Category: Language, Philosophy of

Of ‘Of’

As useful as it is to the poet, the punster, and the demagogue, the ambiguity of ordinary language is intolerable to the philosopher.  Disambiguate we must.  One type of ambiguity is well illustrated by the Old Testament verse, Timor domini initium sapientiae, "The fear of the Lord is the beginning of wisdom."  'Of' functions differently in 'fear of the Lord' and 'beginning of wisdom.'

Clearly, in 'fear of the Lord' the Lord is the object, not the subject of fear: the Lord is the one feared, not the one who fears.  In 'beginning of wisdom,' however, wisdom is the subject of beginning, that which begins; it is not the  object of beginning — whatever that would mean. Thus we could write, "The fear of the Lord is wisdom's beginning," but not, "The Lord's fear is wisdom's beginning."

The foregoing is an example of subject/object ambiguity.  Here is an example of what I will call objective/appositive ambiguity: 'As a young man, I was enamored of the city of Boston.'  The thought here is that the city, Boston, was an object of my love.  Clearly, 'of' is being used in two totally different ways in the sample sentence.

I wonder if all uses of 'of' can be crammed into the following little schema:

A. Subjective Uses of 'Of.'  'The presidency of  Bill Clinton was rocked by scandal.'  'The redness of her face betrayed her embarrasment.'   'She cited the lateness of the hour as her reason for leaving.'  The presidency of Bill Clinton is Bill Clinton's presidency.  And similarly in the other two examples.

Here 'of' expresses possession or belonging.  The sharpness of the knife is the knife's sharpness.  The wife of Tom is Tom's wife.  The uncle of the monkey is the monkey's uncle.  The ace of spades is the ace belonging to the spade suit.  A jack of all trades is all trades' jack.  Of course, if you want to be understood in English you cannot say, 'Marvin is all trades' jack.'  But that's irrelevant.

The set of natural numbers is the natural numbers' set.  The set of all sets is all sets' set. 

'Several are the senses of "of."'   The 'of' which is used — as opposed to mentioned — functions subjectively inasmuch as the thought could be put as follows: '"Of"'s senses are several.'

The square root of -1 is -1's square root.

B. Objective Uses of 'Of.'  'When I first met Mary, thoughts of her occupied my mind from morning until night.' Obviously, her thoughts could not occupy my mind; 'thoughts of her' can only mean my thoughts about her. Note that 'Mary's thoughts' could be construed in three ways: Mary's thoughts; thoughts about Mary; Mary's thoughts about herself.

Pictures of Lily are pictures that depict (are about) Lily.

'What was once called the Department of War is now called the Department of Defense.'  It would not be idiomatic to refer to the Department of Defense as the department about defense, but this is presumably the thought: the DOD is the department concerned with defense.

'The study of logic will profit only those of a certain cast of mind.'    This sentence features first the objective, then the subjective use of  'of.'  The thought is: The study which takes logic as its object will profit only those whose mind's cast is such-and-such.

'The Sage of the Superstitions is a man of leisure.'  This sentence features first the subjective, then the objective use of 'of.'  The thought is: The Superstition Mountains' sage is about (is devoted to) leisure.

'Of all Ponzi schemes, that of Bernie Madoff was the most successful.'  The first 'of' is objective, the second subjective.  The thought is:  Concerning (with respect to) all Ponzi schemes, Bernie Madoff's scheme was the most successful.

C. Dual Uses of 'Of.'  'Thoughts of Mary filled Mary's mind.' In this example, Mary is both the subject and the object of her thoughts, assuming that 'Mary' refers to the same person in all occurrences.  So in 'thoughts of Mary,' 'of' functions both subjectively and objectively.

D. Appositive Uses of 'Of.'  'The train they call The City of New Orleans will go five hundred miles before the day is done.' 'Former NYC mayor Ed Koch referred to the city of Boston as Podunk.' Clearly, 'city of Boston' is not a genitive construction, logically speaking. We could just as well write, 'the city, Boston.' So I call the 'of'  in 'city of Boston' the 'of' of apposition. If the grammarians don't call it that, then they ought to.

The House of the Rising Sun is not the rising sun's house — the sun, rising or setting,  'don't need no stinkin' house' — or the house devoted to the study of the rising sun, but the house, The Rising Sun. 

