise' is 'Pittacus is not wise.' So, given that 'Pittacus' and 'every Pittacus' denote the same individual, we should expect that the negation of 'Every Pittacus is wise' will be 'Every Pittacus is not wise.' But that is not the negation (contradictory) of 'Every Pittacus is wise'; it is its contrary. So 'Pittacus is wise' and 'Every Pittacus is wise' behave differently under negation, which shows that their logical form is different.

My objection, in nuce, was that 'Pittacus is wise' and 'Pittacus is not wise' are contradictories, not contraries, while 'Every Pittacus is wise' and 'Every Pittacus is not wise' ('No Pittacus is wise') are contraries.  Therefore, TFL does not capture or render perspicuous the logical form of 'Pittacus is wise.'

To this, Edward plausibly objected:

As I have argued here before, ‘Pittacus is wise’ and ‘Pittacus is not wise’ are in fact contraries. For the first implies that someone (Pittacus) is wise. The second implies that someone (Pittacus again) is not wise. Both imply the existence of Pittacus (or at least – to silence impudent quibblers – that someone is Pittacus). Thus they are contraries. Both are false when no one is Pittacus.

I now concede that this is a very good point.  A little later Edward writes,

The thing is, you really have a problem otherwise. If 'Socrates is wise' and 'Socrates is not wise' are contradictories, and if 'Socrates is not wise' implies 'someone (Socrates) is not wise', as standard MPC holds, you are committed to the thesis that the sentence is not meaningful when Socrates ceases to exist (or if he never existed because Plato made him up). Which (on my definition) is Direct Reference.

So you have this horrible choice:  Direct reference or Traditional Logic.

But must we choose?  Consider 'Vulcan is uninhabited.'  Why can't I, without jettisoning any of the characteristic tenets of MPL, just say that this sentence, though it appears singular is really general because 'Vulcan' is not a logically proper name but a definite description in disguise?  Accordingly, what the sentence says is that a certain concept — the concept planet between Mercury and the Sun — has as a Fregean mark (Merkmal) the concept uninhabited.

Now consider the pair 'Socrates is dead' – 'Socrates is not dead.'  Are these contraries or contradictories?  If contraries, then they can both be false.  Arguably, they are both false since Socrates does not exist, given that presentism is true. Since both are false, both are meaningful.  But then 'Socrates ' has meaning despite its not referring to anything.  So 'Socrates' has something like a Fregean sense.  But what on earth could this be, given that 'Socrates' unlike 'Vulcan'  names an individual that existed, and so has a nonqualitative thisnsess incommunicable to any other individual?

If, on the other hand, the meaning of 'Socrates' is its referent, then, given that presentism is  true and Socrates does not exist, there is no referent in which case both sentences are meaningless.

So once again we are in deep aporetic trouble.  The proper name of a past individual cannot have a reference-determining sense.  This is because any such sense would have to be a Plantingian haecceity-property, and I have already shown that these cannot exist.  But if we say that 'Socrates' does not have a reference-determining sense but refers directly in such a way as to require Socrates to exist if 'Socrates' is to have meaning, then, given presentism,  'Socrates' and the sentence of which it is a part is meaningless. 

Nota Notae Est Nota Rei Ipsius and the Ontological Argument

(By popular demand, I repost the following old Powerblogs entry.)

"The mark of a mark is a mark of the thing itself." I found this piece of scholasticism in C. S. Peirce. (Justus Buchler, ed., Philosophical Writings of Peirce, p. 133) It is an example of what Peirce calls a   'leading principle.'

Let's say you have an enthymeme:

   Enoch was a man
   —–
   Enoch died.

Invalid as it stands, this argument can be made valid by adding a premise. (Any invalid argument can be made valid by adding a premise.) Add 'All men die' and the argument comes out valid. Peirce writes:

     The leading principle of this is nota notae est nota rei ipsius.
     Stating this as a premiss, we have the argument,

     Nota notae est nota rei ipsius
     Mortality is a mark of humanity, which is a mark of Enoch
     —–
     Mortality is a mark of Enoch.

But is it true that the mark of a mark is a mark of the thing itself? There is no doubt that mortality is a mark of humanity in the following sense: The concept humanity includes within its conceptual content the superordinate concept mortal, which implies that, necessarily, if anything is human, then it is mortal. But mortality is not a mark, but a property, of Enoch. I am alluding to Frege's distinction between a Merkmal and an Eigenschaft. Frege explains this distinction in various places, one being The Foundations of Arithmetic, sec. 53. But rather than quote Frege, I'll explain the distinction in my own way using a totally original example.

Consider the concept bachelor. This is a first-order or first-level concept in that the items that fall under it are not concepts but objects. The marks of a first-order concept are properties of the objects that fall under the concept. Now the marks of bachelor are unmarried, male, adult, and not a member of a religious order. These marks are themselves concepts, concepts one can extract from bachelor by analysis. Given that Tom falls under bachelor, he has these marks as properties. Thus unmarried, etc. are not marks of Tom, but properties of Tom, while unmarried, etc. are not properties of bachelor but marks of bachelor.

To appreciate the Merkmal (mark)-Eigenschaft (property) distinction, note that the relation between a concept and its marks is entirely different from the relation between a concept and its instances. A first-order concept includes its marks without instantiating them, while an object instantiates its properties without including them.

This is a very plausible line to take. It makes no sense to say of a concept that it is married or unmarried, so unmarried cannot be a property of the concept bachelor. Concepts don't get married or remain single. But it does make sense to say that a concept includes certain other concepts, its marks. On the other hand, it makes no sense to say of Tom that he includes certain concepts since he could do such a thing only if he were a concept, which he isn't. But it does make sense to say of Tom that he has such properties as being a bachelor, being unmarried, being an adult, etc.

