Logica Docens – Page 3 – Maverick Philosopher

Is Assertion Closed Under Entailment? Assertion and Presupposition

Suppose a person asserts that p. Suppose also that p entails q. Does it follow that the person asserting that p thereby asserts that q? If so, and if p and q are any propositions you like, then assertion is closed under entailment. If assertion is not closed under entailment, then there will be examples in which a person asserts that p, p entails q, but the person does not assert that q.

By 'entailment' I understand a relation between propositions. P entails q iff it is impossible for p to be true, and q false. By 'assertion' I mean a speech act, an act of asserting, a concrete, datable, linguistic performance, not a proposition. By 'the content of an assertion' I mean the proposition expressed when a person makes an assertion. A proposition is not the same as a sentence. 'The war has come to an end' is a sentence in English. 'Der Krieg hat zu Ende gekommen' is a sentence in German. The sentences are different, both at the type level and at the token level. And yet they can both be used to express one and the same thought. That same thought is the proposition. By 'thought' here I do not mean an occurrent episode of thinking, but the accusative (direct object) of such an act of thinking. You could also call it a 'content' although that term is ambiguous for reasons I won't go into now.

Preliminaries aside, back to our question.

That James no longer works for Amazon has among its entailments that James worked for Amazon, that someone named 'James' worked for Amazon, and that someone no longer works for Amazon.

Now suppose I assert that James no longer works for Amazon. Do I thereby assert that James worked for Amazon? I say No.

Here is a more striking example. Sophomore Sam asserts that there are no truths. The content of his act of assertion, namely, the proposition that there are no truths, entails that the content of his assertion is not true. But surely the latter is no part of what Sam asserts.

So assertion is not closed under entailment.

Suppose that Tom asserts that he is glad that Trump beat Hillary. The content of the assertion entails that Trump beat Hillary. But that Trump beat Hillary is not what Tom asserts. We can say that Tom's act of assertion presupposes that Trump beat Hillary. But neither Tom nor his act of assertion is a proposition. So if Tom's act of assertion presupposes that Trump beat Hillary, then presupposition is not a relation between propositions, but a relation between a non-proposition (a person or his speech act) and a proposition.

On the other hand, that Tom is glad that Trump beat Hillary entails that Trump beat Hillary. This is a relation between propositions and it makes some sense to say that the first presupposes the second.

This raises a question. Is presupposition primarily something that people do, or is it primarily a relation between propositions?

Paradox and Contradiction

A form of words can be paradoxical but not contradictory, e.g., "Most people want to become old, but few want to be old."

The expression is paradoxical, and therein lies its literary charm, but the thought is non-contradictory. The thought, expressed non-paradoxically, is: Most want to live a long time, but few if any want to suffer the decrepitude attendant upon living a long time.

One logic lesson to be drawn is that a paradox is not the same as a contradiction.

It is therefore a mistake to refer to Russell's Antinomy as 'Russell's Paradox.'

Thus spoke the Language Nazi.

Is Assertion External or Internal to Logic? A Note on Irad Kimhi

The main point of Peter Geach's paper, "Assertion" (Logic Matters, Basil Blackwell, 1972, pp. 254-269) is what he calls the Frege point: A thought may have just the same content whether you assent to its truth or not; a proposition may occur in discourse now asserted, now unasserted, and yet be recognizably the same proposition. This seems unassailably correct. One will fail to get the Frege point, however, if one confuses statements and propositions. An unstated statement is a contradiction in terms, but an unasserted proposition is not. The need for unasserted propositions can be seen from the fact that many of our compound assertions (a compound assertion being one whose content is propositionally compound) have components that are unasserted.

To assert a conditional, for example, is not to assert its antecedent or its consequent. If I assert that if Tom is drunk, then he is unfit to drive, I do not thereby assert that he is drunk, nor do I assert that he is unfit to drive. I assert a compound proposition the components of which I do not assert. I assert a relation between two propositions without asserting either of them.

The same goes for disjunctive propositions. To assert a disjunction is not to assert its disjuncts. Neither propositional component of Either Tom is sober or he is unfit to drive is asserted by one who merely asserts the compound disjunctive proposition.

On one view of logic, it studies propositions and the relations between them such as entailment, consistency, and inconsistency in abstraction from the concrete mental acts in which the propositions are accepted, rejected, or merely entertained. Logic is thus kept apart from psychology. If so, then assertion, as a speech act founded in the mental act of acceptance, is external to logic. If this were not the case, then how would one account for the validity of the following obviously valid argument?

a) If Tom is drunk, then Tom is unfit to drive
b) Tom is drunk
Therefore
c) Tom is unfit to drive.

For the argument to be an instance of the valid argument form modus ponendo ponens, the protasis of (a) must be the same proposition as is expressed by (b). But then the assertoric force that (b) carries when the argument is given by someone cannot be part of the proposition. For the assertoric force is no part of the proposition that is the protasis of (a).

So if formal logic studies propositions in abstraction from the concrete episodes of thinking in which they are brought before minds, then assertion is external to formal logic.

But according to the NYT, a philosopher with a cult following among the cognoscenti rejects the above view:

[Irad] Kimhi argues that this view is wrong, and that the distinction between psychology and logic has led our understanding of thinking astray. Consider that the following statement does not, according to the standard view, constitute a logical contradiction: “It’s raining, but I don’t believe it’s raining.” Why? Because the first part of the sentence concerns a state of affairs in the world (“it’s raining”), whereas the second part concerns someone’s state of mind (“I don’t believe it’s raining”).

Kimhi wants to rescue the intuition that it is a logical contradiction to say, “It’s raining, but I don’t believe it’s raining.” But to do this, he has to reject the idea that when you assert a proposition, what you are doing is adding psychological force (“I think … ”) to abstract content (“it’s raining”). Instead, Kimhi argues that a self-conscious, first-person perspective — an “I” — is internal to logic. For him, to judge that “it’s raining” is the same as judging “I believe it’s raining,” which is the same as judging “it’s false that it’s not raining.” All are facets of a single act of mind.

I haven't read Kimhi's book, and I am not sure I should trust the NYT account, but Kimhi seems to be recycling Kant in a confused way. At B 132 of Critique of Pure Reason, Kant writes, "It must be possible for the 'I think' to accompany all my representations; for otherwise something would be represented in me which could not be thought at all, and that is equivalent to saying that the representation would be impossible, or at least would be nothing to me." (NKS tr.)

Consider a propositional representation. One's awareness that it is raining need not be accompanied by an explicit act of reflection, the one expressed by 'I think that it is raining,' but it must be possible that this reflection occur. Thus there is a necessary connection between the propositional representation 'It is raining' and Kant's transcendental unity of apperception. The latter could be described as " a self-conscious, first-person perspective — an “I” — [that] is internal to logic." But it is a transcendental I, one common to all cognitive subjects, and not the psychological I of a particular cognitive subject. Kimhi seems to be speaking of the latter.