The kingdom of Heaven is the kingdom, Heaven.

ADDENDUM:  A little more thought reveals that my quick little schema is inadequate.  Where would these examples fit:  'He drank a glass of wine.'  'She purchased ten gallons of gasoline.'  'Boots of Spanish leather are all I'm wishin' to be ownin'." (Bob Dylan)  'He is a man of the cloth.'

'Glass of wine' expresses a relation between a container and what it contains, and that does not seem to fit any of the four heads above.  And note that 'a gallon of gasoline' is unlike 'a glass of wine.'  A gallon is a unit of measure whereas a glass, though it could be a unit of measure, is a receptacle.  A gallon is not a receptacle.  'Hand me that gallon' makes no sense.  'Hand me that gallon can' does.

Collective Inconsistency and Plural Predication

We often say things like

1. The propositions p, q, r are inconsistent.

Suppose, to keep things simple, that each of the three propositions is self-consistent.  It will then be false that each proposition is self-inconsistent. (1), then, is a plural predication that cannot be given a distributive paraphrase.  What (1) says is that the three propositions are collectively inconsistent.  This suggests to many of us  that there must be some one single entity that is the bearer of the inconsistency.  For if the inconsistency does not attach distributively to each of p, q, and r, then it attaches to something distinct from them of which they are members.  But what could that be?

If you say that it is the set {p, q, r} that is inconsistent, then the response will be that a set is not the sort of entity that can be either consistent or inconsistent.  Note that it is not helpful to say

A set is consistent (inconsistent) iff its members are consistent (inconsistent).

For that leaves us with the problem of the proper parsing of the right-hand side, which is the problem with which we started.

And the same goes for the mereological sum (p + q + r).  A sum or fusion is not the sort of entity that can be either consistent or inconsistent.

What about the conjunction p & q & r?  A conjunction of propositions is itself a proposition.  (A set of propositions is not itself a proposition.) This seems to do the trick. We can parse (1) as

2. The conjunctive proposition p & q & r is (self)-inconsistent.

In this way we avoid construing (1) as an irreducibly plural predication.  For we now have a single entity that can serve as the logical subject of the predicate ' . . . is/are inconsistent.'  We can avoid saying, at least in this case, something that strikes me as only marginally intelligible, namely, that there are irreducible monadic non-distributive predicates.  My problem with irreducibly plural predication is that I don't know what it means to say of some things that they are F if that doesn't mean one of the following: (i) each of the things is F; (ii) there is a single 'collective entity' that is F; or (iii) the predicate 'is F'  is really relational. 

One could conceivably object that in the move from (1) to (2) I have 'changed the subject.'  (1) predicates inconsistency of some propositions, while (2) predicates (self)-inconsistency of a single conjunctive proposition.  Does this amount to a changing of thr subject?  Does (2) say something different about something different?

A Problem With the Multiple Relations Approach to Plural Predication

Consider

1. Sam and Dave are meeting together.

2. Al, Bill, and Carl are meeting together.

3. Some people are meeting together.

Obviously, neither (1) nor (2) can be decomposed into a conjunction of singular predications.  Thus (2) cannot be analyzed as 'Al is meeting together & Bill is meeting together & Carl is meeting together.'  So it is natural to try to analyze (1) and (2) using relational predicates.  (1) becomes

1R. Meeting(Sam, Dave)   In symbols: Msd

But if 'meeting' is a dyadic (two-place) predicate, then we should expect (2) to give way to

2R. Mab & Mbc & Mac.

Unfortunately, (2R) is true in circumstances in which (2) is false.  Suppose there are three separate meetings.  Then (2R) is true and (2) false.  To get around this difficulty, we can introduce a triadic relation M* which yields as analysans of (2):

2R*. M*abc.

But then we need a tetradic relation should Diana come to the meeting.  And so on, with the result that 'meeting together' picks out a family of relations of different polyadicities.  But what's wrong with that?  Well, note that (1) and (2) each entail (3) by Existential Generalization in the presence of the auxiliary premise 'Al, Bill, Carl, Dave, and Sam are people.' 