Reverting to Peirce's example, mortality is a mark of humanity, but not a mark of Enoch. It is a property of Enoch. For this reason the scholastic formula is false. Nota notae NON est nota rei ipsius. The mark of a mark is not a mark of the thing itself but a property of the thing itself.

No doubt commenter Edward the Nominalist will want to wrangle with me over this slight to his scholastic lore, and I hope he does, since his objections will aid and abet our descent into the labyrinth of this fascinating cluster of problems. But for now, two quick applications.

One is to the ontological argument, or rather to the ontological argument aus lauter Begriffen as Kant describes it, the ontological argument "from mere concepts." So we start with the concept of God and analyze it. God is omniscient, etc. But 'surely' existence is also contained in the concept of God. For a God who did not exist would lack a perfection, a great-making property; such a God would not be id quo maius cogitari non posse. He would not be that than which no greater can be conceived. To conceive God, then, is to conceive an existing God, whence it follows that God exists! For if you are conceiving a nonexistent God, then you are not conceiving God.

Frege refutes this version of the OA — not the only or best version I hasten to add — in one sentence: Weil Existenz Eigenschaft des Begriffes ist, erreicht der ontologische Beweis von der Existenz Gottes sein Ziel nicht. (Grundlagen der Arithmetik, sec. 53)  "Because existence is a property of concepts, the ontological argument for the existence of God fails to attain its goal." What Frege is saying is that the OA "from mere concepts" rests on the mistake of thinking of existence as a mark of concepts as opposed to a property of concepts.  No concept for Frege is such that existence is included within it. Existence is rather a property of concepts, the property of having an instance.

The other application of my rejection of the scholastic formula above is to the logical question of the correct interpretation of singular propositions. The scholastics treat singulars as if they are generals as I explained fully in previous posts. But if Frege is right, this is a grave logical error since it rides roughshod over the mark/property distinction. To drag this all into the full light of day will take many more posts.

On the TFL (Mis)Representation of Singular Propositions as General

The following is a valid argument:

1. Pittacus is a good man
2. Pittacus is a wise man
—–
3. Some wise man is a good man.

That this argument is valid I take to be a datum, a given, a non-negotiable point. The question is whether traditional formal logic (TFL) is equipped to account for the validity of this argument. As I have already shown, it is quite easy to explain the validity of arguments like the above in modern predicate logic (MPL). In MPL, the logical form of the above argument is

Inferences Involving Singular Propositions

In Modern Predicate Logic (MPL), logical quantity comes in three 'flavors,' universal, particular, and singular. Thus 'All bloggers are self-absorbed' and 'No bloggers are self-absorbed' are universal; 'Some bloggers are self-absorbed' and 'Some bloggers are not self-absorbed' are particular; 'Bernie is self-absorbed' and 'Bernie is not self-absorbed' are singular. Traditional Formal Logic (TFL), however, does not admit a separate category of singular propositions.

So, just to draw out commenter Edward the Nominalist and Co., how would a defender of TFL account for the validity of the following obviously valid argument:

   1. Mars is red
   2. Mars is a planet
   —–
   3. Some planet is red.

A supporter of MPL could construct a derivation as follows:

   4. Mars is a planet & Mars is red. (From 1, 2 by Conjunction)
   5. There is an x such that: x is a planet & x is red. (From 4 by
        Existential Generalization)
   3. Some planet is red. (From 5 by translation back into ordinary
       language)

No sweat for the MPL boys, but how do you TFL-ers do it? (Of course I am aware that it can be done. The point of this post is mainly  didactic.)

Being as the Apotheosis of the Copula: Frege’s Eliminativism in his Dialogue with Pünjer on Existence

Some time before 1884, Gottlob Frege had a discussion about existence with the Protestant theologian Bernard Pünjer (1850-1885). A record of the dialogue was found in Frege's Nachlass, and an English translation is available in Gottlob Frege: Posthumous Writings, eds. Hans Hermes et al., University of Chicago Press, 1979. Herewith, some critical commentary on part of the dialogue.

1. We have often discussed  'thin' or deflationary approaches to Being or existence. On a thin approach, existence is not a metaphysical or ontological topic, but a merely logical one. Consider the general   existential, 'Cats exist.' For Frege, the content of such a general existential does not lie in 'exist' but "in the form of the particular judgment." (63) Frege uses the good old 19th century term 'judgment' (Urteil) but the point could also be put, with minor adjustments, in terms of  indicative sentences, statements, and propositions. Particular judgments are the I- and O-judgments of the Square of Opposition: those of the form Some S is P and Some S is not P.

Frege's contention, then, is that the content of affirmative general existentials lies in the logical form: Some S is P. But how do we put 'Cats exist' into this form? We need a concept superordinate to the   concept cat, say, the concept mammal. We can then write, 'Some mammals are cats.' If we acquiesce in the natural anti-Meinongian presupposition that there are no nonexistent items, then 'Cats exist' is true if and only if  'Some mammals are cats' is true.

This translation illustrates what Frege means when he says that the content of affirmative general existentials does not lie in 'exist'  but in the [logical] form of the particular judgment. The logical form is Some S is P, which is just a bit of syntax, whence we are to conclude that 'exists' is bare of semantic content, whether sense or reference, and merely functions as a stylistic variant of 'Some ___ is    —.'

Those who take a deflationary tack, therefore, can be dubbed someists.  We who resist deflation can then be called existentialists.