Kant's Ich denke points us back to Descartes' cogito. The Frenchman discovers that while he can doubt many things, he cannot doubt that he is doubting these things. He can doubt the existence of the cat he 'sees' — using 'see' in a strictly phenomenological way — but he cannot doubt the existence of his 'seeing' as a mental act or cogitatio. His doubting is a thinking, but it is not a believing. The Dubito ergo sum is but a special case of the generic Cogito ergo sum. His doubting that he has a body is not a believing that he has a body but it is a thinking in the broad Cartesian sense that subsumes all intentional states or mental acts.

Accordingly, the 'I think' that must be able to accompany all my representations does not have the specific sense of 'I believe.' Belief is one type of mental act among many. One who believes does not doubt, and conversely. But both think. The 'I think' expresses an explicit reflection on the occurrent intentional state one is in, whether one is doubting, believing, wishing, hoping remembering, etc.

So there is a defensible sense in which there is an I internal to logic, but this is the transcendental I of the original synthetic unity of apperception, not the I of the psychophysical subject in nature. If there is an I internal to logic, it is the I of the transcendental prefix, the 'I think ___' which must be able to accompany all my representation. But this 'I think ___' of the transcendental prefix does not have the sense of the ordinary language 'I think so' which means 'I believe so.'

One consequence of Kimhi’s view is that “It’s raining, but I don’t believe it’s raining” becomes a logical contradiction. Another consequence is that a contradiction becomes something that you cannot believe, as opposed to something that you psychologically can but logically ought not to believe (as the traditional cleavage between psychology and logic might suggest). A final consequence is that thinking is not just a cognitive psychological act, but also one that is governed by logical law.

In other words, the distinction between psychology and logic collapses. Logic is not a set of rules for how to think; it is how we think, just not in a way that can be captured in conventional scientific terms. Thinking emerges as a unique and peculiar activity, something that is part of the natural world, but which cannot be understood in the manner of other events in the natural world. Indeed, Kimhi sees his book, in large part, as lamenting “the different ways in which philosophers have failed to acknowledge — or even denied — the uniqueness of thinking.”

The above strikes me as based on a confusion of the transcendental 'I think' with the psychological 'I believe.' It seems to me that one can have a reflective awareness as of rain falling without believing that rain is falling. What is impossible, and contradictory, is to have a reflective awareness as of rain falling without thinking (in the broad Cartesian sense that subsumes specific types of mental act) that rain is falling.

The transcendental I's thinking is governed by logical law, but not the thinking of the empirical I in nature. So the distinction between psychology and logic does not collapse. To the extent that I can make sense of what Kimhi is saying on the basis of the NYT article he seems to be trying to naturalizer Kant's transcendental ego. Good luck with that.

Perhaps talk of a transcendental I is nonsense if it is supposed to be a real entity that thinks; but only a transcendental I could be internal to formal logic.

If anyone has read Kimhi's book, his comments would be appreciated.

Does the Validity of an Argument Depend on the Order of its Premises?

Suppose you have a valid argument. Can you render the argument invalid by changing the display order of the premises?

I should think never. The Dark Ostrich, however, offers the following putative counterexample. He says he got it from Sainsbury; I should like to see a reference. And if there is a literature on this, I should like to see a bibliography.

(A) Some Greek is called ‘Mark’, Mark is an evangelist, therefore some Greek is an evangelist. (VALID)

(B) Mark is an evangelist, some Greek is called ‘Mark’, therefore some Greek is an evangelist. (NOT VALID)

(A) is valid and (B) is not. But this is not evidence that premise order affects validity. For while the sentences are the same, the premises of the two arguments are not the same. Made explicit, (A) becomes

(A*) Some Greek is called 'Mark', this same individual called 'Mark is an evangelist, therefore some Greek is an evangelist.

Clearly, (A*) and (B) have different premises. So it is not the different order of the premises in (B) that causes it to be invalid.

The Two Opposites of ‘Nothing’ and the Logical Irreducibility of Being (2018 Version)

This entry is part of the ongoing debate with the Opponent a. k. a. the Dark Ostrich.

It is interesting that 'nothing' has two opposites. One is 'something.' Call it the logical opposite. The other is 'being.' Call it the ontological opposite. Logically, 'nothing' and 'something' are interdefinable quantifiers:

D1. Nothing is F =_df it is not the case that something is F.

D2. Something is F =_df it is not the case that nothing is F.

These definitions, which are part of the articulation of the Discursive Framework (DF), give us no reason to think of one term as more basic than the other. Logically, 'nothing' and 'something' are on a par. Logically, they are polar opposites. Anything you can say with the one you can say with the other, and vice versa.

We also note that as quantifiers, as terms expressing logical quantity, 'nothing' and 'something' are not names or referring expressions.

So far I have said nothing controversial.

Ontologically, however, being and nothing are not on a par. They are not polar opposites. Being is primary, and nothing is derivative. (Note the ambiguity of 'Nothing is derivative' as between 'It is not the case that something is derivative' and 'Nothingness is derivative.' The second is meant.)

Now we enter the arena of controversy. For it might be maintained that there are no ontological uses of 'being,' and 'nothing,' that talk of being and nothing is replaceable without remainder by use of the quantifiers defined in (D1) and (D2).

Quine said that "Existence is what existential quantification expresses." (Ontological Relativity and Other Essays, p. 97)I deny it: there is more to existence than what the existential quantifier expresses. Quine's is a thin theory of existence; mine is a thick theory. Metaphorically, existence possesses an ontological thickness. This is very important for metaphysics if true.

I won't be able to prove my point because nothing in philosophy can be proven. But I can argue for my point in a fallacy-free manner. I am justified in holding my view so long as no one can convict me of a clear-cut error.

Suppose we try to define the existential 'is' in terms of the misnamed because question-begging 'existential' quantifier. (The proper moniker is 'particular quantifier.') This is standardly done as follows.

D3. y is/exists =_df for some x, y = x.

In plain English, for y to be or exist is for y to be identical to something. For Quine to be or exist is for Quine to be identical to something. In general, to be is to be identical to something, not some one thing of course, but something or other. This thing, however, must exist, and in a sense not captured by (D3). Thus

Quine exists =_df Quine is identical to something that exists

and

Pegasus does not exist =_df nothing that exists is such that Pegasus is identical to it

Pegasus is diverse from everything that exists.

The point, which many find elusive, is that the items in the domain of quantification must be there to be quantified over, where 'there' has not a locative but an existential sense. For if the domain includes nonexistent objects, then, contrary to fact, Pegasus would exist in virtue of being identical to an item in this widened domain, namely, Pegasus.