But then we are going to have difficulty explaining the validity of the two instances of Existential Generalization.  For the one instance features a dyadic meeting relation and  the other a triadic.  If two different relations are involved, then what is the logical form of (3) — Some people are meeting together — which is the common conclusion of both instances of Existential Generalization?  If 'meeting together picks out a family of relations of different 'adicities, then (3) has no one definite logical form.

Does this convince you that the multiple relations approach is unworkable?

REFERENCE:  Thomas McKay, Plural Predication (Oxford 2006), pp. 19-21.

 

Irreducibly Plural Predication: ‘They are Surrounding the Building’

Let's think about the perfectly ordinary and obviously intelligible sentence,

1. They are surrounding the building.

I borrow the example from Thomas McKay, Plural Predication (Oxford 2006), p. 29.  They could be demonstrators.  And unless some of them have very long arms, there is no way that any one of them could satisfy the predicate, 'is surrounding the building.'  So it is obvious that (1) cannot be analyzed in terms of 'Al is surrounding the building & Bill is surrounding the building & Carl is surrounding the building & . . . .'  It cannot be analyzed in the way one could analyze 'They are demonstrators.'  The latter is susceptible of a distributive reading; (1) is not.  For example, 'Al is a demonstrator & Bill is a demonstrator & Carl is a demonstrator & . . . .'  So although 'They are demonstrators' is a plural predication, it is not an irreducibly plural predication.  It reduces to a conjunction of singular predications.

Continue reading “Irreducibly Plural Predication: ‘They are Surrounding the Building’”

The Hatfields and the McCoys

Whether or not it is true, the following  has a clear sense:

1. The Hatfields outnumber the McCoys.

(1) says that the number of Hatfields is strictly greater than the number of McCoys.  It obviously does not say, of each Hatfield, that he outnumbers some McCoy.  If Gomer is a Hatfield and Goober a McCoy, it is nonsense to say of Gomer that he outnumbers Goober. The Hatfields 'collectively' outnumber the McCoys. 

It therefore seems that there must be something in addition to the individual Hatfields (Gomer, Jethro, Jed, et al.) and something in addition to the individual McCoys (Goober, Phineas, Prudence, et al.) that serve as logical subjects of number predicates.  In

2. The Hatfields are 100 strong

it cannot be any individual Hatfield that is 100 strong.  This suggests that there must be some one single entity, distinct but not wholly distinct from the individual Hatfields, and having them as members, that is the logical subject or bearer of the predicate '100 strong.'

So here is a challenge to William the nominalist.  Provide analyses of (1) and (2) that make it unnecessary to posit a collective entity (whether set, mereological sum, or whatever) in addition to individual Hatfields and McCoys.

Nominalists and realists alike agree that one must not "multiply entities beyond necessity."   Entia non sunt multiplicanda praeter necessitatem!  The question, of course, hinges on what's necessary for explanatory purposes.  So the challenge for William the nominalist is to provide analyses of (1) and (2) that capture the sense of the analysanda and obviate the felt need to posit entities in addition to concrete particulars.

Now if such analyses could be provided, it would not follow that there are no 'collective entities.'  But a reason for positing them would have been removed.

I Need to Study Plural Predication

Here is a beautiful aphorism from Nicolás Gómez Dávila (1913-1994), in Escolios a un Texto Implicito (1977), II, 80, tr. Gilleland: 

Stupid ideas are immortal. Each new generation invents them anew.

Clearly this does not mean:

1. Each stupid idea is immortal and is invented by each new generation anew.

So we try:

2. The set of stupid ideas is immortal in the sense that every new generation invents some stupid idea or other.

(2) is much closer to the intended meaning. The idea is that there are always stupid ideas around, not that any one stupid idea is always around. (2) seems to capture this notion. But (2) presents its own puzzles. A set is a collection, and a collection is not the mere manifold of its members: it is "a further entity over and above them" as Michael Potter puts it in Set Theory and its Philosophy (Oxford 2004, p. 22).

Potter speaks of collections versus fusions. The distinction emerges starkly when we consider that there is a distinction between a singleton collection and its member, but no distinction between a 'singleton' fusion and its member. Thus Quine is distinct from {Quine}, the set consisting of Quine and nothing else. But there is no distinction between Quine and the sum or fusion, (Quine). {Quine}, unlike Quine, has a member; but neither (Quine) nor Quine have members. A second difference is that, while it makes sense to speak of a set with no members, the celebrated null set, it makes no sense to speak of a null fusion. The set consisting of nothing, the null set { } is something; the fusion of nothing is nothing.