By showing that 'exist(s)' and cognates are eliminable, Frege thinks he has eliminated those hoary metaphysical subjects Being or existence which fascinate Thomists, Heideggerians, and such other 'thicks' as your humble correspondent.

2. But does Frege's schedule of elimination really work? We saw how 'Cats exist' can be rendered as 'Some mammals are cats.' But what about 'Mammals exist'? This in turn needs elimination. Assuming that the domain of quantification is a domain of existents, this can be translated salva veritate as 'Some animals are mammals.' And so on up the tree of Porphyry, or, if you deem that to be barking up the  wrong tree, then supply some other scheme of classification. 'Animals exist' becomes 'Some living things are animals.' 'Living things exist'  becomes 'Some bodies are living things.' 'Bodies exist' gets translated as 'Some substances are bodies.'

Clearly, we either now or very soon must call a halt to the ascent by resting in "a concept superordinate to all concepts." (p. 63) Superordinate to all concepts except itself, of course. And what concept might that be? Such a concept must have maximal extension and so will have minimal intension. It will be devoid of all content,  abstracting as it does from all differences. Frege suggests 'something identical with itself' as the maximally superordinate concept. 'There are men' and 'Men exist' thus get rendered as 'Something identical  with itself is a man.' (63)

3. In ordinary language, the role of maximally superordinate concept, a "concept without content," (63) is played by an hypostatization of the copula. In 'The sea is blue' the content of the predicate lies in   'blue': 'is' is contentless. But from the copulative 'is'  we form a quasi-concept — 'being' — without content since its  extension is unlimited. This makes it possible to say: men = men  that have being; 'There are men' is the same as 'Some men are' or 'Something that has being is a man.' Thus here the real content of  what is predicated does not lie in 'has being' but in the form of  the particular judgment. Faced with an impasse, language has simply created the word 'being' in order to enable the form of the particular judgment to be employed. When philosophers speak of  'absolute being,' that is really an apotheosis of the copula. (64)

This is an excellent statement of the thin or deflationary or eliminativist line: there is in reality no such 'thing' as Being or existence. Being (as a metaphysical topic) is a result of an illicit reification or hypostatization of the copula, an apotheosis (deification) of the copula.

4. Now why can't I accept this? We saw that to eliminate existence in all cases and make it disappear into the logical form Some S is P we must ascend a classificatory tree at the apex of which is a concept or "quasi-concept" unlimited in extension and empty in intension. This is the concept a being, an existent, something self-identical. Using this concept we can translate salva veritate every sentence of the form Fs exist into a sentence of the form Some being is an F. The availability of such translations seems to strip 'exist(s)' and cognates of all semantic content.

The problem with this was appreciated by Aristotle long ago when he argued that Being is not a summum genus, a highest genus, or a genus generallisimum, a most general genus. (See Metaphysics 998b22 and   Posterior Analytics 92b14). Being, as that which makes beings be, does not abstract from the differences among beings. But a concept  superordinate to every quidditative concept, which is what the concept a being and the concept something self-identical are, does abstract from the differences among beings. To put it another way, Being, as that which constitutes beings as beings, is not superordinate to every  quidditative concept since it belongs to a different order entirely, the non-quidditative order of existence. The Being of a being is its thatness, not its whatness.

The mistake that Frege makes is to think that Being is a highest quidditative determination, a highest what-determination. The concept a being, ens, is such a concept, but this concept is not Being, esse.

In sum: Frege's elimination of existential judgments by translation into copulative judgments works only if Being (esse, das Sein) is a maximally abstract quidditative concept, the concept a being (ens, das  Seiende). But this is precisely what Being is not. Ergo, etc.

Burden of Proof in Philosophy?

1. The question this post raises is whether it is at all useful to speak of burden of proof (BOP) in dialectical situations in which there is no judge or tribunal to lay down and enforce rules of procedure.  By a dialectical situation I mean a context in which orderly discussion occurs among two or more competent and sincere interlocutors who share the goal of arriving as best they can at the truth about some matter, or resolving some question in dispute.  My main concern is with dialectical situations that are broadly  philosophical.   I suspect that in philosophical debates the notion of burden of proof is out of place and not usefully deployed.  That is what I will now try to argue.

2. I will begin with the observation that the presumption of innocence (POI) in an Anglo-American court  of law is never up for grabs in that arena.  Thus the POI is not itself presumptively maintained and subject to defeat.  If Jones is accused of a crime, the presumption of his innocence can of course be defeated, but that he must be presumed innocent until proven guilty is itself never questioned and of course never defeated.  The POI is not itself a defeasible presumption.  And if Rescher is right that there are no indefeasible presumptions, then the POI is not even a presumption.  The POI is a rule of the 'game,' and constitutive of the 'game.'  The POI in a court room situation  is like a law of chess.  The laws of chess, as constitutive of chess, cannot themselves be contested within a game of chess.  The reason there is always a definite outcome in chess (win, lose, or draw) is precisely because of those nonnegotiable chess-constitutive laws. 

As I pointed out earlier, defeasible presumption (DP) and burden of proof are correlative notions.  The defeasible presumption that the accused is innocent until proven guilty places trhe onus probandi on the prosecution.  Therefore, from the fact that the POI is not itself a defeasible presumption in a court of law, it follows that neither is the BOP.  Where the initating BOP lies — the BOP that remains in force and never shifts during the proceedings — is never subject to debate.  It lies on the state in a criminal case and on the plaintiff in a civil case.