The conclusion is (to me!) obvious: one cannot explicate the existential 'is' in terms of the particular quantifier without circularity, without presupposing that things exist in a sense of 'exist' that is not captured by (D3).

Mere logicians won't accept or perhaps even understand this since existence is "odious to the logician" as George Santayana observes. (Scepticism and Animal Faith, Dover, 1955, p. 48, orig. publ. 1923.) You have to have metaphysical aptitude to understand it. (But now I am tending toward the tendentious.)

Intellectual honesty requires that I admit that I am basing myself on an intuition, what J. Maritain calls the intuition of Being. I find it self-evident that the existence of a concrete individual is an intrinsic determination that makes it be as opposed to not be. This implies a real distinction between x and the existence of x. Accordingly, the existence of an individual cannot be reduced to its self-identity: the existence of Quine does not reduce to Quine's being (identical to) Quine, as on the thin theory. And the nonexistence of Pegasus does not reduce to its being diverse from everything. (If to be is to be identical to something, then not to be is to be diverse from everything.)

The Opponent does not share my intuition. In the past I have berated him for being 'existence-blind' but he might plausibly return the 'compliment' by accusing me of double vision: I see Socrates but I also 'see' the existence of Socrates when there is no such 'thing.'

So far, not good: I can't refute the Opponent but he can't refute me. Stand-off. Impasse, a-poria.

Let me try a different tack. Does the Opponent accept

ENN. Ex nihilo nihil fit?

Out of nothing nothing comes. Note that 'nothing' is used here in two different ways, ontologically and logically/quantificationally. For what the hallowed dictum states is that it is not the case that something arises from nothing/Nothingness.

Now if the Opponent accepts the truth or even just the meaningfulness of (ENN), then he must (!) admit that there are two senses of 'nothing,' the logical and the ontological, and correspondingly, two senses of 'something.' If so, then being and nothing cannot be exhaustively understood in terms of logical quantifiers and propositional negation, and then the thin theory bites the dust.

But if the thin theory succumbs, then there is more to existence than can be captured within the Discursive Framework.

Singular Existence and Quantification

For Tim M. who wants to discuss this topic with me. ComBox open.

…………………….

Singular existence is the existence of particular individuals. It is the existence attributed by a use of a singular sentence such as 'Max exists,' where 'Max' is a proper name.

A standard way to conceptualize singular existence, deriving from Quine and endorsed by Peter van Inwagen, is in terms of the 'existential' — I prefer to say 'particular' — quantifier of standard predicate logic. Thus,

Max exists =_df for some x, x = Max.

In general,

x exists =_df for some y, x = y.

In the standard notation of modern predicate logic with identity,

x exists =_df (∃y)(x = y).

What the latter two formulae express is that an individual exists if and only if it is identical to something. Assuming that there are no nonexistent objects in the domain of quantification, these biconditionals are undoubtedly true, and indeed necessarily true. Meinongians reject the assumption but it is quite reasonable, so let it stand. Even so, I cannot see that the biconditionals just listed sanction the reduction of existence to identity-to-something.

Those of a deflationary bent would welcome such a reduction. For it would allow the elimination of existence as a topic of metaphysical investigation in favor of the sober logic of 'exists.' You will notice that on the left-hand side of the biconditionals there is the apparently non-logical, content-rich word 'exists' whereas on the right-hand side all the symbols are logical. If we can get rid of the word 'exists,' then perhaps we can get rid of the temptation to ask about Existence and Being. Aquinas, for example, tells us that God is not an ens among entia, but esse, Being or To Be: Deus est ipsum esse subsistens. This presupposes that there is such a 'thing' as Being. If the deflationary account is correct, there isn't.

So my question is this: is the deflationary account adequate? Or is there more to existence than can be captured by the so-called 'existential' quantifier of modern predicate logic?

An Argument Against Reduction

If Max is identical to something, then this thing can only be Max. The upshot is that the existence of Max is his self-identity. But note that whereas my cat Max, being a contingent being, might not have existed, it is not the case that Max might not have been self-identical. It is true that Max might not have existed, but it is false that Max might not have been Max. So existence cannot be reduced to self-identity. This holds for all contingent beings. Only a necessary being such as God could be such that existence and self-identity are one and the same. The argument, then, is this:

P1. Every contingent existent is possibly nonexistent
P2. No contingent existent is possibly non-self-identical
————
C1. No contingent existent is such that its possible nonexistence = its possible non-self-identity
————
C2. No contingent existent is such that its existence = its self-identity.

It follows that there is more to existence than what is captured by our Quinean biconditionals.

An Objection

Is the above argument decisive? A Quinean might respond by denying (P2) and running the argument in reverse. Insisting that to exist = to be self-identical, he argues that if a thing is contingent (possibly nonexistent), then it is possibly non-self-identical. If Max is contingent, then there is a possible world W in which he doesn't exist. Since Max does not exist in W, he has no properties there. Hence he is neither self-identical nor non-self-identical in W.

Is this objection any good?

Ambiguity, Vagueness, Generality, Disambiguation

Ambiguity. A property of linguistic expressions, primarily. An expression is ambiguous if it has two or more distinct meanings. Back in the day a guy asked me, "Where's your head, man?" I thought he was inquiring into my psychological state, but he merely needed to relieve himself. 'Head' is ambiguous. In its nautical use it refers to a toilet. Ambiguity is either syntactic or semantic. The example lately offered is semantic.

Amphiboly. An amphiboly is a syntactic ambiguity. Scope ambiguity is one subspecies. Consider 'Whatever happens must happen.' On an innocuous parsing with the modal operator operating on the whole sentence, it comes out a trivial logical truth:

Necessarily, whatever happens, happens.

But if the modal operator is imported into the sentence and attached to the consequent of the conditional, we get a probably false piece of fatalist metaphysics:

Whatever happens, necessarily happens.

Equivocation. An equivocation is a semantic ambiguity. Consider this abortion argument:

The fetus is a part of a woman's body.
A woman has the right to do whatever she wants with any part of her body.
Therefore
A woman has the right to do whatever she wants with the fetus, including having it killed.

Is 'part' being used in the same sense in the first and second premises? If not, the argument succumbs to the fallacy of equivocation. I would say that the argument does so succumb. For the minor to be uncontroversially true, the term 'part' must be given a narrow reading that exclude the fetus. But for the major to be true, 'part' must be construed broadly so as to include it. Ergo, etc.

Vagueness. If an ambiguous expression harbors a multiplicity of distinct meanings, a vague expression lacks a definite meaning. Ambiguity and vagueness should therefore not be confused. To have multiple definite meanings is not the same as to have no one definite meaning.