Getting back to stupid ideas, what I want to say is that 'stupid ideas are immortal' can be understood neither along the lines of (1) nor along the lines of (2). The generality expressed is quite obviously not distributive, but it is not quite collective either. We are not expressing the idea that there is some one entity "over and above" its members to which immortality is being ascribed. 'Stupid ideas' seems to pick out a fusion; but if a fusion is a pure manifold, how can it be picked out?  

The puzzle is that immortality is not being predicated of each stupid idea, but it is also not being predicated of some one item distinct from stupid ideas which has them as members, whether this one item be a mathematical set or a mereological sum.

We know what we mean when we say that stupid ideas are immortal, but we cannot make it precise, or at least I can't make it precise given my present level of logical acumen.

So rather than contribute any stupid ideas of my own, I will go to the library and check out Thomas McKay's Plural Predication.  

 

More on the God of the Philosophers

Spencer Case, 'on the ground' in Afghanistan, e-mails:

Your recent post discussing the God of the philosophers and the God of Abraham and Isaac caught my interest. Having grown up in a religious home, I have always been of the opinion that arguments for theism argue for something different than what believers take themselves to believe in. After all, how many religious people take themselves to be praying to an unmoved mover or a-being-greater-than-which-cannot-be-conceived? For this reason, I have not felt that my atheism could be threatened by any of the arguments for theism, even if they turn out to be successful because they argue not for God but for God*.

No doubt it could be true that you could make an identification between the God of the philosophers and the God of the believers if you have established the existence of both. My point is none of the arguments for the existence of God even try to argue for the God of the believers.

I look forward to hearing your thoughts.

Well, Spencer, it looks as if my earlier post, despite its pellucidity and penetration, made no impression on you.

Let's use 'God-P' to mean 'God of the philosophers' and 'God-R' to mean 'God of the religionists.'  Now my claim is that the two phrases, though the differ in sense, have the same referent, if they have a referent.  Thus I do not assume that they in fact have a common referent; my claim is that, if they have a referent, then they have a common referent.  You are undoubtedly familiar with Frege's distinction between Sinn and Bedeutung.  To use his old example, 'morning star' and 'evening star' have the same referent despite their difference in sense and in mode of presentation (Darstellungsweise).    One and the same celestial body — the planet Venus — is presented in two different ways.  Now in this case we know that the terms 'morning star' and 'evening star' have a common referent whereas in the God case we do not know this.  So my claim is merely that 'God-P' and 'God-R' refer to one and the same entity if they refer to anything.

It may help to distinguish between REFERENCE and REFERENT.  'Meinong's favorite impossible object' and 'the round square' both lack a referent; but they have the same REFERENCE despite their manifest difference in sense.

Therefore, I reject your assertion that one needs to establish the existence of a common referent of 'God-P' and 'God-R' as a condition of establishing that they refer to the same thing if they refer at all. 

Your main argument seems to be as follows:

1.  The philosophical arguments for God are arguments for the existence of God-P, not of God-R.

2.  Religious people qua religious people do not believe in or affirm the existence of God-P, but of God-R. (E.g. religious people who think about God or address God in prayer are not relating to an unmoved mover.)

3.  Atheism is the denial of the existence of God-R.  Therefore:

4.  The philosophical God arguments, even if sound, have no tendency to show that atheism is false.

A very interesting argument!  I reject the argument  by rejecting the assumption on which it is based, namely, that God-P is not identical to God-R.  To the contrary, I claim that they are the same God, albeit approached in different ways.  The philosopher qua philosopher approaches God via discursive reason unassisted by scriptural or other revelation, whereas the religionist approaches God via faith and revelation.  Now it may be (it is epistemically possible that) there is no God; but that does not alter the fact that the REFERENCE of the God-talk of philosophers and that of religionists is the same.

Think about it:  when Aquinas was working out his Five Ways, was he trying to establish the existence of a mere concept or abstract idea?  How could a mere concept create heaven and earth?  Was he trying to prove the existence of something numerically different from the God of the Bible?  Of course not.  Aquinas was a philosopher, a religionist, and a mystic.  It was the same God he was aiming at (and from his point of view, contacting) in his philosophical reasoning, his prayerful devotions, and his mystical experiences.