3. But in philosophy matters are otherwise. For in philosophy everything is up for grabs, including the nature of philosophical inquiry and the rules of procedure.  (This is why metaphilosophy is not 'outside of' philosophy but a branch of same.)  And so where the BOP lies in a debate between, say, atheists and theists is itself a matter of debate and bitter contention.  Each party seeks to put the BOP on the other, to 'bop' him if you will.  The theist is inclined to say that there is a defeasible presumption in favor of the truth of theism; but of course few atheists will meekly submit to that pronunciamento.  If the theist is right in his presumption, then he doesn't have to do anything except turn aside the atheist's objections: he is under no obligation to argue positively for thesism any more than the accused is under an obligation to prove his innocence.

4. Now we come to my tentative suggestion.  There is no fact of the matter as to where the BOP lies in any dialectical context, legal, philosophical or any other: it is a matter of decision.  This is because BOP is a procedural matter.  If so, then there must be an adjudicator above the fray (i.e., a judge or arbiter who is not party to the dispute) who makes the decision as to where the BOP lies and has the power to enforce his decision.  There must be an arbiter who lays down and enforces the rules of procedure.  But in philosophy there neither is nor can be an above-the-fray adjudicator  whose decisions are unquestionable and backed by the threat of violence.

For suppose I were to try to play the arbiter in a debate between a theist and an atheist.  I give the following speech:

There is a presumption in favor of every existing institution, long-standing way of doing things, and well-entrenched and widespread way of belief.  Now the consensus gentium is that God exists.  And so I lay it down that there is a defeasible presumption in favor of theism and that the burden of proof  lies squarely on the shoulders of the atheist.  Theism is doxastically innocent until proven guilty.  The theist need only rebut the atheist's objections; he needn't make a positive case for his side.

Not only would the atheist not accept this declaration, he would be justified in not accepting it, for reasons that are perhaps obvious.  For my declaration is as much up for grabs as anything else in philosophy.  And of course if I make an ad baculum move then I remove myself from philosophy's precincts altogether.  In philosophy the appeal is to reason, never to the stick. 

The situation in philosophy could be likened to the situation in a court of law in which the contending parties are the ones who decide on the rules of procedure, including BOP and DP rules.  Such a trial could not be brought to a conclusion.  That's the way it is in philosophy.  Every procedural rule and methodological maxim is further fodder for philosophical Forschung. (Sorry, couldn't resist the alliteration.)

My tentative conclusion is as follows.  In philosophy no good purpose is served by claims that the BOP lies on one side or the other of a dispute, or that there is a DP in favor of this thesis but not in favor of that one. For there is no fact of the matter as to where the BOP lies.  BOP considerations are usefully deployed only in dialectical situations in which some authority presides over the debate and lays down the rules of procedure and has the power to punish those who violate them.  Such an authority constitutes by his decision the 'fact' that the BOP lies on one side rather than on the other.

It follows from what I have said that if you disagree with me, then neither of us bears a burden  of proving his metaphilosophical thesis.  But this is paradoxical.  For if you disagree with me, then presumably you think that BOP considerations are usefully deployed in philosophy, and that there is a fact of the matter as to where the BOP lies, and that therefore one of us must bear a probative burden.  

Notes on Burden of Proof and Defeasible Presumption

Since I don't understand this topic very well, I blog about it.  Nescio, ergo blogo!  Caveat lector!  The following notes are a blend of what I have gleaned from Nicholas Rescher and Douglas Walton and my own reflections.

1. Burden of Proof and Defeasible Presumption are correlative notions.  If there is a defeasible presumption in favor of not-p, then the burden of proof rests on the one who asserts p.  And if p is such that the burden of proof rests on the one who asserts it, then there is a defeasible presumption in favor of not-p.  BOP and DP are two sides of the same coin.

For example, in Anglo-American courts of law there is a defeasible presumption in favor of the innocence of the accused. One is presumed innocent until proven guilty.  This throws the onus probandi upon the state in criminal cases and upon the plaintiff in civil cases.  The presumption of non-guilt induces the burden of proving guilt.

For a second example consider the practice of safety-conscious gun handlers in non-combat situations. Their presumption is that every gun is loaded; this puts the BOP on the one who claims the opposite.  In a combat situation, or just prior to one, however, it is the other way around: the wise soldier does not presume that his weapon is ready to fire; he checks and makes sure.  There is a defeasible presumption that his weapon is unloaded, and the burden is on him to prove that it is loaded.  Either way we have the correlativity of BOP and DP.

This suggests the context-relativity of judgments as to where the BOP lies.

2.  Presumption that p is true is not to be confused with (high) probability that p is true.  If a gun dealer has just received a shipment of  tactical shotguns from Remington the manufacturer, then the probability is very high that none of these guns is loaded.  And yet his safety-conscious presumption will be that they are loaded.  Similarly in a court of law.  The accused is presumed innocent even when the probability of his being innocent is low  or even zero.  (E.g., Jack Ruby's shooting of Lee Harvey Oswald.)

3. Proof  is a logical concept, but burden of proof is not.  Perhaps we could say that BOP lays down a rule of proper conduct in dialectical situations.  The rule pertains to the 'ethics of argumentation.'  The rule is that he who advances a thesis, by so doing, incurs the obligation to substantiate his thesis by adducing reasons or considerations in in its favor, and by answering objections.

4. Accordingly, there is both a burden of proof and a burden of reply.  The proponent of a thesis has the initial burden of defending his thesis.  This remains constant throughout the dialectical proceedings.  But if his opponent lodges a good objection, then the proponent has the additional burden of replying to the objection.  A further complication is that the opponent in the course of objecting to the proponent's contention may make a claim that itself needs defense, in which case the burden of proof shifts onto the opponent in respect of that claim. 