Generality. Statements divide into the singular and the general. General statements divide into the universal, the particular, and the generic. 'Socrates is a man' is singular. 'All men are mortal' and 'Some mortals are men' are universal and particular respectively. 'Germans are industrious' is generic. For more on generics see Generic Statements.

Please avoid the phrase 'vague generalities.' Just as you shouldn't confuse ambiguity with vagueness, you shouldn't confuse vagueness with generality. Most generalizations have a definite meaning.

Disambiguation. If an expression is ambiguous, then it cries out for disambiguation. To disambiguate is to remove ambiguity by listing the different meanings of a word or phrase or sentence.

Class dismissed.

The Function-Argument Schema in the Analysis of Propositions, Part II

A second installment from the Ostrich of London.

Another difficulty with the function-argument theory is staring us in the face, but generally unappreciated for what it is. As Geach says, the theory presupposes an absolute category-difference between names and predicables, which comes out in the choice of ‘fount’ [font] for the schematic letters corresponding to name and predicable. For example ‘Fa’, where the upper case ‘F’ represents the predicable, as Geach calls it, and lower case ‘a’ the name. As a direct result, there is only one negation of the proposition, i.e. ‘~Fa’, where the tilde negates whatever is expressed by ‘Fa’. But ‘F’ is a function mapping the referent of ‘a’ onto the True or the False, so ‘~Fa’ says that a does not map onto the True. The object a is there all right, but maps to a different truth-value. Thus ‘Fa’ implies ExFx, ‘~Fa’ implies Ex~Fx, and excluded middle (Fa or ~Fa) implies that something, i.e. a, does or does not satisfy F. The function-argument account has the bizarre consequence that the name always has a referent, which either does or does not satisfy the predicable. There is no room for the name not being satisfied. Indeed, the whole point of the function theory is to distinguish the idea of satisfaction, which only applies to predicables, from reference, which is a feature of proper names only. As Frege points out here:

The word 'common name' is confusing .. for it makes it look as though the common name stood under the same, or much the same relation to the objects that fall under the concept as the proper name does to a single object. Nothing could be more false! In this case it must, of course, appear as though a common name that belongs to an empty concept were as illegitimate as a proper name that designates [bezeichnet] nothing.

The scholastic two-term account, by contrast, allows for the non-satisfaction of the proper name. ‘Frodo is a hobbit’ is true if and only if something satisfies both ‘hobbit’ and ‘Frodo’. It is essential to Aristotle’s theory of the syllogism, as Geach notes, that the middle term (the one which appears in both premisses) can be subject in one premiss, predicate in another. The notion of ‘satisfaction’ or ‘supposition’ applies to both subject and predicate, even if the subject is a proper name like ‘Frodo’. Thus the negation of ‘Frodo is a hobbit’ can be true in two ways. Either some individual satisfies ‘Frodo’ but does not satisfy ‘hobbit’. We express this in English by so-called predicate negation ‘Frodo is not a hobbit’, where the negative is placed after the copula. Or no individual satisfies ‘Frodo’, which we can express by placing the negation before the whole proposition, ‘it is not the case that Frodo is a hobbit’. So the scholastic theory neatly accounts for empty proper names. Not so for the function-argument theory, a difficulty which was recognised early on. Frege developed a complex and (in my view) ultimately incoherent theory of sense and reference. Russell thought that proper names were really disguised descriptions, which is actually a nod to the scholastic theory.

Of course there is a separate problem for the two term theory, of making sense of a proper name not being ‘satisfied’. What concept is expressed by the proper name that is satisfied or not satisfied, and which continues to exist as a concept even if the individual ceases to exist? Bill and I have discussed this many times, probably too many times for his liking.

BV: What is particularly interesting here is the claim that Russell's theory of proper names is a nod to to the scholastic theory. This sounds right, although we need to bear in mind that Russell's description theory is a theory of ordinary proper names. Russell also allows for logically proper names, which are not definite descriptions in disguise. The Ostrich rightly points out that that for Frege there there is an absolute categorial difference between names and predicables. I add that this is the linguistic mirror of the absolute categorial difference in Frege between objects and concepts (functions). No object is a concept, and no concept is an object. No object can be predicated, and no concept can be named. This leads directly to the Paradox of the Horse: The concept horse is not a concept. Why not? Because 'the concept horse' is a name, and whatever you name is an object.

This is paradoxical and disturbing because it imports ineffability into concepts and thus into logic. If concepts cannot be named and objectified, then they are not wholly graspable. This is connected with the murky notion of the unsaturatedness of concepts. The idea is not that concepts cannot exist uninstantiated; the idea is that concepts have a 'gappy' nature that allows them to combine with objects without the need for a tertium quid to tie them together. Alles klar?

Now it seems to me that Russell maintains the absolute categorial difference between logically proper names and predicates/predicables. ('Predicable' is a Geachian term and it would be nice to hear how the Ostrich defines it.) Correct me if I am wrong, but this presupposition of an absolute categorial difference between logically proper names and predicates/predicables is a presupposition of all standard modern logic. It is 1-1 with the assumption that there are atomic propositions.

Here is one problem. On the Russellian and presumably also on the scholastic theory, an ordinary proper name stands to its nominatum in the same relation as a predicate to the items that satisfy it. Call this relation 'satisfaction.' Socrates satisfies 'Socrates' just as he and Plato et al. satisfy 'philosopher.' Now if an item satisfies a term, then it instantiates the concept expressed by the term. But what is the concept that 'Socrates' expresses? One candidate is: the unique x such that x is the teacher of Plato. Another is: the greatest philosopher who published nothing.

Notice, however, that on this approach singularity goes right out the window. 'Socrates' is a singular term. But 'the greatest philosopher who published nothing' is a general term despite the fact that the latter term, if satisfied, can be satisfied by only one individual in the world that happens to be actual. It is general because it is satisfied by different individuals in different possible worlds. Without prejudice to his identity, Socrates might not have been the greatest philosopher to publish nothing. He might not have been a philosopher at all. So a description theory of names cannot do justice to the haecceity of Socrates. What makes Socrates precisely this individual cannot be some feature accidental to him. Surely the identity of an individual is essential to it.

If we try to frame a concept that captures Socrates' haecceity, we hit a brick wall. Concepts are effable; an individual's haeceity or thisness is ineffable. Aristotle says it somewhere, though not in Latin: Individuum ineffabile est. The individual as such is ineffable. There is no science of the particular qua particular. There is no conceptual understanding of the particular qua particular because the only concepts we can grasp are general in the broad way I am using 'general.' And of course all understanding is conceptual involving as it does the subsumption of particular under concepts.

Some will try the following move. They will say that 'Socrates' expresses the concept, Socrateity, the concept of being Socrates, or being identical to Socrates. But this haecceity concept is a pseudo-concept. For we had to bring in the non-concept Socrates to give it content.