People get confused by the phrases 'God of the philosophers' and 'God of Abraham, Isaac, and Jacob.'  They think that because the phrases are different, and their senses also, that the phrases cannot have the same reference.  But the reference is the same even if there in is no God.  For the concept of God we are operating with is the concept of a being that satisfies both narrowly philosophical and narrowly religious exigencies.  And this is so whether or not the concept is instantiated.  The philosopher qua  philosopher wants an explanation of the existence and intelligibility of contingent beings and finds his explanation in God, who is the real-ground of existence and intelligibility.  The religionist qua religionist has a soteriological interest: he seeks a solution to our awful predicament in this life, and finds his solution is a relationship with a personal Being.  Now what needs to be understood is that that real-ground and this personal Being are the same.

Or do you think that God can't walk down the street and chew gum at the same time?

Richard Gaskin on the Unity of the Proposition

The current issue of Dialectica (vol. 64, no. 2, June 2010) includes a symposium on Richard Gaskin, The Unity of the Proposition (Oxford 2008).  Gaskin's precis of his work is followed by critical evaluations by William F. Vallicella ("Gaskin on the Unity of the Proposition"), Manuel Garcia-Carpintero ("Gaskin's Ideal Unity"), and Benjamin Schnieder ("Propositions United: Gaskin on Bradley's Regress and the Unity of the Proposition").  The symposium concludes with Gaskin's replies ("The Unity of the Proposition: Replies to Vallicella, Schnieder, and Garcia-Carpintero"). 

Predicates and Properties

We are warming up to an examination of deflationary theories of truth according to which truth is either not a property or not a metaphysically substantive property.  (I oppose deflationary theories of truth just as I oppose deflationary theories of existence.) But first some clarification of 'predicate' and 'property.'

1. I begin by resisting the traditional conflation of predicates and properties, a conflation in evidence when we hear a philosopher claim that "existence is not a predicate."  That claim makes no sense unless a predicate is a property.  After all, 'existence,' as an abstract substantive, is not grammattically tuited to occupy predicate position.  If, however, a predicate is a bit of language used to express a property, then the claim should be that " '. . . exists' is not a predicate."  That's in order, as is "Existence is not a property."  As expressing properties, predicates are distinct from properties.  Predicates are linguistic while properties are extralinguistic.

To be a bit more precise, predicates (whether types or tokens) are tied to particular languages whereas the properties they express are not so tied.  Thus schwarz is tied to German in the way black is tied to English, but the property of being black is tied to neither.  Equally, the property of being disyllabic is tied to no one language even though it is a property that only linguistic items can have.  Thus 'Boston' but not Boston is disyllabic.

2. Some of you will question whether there are properties distinct from predicates.  Question away.  But just realize that in order to raise this very question you must first have distinguished predicates and properties.  You must already have made the distinction 'at the level of intension' if not 'at the level of extension.'  For you cannot maintain that there are no properties distinct from predicates unless you understand the term 'property' just as you cannot maintain that there are no unicorns distinct from horses unless you understand the term 'unicorn.'

3. By my lights, you are a very foolish philosopher if you deny properties, but not if you deny universals.  If you deny universals you are merely mistaken.  So let's be clear that 'property' and 'universal' are not to be used interchangeably.  It is a substantive question whether properties are universals or particulars (as trope theorists maintain).  Universals I define as repeatable entities, particulars as unrepeatable entities.

4. The predicate/property distinction under our belts, we need to note three views on their relation.

5. One view is that  no predicate expresses a property.  I rejected this view in #3.  To put it bluntly, there is a real world out there, and the things in it have properties whether or not there are any languages and language-users. Some of our predicates succeed more or less in expressing some of these properties.

6. A second view is that every predicate expresses or denotes a property.  The idea is that for every predicate 'P' there is a property P corresponding to 'P.'  But then, given that 'exists' and 'true' are predicates, it would follow straightaway that existence and truth are properties.  And that seems too easy.  Deflationists, after all, deny for reasons that cannot simply be dismissed that truth is a property.  They cannot be refuted by pointing out that 'true' is a predicate of English.  The following equivalence is undeniable but also not formulable unless 'true'  is a predicate:

'Grass is green' is true iff grass is green.