Bearing this in mind, we see the need to nuance the claim advanced in #1 above according to which the onus probandi in Anglo-American law rests on the state or on the plaintiff.  That is true with respect to the initial allegation, but the defense may assume burdens of proof depending on how it builds its case.

5. Presumptions make up the doxastic status quo.  And so it appears that a certain conservatism is inherent in laying the burden proof on those who would defeat presumptions.  This needs to be explored.

6. Wherein resides the rationality of a presumption?  Rescher claims in his book on presumptions that the rationality of a presumption consists in its conformity to a well-established practive, and that it is not a matter of evidence.  This too needs to be explored.

Burden of Proof in Philosophy: Preliminary Thoughts

A reader asks about burden of proof in philosophy.  I really ought to have a worked-out theory on this, but I don't.  Here are some very tentative remarks.

1. In the law it is clear where the burden of proof lies: on the plaintiff in a civil case and on the prosecutor in a criminal case.  The party bringing the charge must show that the accused is guilty; the accused does not have to show that he is innocent.  One is presumed innocent until proven guilty.  To be presumed innocent is of course not to be innocent.  It is simply false that one is innocent of a crime unless or until proven guilty.  And to be found innocent/guilty is not to be innocent/guilty.  O. J. Simpson, for example, was found innocent of a double homicide.  But I have no doubt in my mind that he was guilty.  I don't mean that autobiographically as a report on my mental state; I mean the S.O.B. really was guilty.  Agree with me on this or not, you must agree that someone found innocent can be guilty and someone found guilty can be innocent. 

We should distinguish between burden of proof and standards of proof.  In the criminal law, the probative standard for guilt is 'beyond a reasonable doubt,' while in civil cases the standard is less demanding: 'preponderance of the evidence.'

2. In philosophy it is not often clear where the burden of proof lies, nor what our probative standards ought to be.  (What the hell did you expect?)  'Proof' can be used in a very strict way to refer to a valid deductive argument with objectively self-evident premises.  But this is not what 'proof' means in 'burden of proof.'  It means something like: burden of argument or burden of persuasion.   It means that some claims need to be argued for, and some don't.  Or perhaps: there is a (perhaps defeasible) presumption in favor of some claims but not in favor of their negations. 

For example, I would say there is a defeasible presumption in favor of the claim that drinking coffee in moderate amounts carries no health risk for most people.  So the burden of proof would be on a researcher who claims that coffee-drinking causes pancreatic cancer.  And because the evidence that coffee-drinking is harmless is so strong,  the probative bar the researcher must clear is correspondingly high.  The researcher needs to give strong evidence for his claim; the rest of us don't need to do anything.

Now consider the Holocaust denier, the 9/11 'truther,' the Obama 'birther,' and the Osama-was-killed-in 2001 kook.  Clearly, the burden lies on them to make their respective cases, and good luck to them.  The appropriate thing to say to those of this stripe is "Put up or shut up."  That 9/11 was an 'inside job' is a claim of such low antecedent probability that the case for it must be correspondingly strong.

A more philosophical example is provided by my present dispute with Peter Lupu about the modal principle that states that if proposition p is necessary, and p entails proposition q, then q is necessary.  He thinks he has found a counterexample to this principle.  Where does the onus probandi lie, and why?  It seem clear to me that the burden lies on Peter since he is controverting a well-known principle of elementary modal propositional logic.  (See. e.g., K. Konyndyk, Introductory Modal Logic, U. of Notre Dame Press, 1986, p. 32.) The burden does not lie on me since I am invoking a well-established, uncontroversial principle. 

Can we generalize from this example and say that whenever one controverts something well-established and long-accepted one assumes the burden of proof?   I doubt it.  Galileo defied Aristotle and the Church when he made certain empirically-based claims about the moon.  He claimed that the moon was not a perfect sphere.  As the story goes, the Church authorties refused to look through his telescope.  But it is at least arguable that the onus probandi rested on the authorities since they were flying in the face of sense perception.

But I hesitate to say that whenever one's case is based on sense perception one can shirk the burden of proof.

3.  I doubt that there is any criterion that allows us to sort claims that need proof or argument from those that don't.  Or can you think of one?  Some maintain that whenever a person make a claim to the effect that X exists, then the burden of proof is on him.  Well, it is in some cases, but surely not in all.  If you claim that extraterrestrial intelligent beings exist, then the burden is on you.  But if you claim that there are Saguaro cacti in Arizona, then the burden of proof is not on you but on the one who denies it.

Others seem to think that whenever one makes an affirmative claim one assumes a burden of proof.  Not so.  'That hillside is studded with Saguaros' said to my hiking companion needs no proof.  I shoulder no probative burden when I make a commonplace observation such as that.

4. Burden of proof and the ad ignorantiam 'fallacy.'  Gun instructors sometimes say that every gun is loaded.  That is plainly false as is stands, but a wise saying nonetheless if interpreted to mean: every gun is to be presumed loaded until proven unloaded.  So if  person A claims to person B that a certain gun is unloaded, the burden of proof is on him to show that it is unloaded; person B does not bear the burden of proving that it is loaded.  Indeed it seems that B would be within his epistemic rights were he to claim that his ignorance of whether or not the gun is loaded is good evidence of its being loaded.  But this is an appeal to ignorance.  It has not been shown that ~p; therefore p gives us the form of the ad ignoratiam 'fallacy.'  But in this case the appeal to ignorance seem nonfallacious.  Safety considerations dictate a defeasible presumption in favor of every gun's being loaded, a presumption that shifts the onus probandi onto the one who maintains the opposite.