There are no haecceity concepts. As the Ostrich appreciates, this causes trouble for the scholastic two-name theory of predication according to which 'Socrates' and 'wise' are both names, and the naming relation is that of satisfaction. It makes sense to say that the concept wise person is uninstantiated. But it makes no sense to say that the concept Frodoity is uninstantiated for the simple reason that there cannot be any such concept.

It looks like we are at an impasse. We get into serious trouble if we go the Fregean route and hold that names and predicates/predicables are radically disjoint and that the naming/referring relation is toto caelo different from the satisfaction relation. But if we regress to the scholastic two-name theory, then we have a problem with empty names.

The Function-Argument Schema in the Analysis of Propositions

The Ostrich of London sends the following to which I add some comments in blue.

Vallicella: ‘One of Frege's great innovations was to employ the function-argument schema of mathematics in the analysis of propositions’.

Peter Geach (‘History of the Corruptions of Logic’, in Logic Matters 1972, 44-61) thinks it actually originated with Aristotle, who suggests (Perihermenias 16b6) that a sentence is composed of a noun (ὄνομα) and a verb (ῥῆμα), and the verb is a sign of something predicated of something else. According to Geach, Aristotle dropped this name-predicate theory of the proposition later in the Analytics, an epic disaster ‘comparable only to the fall of Adam’, so that logic had to wait more than two thousand years before the ‘restitution of genuine logic’ ushered in by Frege and Russell. By ‘genuine logic’ he means modern predicate logic, which splits a simple proposition into two parts, a function expression, roughly corresponding to a verb, and an argument expression, roughly corresponding to a noun. ‘To Frege we owe it that modern logicians almost universally accept an absolute category-difference between names and predicables; this comes out graphically in the choice of letters from different founts [fonts] of type for the schematic letters of variables answering to these two categories’.

The Fregean theory of the proposition has never seemed coherent to me. Frege began his studies (Jena and Göttinge, 1869–74) as a mathematician. Mathematicians naturally think in terms of ‘functions’ expressing a relation between one number and another. Thus

f(3) = 9

where ‘3’ designates the argument or input to the function, corresponding to Aristotle’s ὄνομα, ‘f()’ the function, here y=x², corresponding to Aristotle’s ῥῆμα, and ‘9’ the value of the function. The problem is the last part. There is nothing in the linguistic form of the proposition which corresponds to the value in the linguistic form of the mathematical function. It is invisible. Now Frege thinks that every propositional function or ‘concept’ maps the argument to one of two values, either the True or the False. OK, but this is a mapping which, unlike the mathematical mapping, cannot be expressed in language. We can of course write

___ is wise(Socrates) = TRUE

but then we have to ask whether that equality is true or false, i.e. whether the function ‘is_wise(–) = TRUE’ itself maps Socrates onto the true or the false. The nature of the value (the ‘truth value’) always eludes us. There is a sort of veil beyond which we cannot reach, as though language were a dark film over the surface of the still water, obscuring our view of the Deep.

BV: First a quibble. There is no need for the copula 'is' in the last formula since, for Frege, concepts (which are functions) are 'unsaturated' (ungesaettigt) or incomplete. What exactly this means, of course, is a separate problem. The following suffices:

___wise(Socrates) = TRUE.

The line segment '___' represents the gappiness or unsaturatedness of the concept expressed by the concept-word (Begriffswort).

Quibbling aside, the Ostrich makes two correct interrelated points, the first negative, the second positive.

The first is that while 'f(3) = 9' displays the value of the function for the argument 3, namely 9, a sentence that expresses a (contingent) proposition does NOT display its truth-value. The truth-value remains invisible. I would add that this is so whether I am staring at a physical sententional inscription or whether I am contemplating a proposition with the eye of the mind. The truth or falsity of a contingent proposition is external to it. No doubt, 'Al is fat' is true iff Al is fat.' But this leaves open the question whether Al is fat. After all the biconditional is true whether or not our man is, in fact, obese.

The second point is that there has to be something external to a contingent proposition (such as the one expressed by 'Socrates is wise') that is involved in its being true, but this 'thing,' — for Frege the truth-value — is ineffable. Its nature eludes us as the Ostrich correctly states. I used the somewhat vague phrase 'involved in its being true' to cover two possibilities. One is the Fregean idea that declarative sentences have both sense and reference and that the referent (Bedeutung) of a whole declarative sentence is a truth-value. The other idea, which makes a lot more sense to me, is that a sentence such as 'Socrates is wise' has a referent, but the referent is a truth-making fact or state of affairs, the fact of Socrates' being wise.

Now both of these approaches have their difficulties. But they have something sound in common, namely, the idea that there has to be something external to the contingent declarative sentence/proposition involved in its being true rather than false. There has to be more to a true proposition than its sense. It has to correspond to reality. But what does this correspondence really come to? Therein lies a major difficulty.

How will the Ostrich solve it? My impression is that he eliminates the difficulty by eliminating reference to the extralinguistic entirely.

Logical Form, Equivocation, and Propositions

Ed Buckner wants to re-fight old battles. I'm game. The following post of his, reproduced verbatim, just appeared at Dale Tuggy's site:

The concept of logical form is essential to any discussion of identity, and hence to any discussion of the Trinity. Here is a puzzle I have been discussing with the famous Bill Vallicella for many years.

(Argument 1) ‘Cicero is a Roman, therefore Cicero is a Roman’

(Argument 2) ‘Cicero is a Roman, therefore Tully is a Roman’

My puzzle [is] that the first argument is clearly not valid if the first ‘Cicero’ means the Roman, the second the American town, yet the argument seems to instantiate a valid form. Bill objects that if there is equivocation, then the argument really has the form ‘a is F, therefore b is F’, which fails to instantiate a valid form.

I then ask what is the form of. Clearly not of the sentences, since the sentences do not include the meaning or the proposition. Is it the form of the proposition expressed by the sentences? But then we have the problem of the second argument, where both ‘Cicero’ and ‘Tully’ mean the same man. Then the man is contained in both propositions, and if the form is of the proposition, the argument has the true form ‘a is F, so a is F’, which is valid. But I think no one would agree that the second argument is valid.

So logical form does not belong to the sentences, nor to the propositions expressed by them. So what is it the form of?

My answer is that the logical form of the argument is the form of the Fregean propositions expressed by the sentences that make up the argument. Let me explain.

I agree with Ed that logical form is not the form of an array of sentence-tokens. It is rather the form of an array of propositions expressed by the sentences. (To be painfully precise: it is the form of an array of propositions expressed by the assertive utterance, and thus the tokening, of a series of sentence-types by a speaker or thinker on a given occasion. A sentence-token buried in a book does not express anything by itself!)

To solve Ed's puzzle we need to distinguish three views of propositions: the Aristotelian, the Fregean, and the Russellian. This would be a good topic for an extended post. Here I will be brief. Brevity is the soul of blog.