The deflationist will take an equivalence like this to show that 'true' is a dispensable predicate and therefore one that does not pick out a property.  (On Quine's disquotationalism, for example, 'is true' is a device of disquotation: it merely undoes the semantic ascent displayed on the LHS of the biconditional.)  We should therefore be uneasy about the view that every predicate expresses or denotes a property.  The existence of a predicate does not show the existence of a corresponding property.  A predicate need not predicate a property.  It should not be a matter of terminological fallout that wherever there is a predicate there is a property.

7.  Determined to maintain  that every predicate expresses or denotes a property, a deflationist  could of course hold that existence and truth are properties, but not metaphysically substantive properties.  A deflationist could argue like this:

Every predicate expresses a property

'True' is a predicate

Ergo: Truth is a property, but not a substantive one.

But he could also argue like this:

Every genuine predicate expresses a substantive property

Truth is not a substantive property

Ergo: 'True' is not a genuine predicate.

8.  A third view about the predicate-property relation has it that some predicates pick out properties and some don't.  I suggest this is how we should use 'predicate.'  It then becomes a matter of investigation, not of terminology, whether or not there is a property for a given predicate.

Another Round on Assertoric Force

William Woking comments:

Logical argument is just like a chess game. We have a common understanding of the rules of inference. The game ends either in reaching disagreement about a principle that is demonstrably fundamental, i.e., it self-evidently admits of no proof or disproof (e.g., Bill hates carrots), in which case stalemate, or where both sides end in agreeing upon a set of fundamental principles from which the truth of the winner's thesis follows with logical certainty.

———————- The argument so far ————————-

(Woking Thesis) Expression types (e.g. declarative sentences) can have assertoric force.

[Vallicella objection]
(Major) If an expression-type has assertoric force, every token of it has assertoric force
(Minor) A token of any sentence may occur in a context where it has no assertoric force
(Conclusion) No expression-type has assertoric force.

(Proof of the minor) Take any declarative sentence-type such as 'Socrates runs'. But it has no assertoric force in the consequence 'If Socrates runs, Socrates moves'.

(Reply to objection)
I concede the argument of the objection is valid. I concede the major. I dispute the minor. Against the proof of the minor. 'Socrates runs' does have assertoric force in the 'If Socrates runs, Socrates moves'. However, its force is cancelled out by the 'if then' operator.

The minor is thus the bone of contention.  We agree that in 'If Socrates runs, then he moves' the protasis of the conditional lacks assertoric force.  (I note en passant that the apodosis also lacks assertoric force.) But we disagree as to why the protasis of the conditional lacks assertoric force.  I say it is because no sentence-type intrinsically and as such has assertoric force.  Woking say is it is because there are contexts in which semantic cancellation removes the assertoric force which all declarative sentence-types possess intrinsically and as such. 

One objection to semantic cancellation is that it is inconsistent with the thesis of the compositionality of meaning, a thesis which Woking accepts, together with the thesis that assertoric force is a semantic component.  According to compositionality of meaning, a sentence-type is a semantic whole composed of, and built up out of, semantic parts.  Now given that assertoric force is a semantic component, and that wholes have their parts essentially, then the meaning of a sentence-type has its assertoric meaning component essentially, which implies that no sentence-type can have its assertoric force removed by semantic cancellation.  So either no sentence-type has assertoric force, as I maintain, or every sentence-type has assertoric force, whence it follows, contrary to what Woking maintains, that it is not the case that some sentence-types do, and some do not, have their assertoric force removed by semantic cancellation.  The argument, then, is this:

1. Compositionality of Meaning: The meaning of a sentence-type is a whole of parts.

2. Assertoric force is a semantic component of the meaning of a sentence-type.

3. Mereological Essentialism: wholes have their parts essentially: if x is a part of W, then necessarily x is a part of W.

4. The assertoric force of the meaning of a sentence-type is essential to it. (from 1, 2, 3)

5. If x is essential to y, then y cannot exist without x.

6. The meaning of a sentence-type cannot exist without its assertoric component. (from 4, 5)

7. A sentence-type's assertoric component, if it has one, cannot be removed by semantic cancellation, or in any other way. (from 6)

8. Either no sentence-type or every sentence-type possesses assertoric force intrinsically and as such. (from 7)

9. Some sentence-types do not possess assertoric force.

10. No sentence-type possesses assertoric force intrinsically and as such. (from 8, 9)

It appears that only by rejecting Mereological Essentialism can Woking evade this argument.  For the inferences are valid and the other premises he accepts.  But I should think that ME is far more credible than his somewhat vague talk of semantic cancellation.