The situation is similar to that in a court of law.  The defendant is presumed innocent until proven guilty, so the burden of proof rests on either the state or the plaintiff.  In a criminal case the probative bar is set high: the accused has to be shown guilty beyond a reasonable doubt.  Here too there is a legitimate appeal to ignorance: it has not been shown that the defendant is guilty beyond a reasonable doubt; therefore, he is not guilty.

There are 'safety' considerations in both the gun example and the law example.  It is because we want to be on the safe side — and not get shot — that we presume every gun to be loaded.  And it is because we want to be on the safe side — and not sentence an innocent person — that we presume the accused to be innocent until proven guilty.

But now what about God?  Don't safety considerations apply here as well? If God exists, then our ultimate happiness depends on getting into right relation with him.  So why can't one make a legitimate appeal to ignorance here?  Now of course from the fact that no one has proven that God does not exist, it does not follow that God exists.  That is an invalid deductive argument.  That would be a truly fallacious instance of ad ignorantiam.  But it is also invalid to infer than a gun is loaded because it hasn't been proven to be loaded, or that a man is innocent because he hasn't been proven to be guilty.  It just doesn't follow in any of these cases.  And yet we reasonably consider the gun loaded and we reasonably find the accused to be innocent.  And so why can't we reasonably presume God to exist on the basis of the fact that he hasn't been shown not to exist?  If the burden of proof rests on the one who claims that gun is unloaded, why doesn't the burden of proof rest on the one who claims that God is nonexistent?  We don't want to get shot, but we also don't want to lose our ultimate beatitude — if ultimate beatitude there be. 

You can't say that that the burden of proof rests on the theist because he is making a positive claim; for there are positive claims that need no proof.  And you can't say that the burden of proof rests on the theist becuase he is making an existential claim; for there are existential claims — I gave an example above — that need no proof.  Nor can you say that the burden rests on the theist because he is controverting the widely-accepted; the consensus gentium is that God exists.

But I suppose you could reasonably say that the burden rests on the theist since he is making a claim that goes well beyond what is empirically verifiable.

The Rabbit of Real Existence and the Empty Hat of Mere Logic

Consider again this curious piece of reasoning:

1. For any x, x = x.  Ergo:
2. a = a.  Ergo:
3. (Ex)(x = a). Ergo:
4. a exists.

This reasoning is curious because it seems to show that one can deduce the real existence of an individual a from a purely formal principle of logic, the Law of Identity.  And yet we know that this cannot be done.  We know that the rabbit of real existence cannot be pulled from the empty hat of mere logic. Since the argument cannot be sound, it must be possible to say where it goes wrong.  (It is a strange fact of philosophical experience that arguments that almost all philosophers reject nevertheless inspire the wildest controversy when it comes to the proper diagnosis of the error.  Think of the arguments of Zeno, Anselm, and McTaggart.) 

The move from (1) to (2) appears to be by Universal Instantiation.  One will be forgiven for thinking that if everything is self-identical, then a is self-identical.  But I say that right here is a (or the) mistake.   To move from (1) to (2), the variable 'x' must be replaced by the substituend 'a' which is a constant.   Now there are exactly three possibilities:

Either 'a' refers to something that exists, or 'a' refers to something that does not exist or 'a' does not refer at all.  On the third possibility it would be impossible validly to move from (2) to (3) by Existential Generalization.  The same goes for the second possibility:  if 'a' refers to a Meinongian nonexistent object, then  one could apply existentially-neutral Particular Generalization to (2), but not Existential Generalization.  This leaves the first alternative.  But if 'a' refers to something that exists, then right at this point real existence has been smuggled into the argument. 

I hope the point is painfully obvious.  One cannot move from (1) to (2) by logic alone: one needs an extralogical assumption, namely, that 'a' designates something that exists.  To put it another way, one must assume that the domain of quantification is not only nonempty but inhabited by existing individuals.  After all, (1) is true for every domain, empty or not.  (1) lacks Existential Import.  The truth of (1) is consistent with there being no individuals at all.

Let's now consider Peter's supposed counterexample to the principle that if p entails q and p is necessary, then q is also necessary.  He thinks that the above argument shows that there are cases in which necessary propositions entail contingent ones.  Thus he thinks that the conjunction of (1) and (2) entails (3), but that (3) is contingent.

Well, I agree that if we are quantifying over a domain the members of which are contingent individuals, then (3) is contingent.  But surely the conjunction of (1) and (2) is also contingent.  For the conjunction of a necessary and a contingent proposition is a contingent proposition.  Now of course (1) is necessary.  But (2), despite appearances, is contingent.  For if 'a' designates a contingent individual, then it designates an individual that exists in some but not all worlds, and in those worlds in which a does not not exist it is not true that a = a.

In the worlds in which a exists, a is essentially a.  But a is not necessarily a because there are worlds in which a does not exist.

What accounts for the illusion that if (1) is necessary, then (2) must also be necessary?   Could it be the tendency to forget that while 'x' is a variable,  'a' is an arbitrary constant?

 

Deducing John McCain from the Principle of Identity

What, if anything, is wrong with the following argument:

   1. (x)(x = x) (Principle of Identity)
   Therefore
   2. John McCain = John McCain (From 1 by Universal Instantiation)
   Therefore
   3. (Ex)(x = John McCain) (From 2 by Existential Generalization)
   Therefore
   4. John McCain exists. (From 3 by translation into ordinary idiom)

The initial premise states that everything is identical to itself, that nothing is self-diverse. Surely this is a necessary truth, one true no matter what, or in the jargon of possible worlds: true in every (broadly logically) possible world.