An Aristotelian proposition is an assertively uttered meaningful sentence in the indicative mood that expresses a complete thought. What makes such a proposition 'Aristotelian' as opposed to 'Platonic' is that the meaning of the sentence is not something that can subsist on its own apart from the assertive tokening of the sentence. The meaning of the sentence depends on its being expressed, whether in overt speech or in thought, by someone. If there were no minds there would be no Aristotelian propositions. And if there were no languages there would be no Aristotelian propositions. In this sense, Aristotelian propositions are linguistic entities.

In brief: An Aristotelian proposition is just a declarative sentence in use together with its dependent sense or meaning. Suppose I write a declarative sentence on a piece of paper. The Aristotelian proposition is not the string of physical marks on the paper, nor it is the producing of the marks; it is the marks as produced by a minded organism on a particular occasion together with the meaning those marks embody.

A Fregean proposition is a nonlinguistic entity that subsists independently of minds and language. It is the sense (Sinn) of a declarative sentence from which indexical elements have been extruded. For example, 'I am blogging' does not express a Fregean proposition because of the indexical 'I' and because of the present tense of the verb phrase. But 'BV blogs at 10:50 AM PST on 4 September 2017' expresses a Fregean proposition.

Fregean senses are extralinguistic and extramental 'abstract' or 'Platonic' items. They are not in time or space even when the objects they are about are in time and space. This is what makes Fregean propositions 'Platonic' rather than 'Aristotelian.' Fregean propositions are the primary truth-bearers; the sentences that express them are derivatively true or false.

A Russellian proposition is a blurry, hybrid entity that combines some of the features of a Fregean truth-bearer and some of the features of a truth-maker. A Russellian proposition does not reside at the level of sense (Sinn) but at the level of reference (Bedeutung). It is out there in the (natural) world. It is what some of us call a fact or 'concrete fact' (as in my existence book) and others a state of affairs.

Now consider a singular sentence such as 'Ed is happy.' For present purposes, the crucial difference between a Fregean proposition and a Russellian proposition is that, on the Fregean view, the subject constituent of Ed is happy is not Ed himself with skin and hair, but an abstract surrogate that represents him in the Fregean proposition, whereas in the Russellian proposition Ed himself is a constituent of the proposition!

We needn't consider why so many distinguished philosophers have opted for this (monstrous) view. But this is the view that seems to have Ed in its grip and that powers his puzzle above.

If we take the relatively saner (but nonetheless problematic) view that propositions are Fregean in nature, then the puzzle is easily solved.

Ed asks: What is the logical form the form of? He maintains, rightly, that it cannot be the form of an array of sentences. So it must be the form of an array of propositions. Right again. But then he falls into puzzlement:

. . . ‘Cicero’ and ‘Tully’ mean the same man. Then the man is contained in both propositions, and if the form is of the proposition, the argument has the true form ‘a is F, so a is F’, which is valid.

The puzzlement disappears if we reject the Russsellian theory of propositions. A man cannot be contained in a proposition. and so it cannot be the same man in both propositions.

‘Cicero is a Roman, therefore Tully is a Roman’ is plainly invalid. Its form is: Rc, ergo Rt, which is an invalid form. If we adopt either an Aristotelian or a Fregean view of propositions we will not be tempted to think otherwise.

‘Cicero is a Roman, therefore Cicero is a Roman’ is plainly valid. ‘Cicero is a Roman, therefore Tully is a Roman’ is plainly invalid. The logical forms are different! If, on a Russellian theory of propositions, the forms are the same, then so much the worse for a Russellian theory of propositions!

Why Be Consistent? Three Types of Consistency

A reader inquires:

This idea of the necessity to be consistent seems to be the logician's "absolute," as though being inconsistent was the most painful accusation one could endure. [. . .] What rule of life says that one must be absolutely consistent in how one evaluates truth? It is good to argue from first principles but it can also lead one down a rat hole.

Before we can discuss whether one ought to be consistent, we need to know which type of consistency is at issue. There are at least three types of consistency that people often confuse and that need to be kept distinct. I'll call them 'logical,' 'pragmatic,' and 'diachronic.' But it doesn't matter how we label them as long as we keep them separate.

1. Logical or Propositional Consistency. To say of two propositions that they are consistent is to to say that they can both be true, where 'can' expresses logical or broadly logical possibility. To say of two propositions that they are inconsistent is to say that they cannot both be true, where 'cannot' expresses logical or broadly logical impossibility.

I am blogging but not wearing a hat. My blogging is obviously consistent with my not wearing a hat since both propositions are true. But my blogging is also consistent with my wearing a hat since it is possible that I both be blogging and wearing a hat. But I am blogging now and I am not writing now are inconsistent since they cannot both be true. The first proposition entails the second, which implies the impossibility of the first being true and the second false.

P1. Human fetuses have a right to life which cannot be overridden except in rare cases (e.g. threat to the life of the mother).

P2. Capital punishment for certain offences is morally justified.

Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.)

The ‘Is’ of Identity and the ‘Is’ of Predication: Contra Sommers

Dedication: To Bill Clinton who taught us that much can ride on what the meaning of 'is' is.

………………

The Opponent has a very good post in which he raises the question whether the standard analytic distinction between the 'is' of identity and the 'is' of predication is but fallout from an antecedent decision to adhere to an absolute distinction between names and predicates according to which no name is a predicate and no predicate is a name. If the distinction is absolute, as Gottlob Frege and his epigoni maintain, then names cannot occur in predicate position, and a distinction between the two uses of 'is' is the consequence. But what if no such absolute distinction is made? Could one then dispense with the standard analytic distinction between the two uses of 'is'? Or are there reasons independent of Frege's function-argument analysis of propositions for upholding the distinction between the two uses?

To illustrate the putative distinction, consider

1. George Orwell is Eric Blair

and

2. George Orwell is famous.

Both sentences feature a token of 'is.' Now ask yourself: is 'is' functioning in the same way in both sentences? The standard analytic line is that 'is' functions differently in the two sentences. In (1) it expresses (numerical) identity; in (2) it expresses predication. Identity, among other features, is symmetrical; predication is not. That suffices to distinguish the two uses of 'is.' 'Famous' is predicable of Orwell, but Orwell is not predicable of 'famous.' But if Blair is Orwell, then Orwell is Blair.

Now it is clear, I think, that if one begins with the absolute name-predicate distinction, then the other distinction is also required. For if 'Eric Blair' in (1) cannot be construed as a predicate, then surely the 'is' in (1) does not express predication. The question I am raising, however, is whether the distinction between the two uses of 'is' arises ONLY IF one distinguishes absolutely and categorially between names and predicates.

Fred Sommers seems to think so. The Opponent follows him in this. Referencing the example 'The morning star is Venus,' Sommers writes, "Clearly it is only after one has adopted the syntax that prohibits the predication of proper names that one is forced to read 'a is b' dyadically and to see in it a sign of identity." (The Logic of Natural Language, Oxford 1982, p. 121, emphasis added) The contemporary reader will of course wonder how else 'a is b' could be read if it is not read as expressing a dyadic relation between a and b. How the devil could the 'is' in 'a is b' be read as a sign of predication?

The question can be put like this. Can we justify a distinction between the 'is' of identity and the 'is' of predication even if we do not make an absolute distinction between names (object words) and predicates (concept words)? I think we can.

Is it not obvious that if an individual has a property, then it is not identical to that property? Tom is hypertensive. But it would be absurd to say that Tom is identical to this property. This is so whether you think of properties as universals or as particulars (tropes). Suppose the property of being hypertensive (H-ness) is a universal and that Tom's brother Sal is also hypertensive. It follows that they share this property. So if Tom = H-ness, and Sal = H-ness, then, by the transitivity and symmetry of identity, Tom = Sal, which is absurd.

If properties are tropes, we also get an absurdity. On a trope bundle theory, Tom is a bundle of tropes. But surely Tom cannot be identical to one of his tropes, his H-trope. On a trope substratum theory, tropes are like Aristotelian accidents inhering in a substance. But surely no substance is identical to one of its accidents.

So whether properties are universals or tropes, we cannot sensibly think of an individual's having a property in terms of identity with that property. If H-ness is a universal, then we would speak of Tom's instantiating H-ness, where this relation is obviously asymmetrical and for this reason and others distinct from identity.

Now 'H' is a predicate whereas 'H-ness' is a name. But nothing stops us from parsing 'Tom is hypertensive' as 'Tom instantiates hypertensiveness.' This shows that we can uphold the distinction between the 'is' of identity and the 'is' of predication with a two-name theory of predication, and thus without making Frege's absolute distinction between names and predicates. It appears that Sommers is mistaken in his claim that "Clearly it is only after one has adopted the syntax that prohibits the predication of proper names that one is forced to read 'a is b' dyadically and to see in it a sign of identity."

I am assuming of course that we cannot eke by on predicates alone: we need properties. By my lights this should not be controversial in the least. My nominalist Opponent will demur. In 'Orwell is famous' he seems to be wanting to say that 'Orwell' and 'famous' refer to the same thing. But what could that mean?

First of all, 'Orwell' and 'famous' do not have the same extension: there are many famous people, but only one Orwell. 'Orwell is famous' is true. What makes it true? Presumably the fact that 'Orwell' and 'famous' denote one and the same individual. And which individual is that? Why, it's Orwell! But Orwell might not have been famous. Since it is contingent that Orwell is famous, but noncontingent that Orwell is Orwell, the truth-maker of 'Orwell is famous' cannot be Orwell alone. It has has to be the fact of Orwell's being famous, which fact involves the property of being famous in addition to Orwell.

Nominalists insist that we ought not multiply entities beyond necessity. They are right! But there is no multiplication beyond necessity here since we need to admit properties as features of extralinguistic reality. To explain why 'Orwell is famous' is contingent, one must distinguish Orwell from his contingently possessed properties. Man does not live or think truly by predicates alone.

Generic Statements

Statements divide into the singular and the general. General statements divide into the universal, the particular, and the generic. Generic statements are interesting not only to the logician and linguist and philosopher but also to critics of ideology and conservative critics of leftist ideology critique. For example, leftists will find something 'ideological' about the generic 'Women are nurturing' whereas conservatives will hold that the sentence expresses the plain truth and that some sort of obfuscation and chicanery is involved when leftists deny this plain biologically-based truth and try to tie its very meaning to the legitimation and preservation of existing power relations in society.

In this entry, perhaps the first in a series, I confine myself to presenting examples of generic statements and to giving a preliminary exegesis of the linguistic data, noting some features of generic generalizations, and some philosophical questions that arise.

Examples of Generic Statements

Some of the examples are my own, some are culled from the literature. Some of the following are true, some false, and some politically incorrect. Trigger Warning! All girly girls and pajama boys out of the seminar room and into their safe spaces! Uncle Bill will visit you later with milk and cookies and cuddly animals.

Dutchmen are good sailors. (Arnauld)
Germans are industrious.
Jews are very intelligent.
Birds fly.
Chickens lay eggs.
Germans make better soldiers than Italians.
Cigars are what Bill smokes these days.
Men are taller than women.
Blacks are more criminally prone than whites.
Priests don't ride motorcycles.
Reducing taxes leads to increased economic growth.
Turks are hospitable.
Turks are very bad drivers.
Analytic philosophers do not know the history of philosophy very well.
Humanities departments are lousy with leftists.
The dodo is extinct.
Schockley invented the transistor.
The lion has a mane.
Blacks are not good at deferring gratification.
Conservatives are racists.
Women are nurturing and better with children.
Fred drinks wine with dinner.
The potato is highly digestible.

Some Features of Generic Statements

One obvious feature of generic statements is that they are not replaceable either salva veritate or salva significatione by either universal or particular quantified statements. It is true that Germans are industrious, but false that all are. That some are is true, but 'Some Germans are industrious' does not convey the sense of 'Germans are industrious.' The generic and the particular generalization agree in truth value but differ in sense.

In a vast number of cases, if I assert that the Fs are Gs I do not mean to endorse the corresponding universal generalization. No doubt birds fly, but it is false that all birds fly: the penguin is a bird, but it doesn't fly. And I know that. So if I say that birds fly, you can't refute me by bringing up the penguin. And if I say that Italians and those of Italian extraction are frugal and masters of personal finance, which is manifestly true, you cannot refute me by bringing up your cousin Vinny, the spendthrift of Hoboken. The same goes for 'Humanities departments are lousy with leftists.' 'Chickens lay eggs' has the interesting property that all the roosters strutting around in the world's barnyards cannot counterexample it into falsehood.

It is interesting to note that one can make a generic statement (express a generic proposition) using a sentence with 'all' or 'every.' My example: Omnis homo mendax. 'Every man is a liar.' An assertive utterance of this sentence in normal contexts expresses the proposition that people lie, not the proposition that all people lie. Or if someone says, unguardedly, or Trumpianly, 'All politicians are crooks,' he won't be fazed if you point out that the late Patrick Daniel Moynihan was no crook. The speaker may have engaged in a hasty generalization, but then again he may have intended a generic statement.

On the other hand, we sometimes omit the universal quantifier even though the proposition we intend to express is a universal quantification. An assertive utterance of 'Arguments have premises' intends Every argument has premises. The possibility of counterexamples is not countenanced. Contrast this with the generic 'Chickens lay eggs' which is plainly true even though only hens lay eggs.