(2) follows from (1) by the intuitively clear inference rule of Universal Istantiation.  Surely, if everything is self-identical, then John McCain is  self-identical. The inferential move from (2) to (3) is also quite obvious: if McCain is self-identical, then something is identical to McCain. But (3) is just a complicated way of saying that John McCain exists. So we get the surprising result that the existence of John McCain is validly deducible from an a priori knowable necessary truth  of logic!

You understand, of course, that the argument is not about John McCain: it is about any nameable entity. Supposedly, Wilhelm Traugott Krug (1770-1842) once demanded of Hegel that he deduce Herr Krug's pen. If we name that pen 'Skip,' we can then put that name in the place of 'John McCain' and run the argument as before.

There is one premise and three inferences. Does anyone have the chutzpah to deny the premise? Will anyone make bold to question inference rules U.I. and E.G.? And yet surely something has gone wrong. Intuitively, the existence of a contingent being such as McCain cannot be deduced from an a priori knowable necessary truth of logic.  For that matter, the existence of a necessary being such as God cannot be deduced from an a priori knowable necessary truth of logic.  Surely nothing concrete, not even God, is such that its existence can be derived from the Law of  Identity.

So what we have above is an ontological argument gone wild whereby the  rabbit of real existence is pulled from the empty hat of mere logic!

St. Bonaventura said that if God is God, then God exists. If such  reasoning does not work in the case of God, then a fortiori it does not work  in the case of McCain or Herr Krug's pen.

Note that (1) is necessarily true. (It doesn't just happen to be the case that each thing is self-identical.) If (2) follows immediately  from (1), (2) is also necessarily true. And if (2) is necessarily true, then (3) is necessarily true. And the same holds for (4). But surely it is not the case that, necessarily, John McCain exists. He cannot be shown to exist by the above reasoning, and he certainly cannot be shown to necessarily exist by it.

So what went wrong? By my count there are three essentially equivalent ways of diagnosing the misstep.

A. One idea is that the argument leaves the rails in the transition from (3) to (4). All that (3) says is that something is identical to John McCain. But from (3) it does not follow that John McCain exists.   For the something in question might be a nonexistent something. After all, if something is identical to Vulcan, you won't conclude that  Vulcan exists. To move validly from (3) to (4), one needs the auxiliary premise:

3.5  The domain of quantification is a domain of existents only.

Without (3.5), John McCain might be a Meinongian nonexistent object. If he were, then everything would be logically in order up to (3). But  to get from (3) to (4) one must assume that one is quantifying over existents only.

But then a point I have been hammering away  at all my philosophical life is once again thrown into relief:  The misnamed 'existential' quantifier, pace Quine, does not express existence, it presupposes existence!

B. Or one might argue that the move from (1) to (2) is invalid. Although (1) is necessarily true, (2) is not necessarily true, but  contingently true: it is not true in possible worlds in which McCain does not exist. There are such worlds since he is a contingent being. To move validly from (1) to (2) a supplementary premise is needed:

1.5 'John McCain' refers to something that exists.

(1.5) is true in some but not all worlds. With this supplementary premise on board, the argument is sound. It also loses the  'rabbit-out-of-the-hat' quality. The original argument appeared to be  deducing McCain from a logical axiom. But now we see that the argument  made explicit does no such thing. It deduces the existence of McCain  from a logical axiom plus a contingent premise which is indeed   equivalent to the conclusion.

C. Finally, one might locate the error in the move from (2) to (3). No doubt McCain = McCain, and no doubt one can infer therefrom that something is identical to McCain. But this inferential move is not existential generalization, if we are to speak accurately and nontendentiously, but particular generalization. On this diagnosis,  the mistake is to think that the particular quantifier has anything to do with existence. It does not. It does not express existence, pace Quine, it expresses the logical quantity someness.

In sum, one cannot deduce the actual existence of a contingent being from a truth of logic alone. One needs existential 'input.' It follows that there has to be more to existence than someness, more than what  the 'existential' quantifier expresses. The thin conception of existence,  therefore, cannot be right.

Now let me apply these results to what Peter Lupu has lately been arguing.   Here he argues:

(i) (x)(x=x);

(ii) a=a, for any arbitrarily chosen object a; (from (i))

(iii) (Ex)(x=a); (from (ii) by existential generalization);

Now, (i) is necessary, but (iii) is contingent. Yet (i) entails (iii) via (ii), which is also necessary. So I simply do not see how the principle (1*) which you and Jan seem to accept applies in modal logics that include quantification plus identity.

Peter thinks he has a counterexample to the principle that if p entails q, and p is necessary, then q is also necessary.  For he thinks that *(x)( x = x)*, which is necessary, entails *(Ex)(x = a)*, which is contingent.

But surely if *a = a* is necessary, i.e. true in all worlds, then *(Ex)(x = a)* is necessary as well.

The mistake in Peter's reasoning comes in with the move from *Necessarily, (x) (x = x)* to *Necessarily, a = a*.   For surely it is false that in every possible world, a = a.  After all, there are worlds in which a does not exist, and an individual cannot have a property in a world in which it doesn't exist.  One must distinguish between essential and necessary self-identity.  Every individual is essentially (as opposed to accidentally) self-identical: no individual can exist without being self-identical.  But only some individuals are necessarily self-identical, i.e, self-identical in every world.  Socrates, for example, is essentially but not necessarily self-identical: he is self-identical in every world in which he exists (but, being contingent, he doesn't exist in every world).  By contrast, God is both essentially and necessarily self-identical: he is self-identical in every world, period (because he is a necessary being).   

Does Any Noncontingent Proposition Entail a Contingent Proposition?

This post continues the discussion in the comment thread of an earlier post.  