'Arguments have premises' is non-generic and elliptical for 'All arguments have premises.' But what about 'Men are mortal'? Is it replaceable salva significatione with 'All men are mortal'? Perhaps not, perhaps it is a generic statement that admits of exceptions, as generics typically do. After all, Christ was a man but he was not mortal inasmuch as he was also God.

A clearer example is 'Man is bipedal.' This cannot be replaced salva veritate by 'All men are bipedal' since the latter is false. Nor can it be replaced salva significatione by 'Some man is bipedal, which, though plainly true, is not what 'Man is bipedal' means. And the same holds for translations using the quantifiers 'many' and 'most' and 'almost all.'

We are tempted to say that 'Man is bipedal' by its very sense cannot be about individual humans, whether all of them, most of them, many of them, or some of them, but must be about a common generic essence that normal, non-defective humans instantiate. But how could this be? No generic essence has two feet. It is always only an individual man that has or lacks two feet. Here, then, is one of the philosophical puzzles that arise when we think about generic statements. It is the problem of what generic statements are about, which is not to be confused with the question whether they have truth makers.

And then there is 'Man is a rational animal.' Let us agree that to be rational is either to possess the capacity to reason or to possess the second-order capacity to develop this first-order capacity. Aristotle's dictum is true, while 'All humans are rational animals' is false. So Aristotle's dictum is a generic sentence that cannot be replaced by a quantified sentence. It is false that all humans are rational animals because an anencephalic human fetus, while obviously human (not bovine, canine, etc.), having as it does human parents, is not rational in the sense defined.

And of course we cannot replace 'Man is a rational animal' with 'Most men are rational animals.' For the dictum plainly intends something like: it the nature or essence of man to be rational. What then is the dictum about? If you tell me that it is about the generic essence man, then I will point out the obvious: no abstract object reasons, is capable of reasoning, or has the potentiality to acquire the power to reason.

Some philosophers hold that every truth has a truth-maker. What then are the truth-makers for the vast class of true generics? Do they have any?

REFERENCE

Panayot Butchvarov, Anthropocentrism in Philosophy: Realism, Antirealism, Semirealism, de Gruyter, 2015, Chapter 8, "Generic Statements," pp. 151-168.

‘Women are Better at Looking After Children’

The Opponent supplies the above-captioned sentence for analysis. He reports that a female family member was widely defriended (unfriended?) on Facebook for agreeing that it is true. Of course the sentence is true as anyone with common sense and experience of life knows.

It is an example of a generic statement or generic generalization. It obviously does not mean that all women are better at looking after children. The Opponent writes,

I think the PC brigade would claim that any utterance whatsoever of ‘women are better at looking after children’ has a separate implicature, i.e. ‘what is suggested in an utterance, even though neither expressed nor strictly implied.’ Something like ‘women belong in the home’, i.e. the normative 'women ought to be at home looking after the children.'

No?

The Opponent and I agree that the sentence under analysis is true. This leaves three questions.

First, does the non-normative sentence conventionally imply the normative one? Is there conventional implicature here? We of course agree that we are not in the presence of logical implication or entailment.

Second, is there conversational implicature here?

Third, is the normative sentence true?

As for the first question,I find no conventional implicature. A conventional implicature is a non-logical implication that is not context-sensitive but depends solely on the conventional meanings of the words in the relevant sentences. For example, 'Tom is poor but happy' implies that poverty and happiness are not usually found together. This is not a logical implication; it is a case of conventional implicature. Same with 'Mary had a baby and got married.' This is logically consistent with the birth's coming before the marriage and the marriage's coming before the birth. But it conventionally implies that Mary had a baby and then got married. This implicature is not sensitive to context of use but is inscribed in (as a Continental philosopher might say) the language system itself.

What about conversational implicature? This varies from context of use to context of use. Consider my kind of conservative, the traditional conservative that rejects both the conservatism of the neo-cons and the white-race-based identity-political conservatism of the Alternative Right. My brand of conservatism embraces certain classical liberal commitments, including: universal suffrage, the right of women to own property in their own names, and the right of women to pursue careers outside the home.

So if conservatives of my type are conversing and one says, 'Women are better at looking after children,' then this does not conversationally imply that women ought to be at home looking after the children. But among a different type of conservative, an ultra-traditional conservative who holds that woman's place is in the home, then we are in the presence of a conversational implicature.

Finally, is it true that women ought to be at home looking after children? I would say No in keeping with my brand of conservatism, which I warmly recommend as the best type there is, avoiding as it does the extremism of the ultra-traditional throne-and-altar, women-tied-to-the-stove conservatism (men are better cooks in any case), the namby-pamby libertarian-conservative fusionism of the Wall Streer Journal types, and the race-based identity-political extremism of the 'alties' and the neo-reactionaries.

Now if this were part of a journal article, I would not preen like this. But this ain't no journal article. This here's a blog post, bashed out quickly.

Blogging's a 'sport' like speed chess.

Your move, Opponent.

The Two Opposites of ‘Nothing’ and the Logical Irreducibility of Being

This entry is part of the ongoing debate with the Opponent.

D1. Nothing is F =_df It is not the case that something is F.

D2. Something is F =_df it is not the case that nothing is F.

We also note that as quantifiers, as terms expressing logical quantity, 'nothing' and 'something' are not names or referring expressions.

So far I have said nothing controversial.

Quine said that "Existence is what existential quantification expresses." I deny it: there is more to existence than what the existential quantifier expresses. Quine's is a thin theory of existence; mine is a thick theory. Metaphorically, existence possesses an ontological thickness. This is very important for metaphysics if true.

I won't be able to prove my point because nothing in philosophy can be proven. But I can argue for my point in a fallacy-free manner.

D3. y is/exists =_df for some x, y = x.

Quine exists =_df Quine is identical to something that exists

and

Pegasus does not exist =_df nothing that exists is such that Pegasus is identical to it

Pegasus is diverse from everything that exists.

The conclusion is obvious: one cannot explicate the existential 'is' in terms of the particular quantifier without circularity, without presupposing that things exist in a sense of 'exist' that is not captured by (D3).

So far, not good: I can't refute the Opponent but he can't refute me. Stand-off. Impasse, a-poria.

Let me try a different tack. Does the Opponent accept

ENN. Ex nihilo nihil fit?

Now if the Opponent accepts the truth or even just the meaningfulness of (ENN), then he must admit that there are two senses of 'nothing,' the logical and the ontological, and correspondingly, two senses of 'something.' If so, then being and nothing cannot be exhaustively understood in terms of logical quantifiers and propsitional negation, and then the thin theory bites the dust.

But if the thin theory succumbs, then there is more to existence than can be captured within the Discursive Framework.