Propositions divide into the contingent and the noncontingent.  The noncontingent divide into the necessary and the impossible.  A proposition is contingent iff it is true in some, but not all, broadly logical possible worlds, 'worlds' for short.   A proposition is necessary iff it is true in all worlds, and impossible iff it true in none.  A proposition p entails a proposition q iff there is no world in which p is true and q false.

The title question divides into two:  Does any impossible proposition entail a contingent proposition?  Does any necessary proposition entail a contingent proposition?

As regards the first question, yes.  A proposition A of the form p & ~p is impossible.  If B is a contingent proposition, then there is no possible world in which  A is true and B false.  So every impossible proposition entails every contingent proposition.  This may strike the reader as paradoxical, but only if he fails to realize that 'entails' has all and only the meaning imputed to it in the above definition.

As for the second question, I say 'No' while Peter Lupu says 'Yes.'  His argument is this:
1. *Bill = Bill* is necessary.
2. *Bill = Bill* entails *(Ex)(x = Bill)*
3. *(Ex)(x = Bill)* is contingent.
Ergo
4. There are necessary propositions that entail contingent propositions.

Note first that for (2) to be true, 'Bill' must have a referent and indeed an existing referent.  'Bill' cannot be a vacuous (empty) name, nor can it have a nonexisting 'Meinongian' referent.  Now (3) is surely true given that 'Bill' is being used to name a particular human being, and given the obvious fact that human beings are contingent beings.  So the soundness of the argument rides on whether (1) is true.

I grant that Bill is essentially self-identical: self-identical in every world in which he exists.  But this is not to say that Bill is necessarily self-identical: self-identical in every world.  And this for the simple reason that Bill does not exist in every world.  So I deny (1).  It is not the case that Bill = Bill in every world.  He has properties, including the 'property' of self-identity, only in those worlds in which he exists.

My next post will go into these matters in more detail.

Addendum 28 May 2011.  Seldom Seen Slim weighs in on Peter's argument as follows:

I believe your reply to Peter is correct. It follows from how we should define constants in 1st order predicate logic. A domain or possible world is constituted by the objects it contains. Constants name those objects. If a domain has three objects, D = {a,b,c}, then the familiar expansion for identity holds in that domain, i.e., (x) (x = x) is equivalent to a = a and b = b and c = c. But notice that this is conditional and the antecedent asserts the existence in D of (the objects named by) a, b, and c. Thus premise 2 of Peter's argument is actually a conditional: IF a exists in some domain D, then a = a in D. The conclusion (3) must also be a conditional: if a exists in D , then something  in D is self-indentical. That of course does not assert the existential Peter wants from (x)(x = x). Put simply, a = a presumes [presupposes] rather than entails that a exists.

Butchvarov on Metaphysical Realism and Logical Nonrealism

This post is a  stab at a summary and evaluation of Panayot Butchvarov's "Metaphysical Realism and Logical Nonrealism" which is available both online and in R. M. Gale, ed., The Blackwell Guide to Metaphysics (Oxford: Blackwell 2002), pp. 282-302.  Page references are to the Blackwell source. The ComBox stands open if readers have some informed commentary to offer. ('Informed' means that you have read Butchvarov's paper, and my response, and you have something pertinent to contribute either in objection to or agreement with either Butchvarov or me.)

Continue reading “Butchvarov on Metaphysical Realism and Logical Nonrealism”

‘Material’ as *Alienans* in ‘Material Implication’

The topic of conditionals is ancient, not as ancient as Aristotle and logic itself, but damn near: hard thinking on this topic began with the Dialectical School which featured such worthies as Philo the   Logician and Diodorus Cronus, circa late 4th to mid-3rd centuries B.C. In nuce, those gentlemen had wrapped their minds around what much later came to be called material and strict implication, Philo around the former, Diodorus around the latter. The topic of conditionals is also deep and fascinating. But then no topic in philosophy lacks for fascination. The mansion of philosophy has countless rooms, each a labyrinth. Be sure to secure your thread of Ariadne before plunging on . . . .

The other day it occurred to me that 'material' in 'material implication' is best thought of as an alienans adjective. Normally, an FG is a G.  Thus a nagging wife is a wife, a female duck is a duck, cow's leather is leather, and a contingent truth is a truth. But if 'F' is alienans, then either an FG is not a G, or it does not follow from x's being an FG that x is a G. For example, your former wife is not your wife, your quondam lover is not your lover, a decoy duck is not a duck, artificial leather is not leather, negative growth is not growth, and a relative truth is not a truth. Is an apparent heart attack a heart attack? It may or may not be. One cannot infer from 'Jones had an apparent heart attack' to 'Jones had a heart attack.' So 'apparent' in 'apparent heart attack' is alienans.

Now if p materially implies q, does it follow that p implies q? Obviously not. I am breathing materially implies 7 + 5 = 12, but the first does not imply the second. Material implication is no more a kind or species of implication than former wives are a kind of wives, or artificial leather is a kind or species of leather. Just as 'artificial' shifts or alienates the sense of 'leather,' 'material' shifts or alienates the sense of 'implication.'

Material implication is rather a necessary condition any implication must satisfy if it is to be what it is, namely, a genuine implication. For all will agree that in no case does p imply q if p is true and q false. Thus material implication does capture something essential to every genuine implication. But if X is essential to Y, it does not follow that X is a kind of Y.

Once we appreciate that 'material' in 'material implication' is an alienans adjective, and that material implication is not a kind of implication, we are in a position to see that that the 'paradoxes' of   material implication are not paradoxes strictly speaking, but arise from foisting the ordinary sense of 'implication' upon 'material implication.'