Is There a Paradox of Conjunction?

There are supposed to be paradoxes of material and strict implication. If there are, why is there no paradox of conjunction? And if there is no paradox of conjunction, why are there paradoxes of material and strict implication? With apologies to the friends and family of Dennis Wilson, the ill-starred original drummer of the Beach Boys, let's take this as our example:

1. Wilson got drunk, fell overboard, and drowned.

Translating (1) into the Propositonal Calculus (PC), we get

2. Wilson got drunk & Wilson fell overboard & Wilson drowned. 

Now the meaning of the ampersand (or the dot or the inverted wedge in alternative notations) is exhausted by its truth table. This meaning can be summed up in two rules. A conjunction is true if and only if all of its conjuncts are true. A conjunction is false if and only if one or more of its conjuncts is false. That is all there is to it. The ampersand, after all, is a truth-functional connective which means that the truth-value of any compound proposition formed with its aid is a function (in the mathematical sense) of the TVs of its components and of nothing besides. You will recall from your college calculus classes that if f is a function and y = f(x), then for each x value there is a unique y value.

Now are the conjuncts of (2) related? Well, they are related in that they all have the same truth-value, namely True. But beyond this they are not related qua components of a truth-functional compound proposition. The 'conjuncts' — note the inverted commas! — of (1), however, are related beyond their having the same truth-value. For it is because Wilson got drunk that he fell overboard, and it is because he fell overboard that he drowned. So causal and temporal relations come into play in (1), relations that are not captured by (2).

Note also that the ampersand has the commutative property. But this is not so for the comma and the 'and' in (1). Tampering with the order of the clauses in (1) turns sense into nonsense:

3. Wilson drowned, fell overboard, and got drunk.

We should conclude that the ampersand abstracts from some of the properties of occurrences of the natural language 'and' and cognates. Despite this abstraction, (1) entails (2), which means that (2) does capture part of the meaning of (1), that part of the meaning relevant to the purposes of logic. But surely there is no 'paradox' here. Any two propositions can be conjoined, and the truth-value of the compound can be computed from the TVs of the components. It is the same with material implication: any two propositions can be connected with a horseshoe or an arrow and the TV of the result is uniquely determined by the TVs of the component propositions. Thus we get a curiosity such as

4. Snow is red –> Grass is green

which has the value True. This is paradoxical only if you insist on reading the arrow as if it captured all the meaning of the natural language 'if' or 'if…then___.' But there is no call for this insistence any more than there is call for reading the ampersand as if it captures the full meaning of 'and' and cognates in ordinary English.

What I am suggesting is that, just as there is no paradox of conjunction, there is no paradox of material implication either.

Deflationism: Ramsey and Redundancy

I am using 'deflationism' as an umbrella term subsuming several different deflationary theories of truth, among them Ramsey's redundancy theory, Quine's disquotationalism, Horwich's minimalist theory, and others. Deflationary theories contrast with what might be called 'robust' or substantive' theories of truth. It is not easy to focus the issue that divides these two types of theory. One way to get a feel for the issue is by considering the traditional-sounding question, What is the nature of truth? This 'Platonic' question — compare What is the nature of knowledge? (Theaetetus); What is the nature of justice? (Republic) — presupposes that truth has a nature, a nature that can be analyzed or otherwise explicated in terms of correspondence, or coherence, or 'what conduces to human flourishing,' or what would be accepted at the Peircean limit of inquiry, or something else. 

The deflationist questions the presupposition. He suspects that truth has no nature. He suspects that there is no one property that all truths have, a property the having of which constitutes them as truths. His project is to try to account for our truth-talk in ways that do not commit us to truth's having a nature, or to truth's being a genuine property. Of course, we English speakers have and use the word 'true.'  But the mere fact that we have and use the predicate 'true' does not suffice to show that there is a property corresponding to the predicate. (Exercise for the reader: find predicates to which no properties correspond.)

So if we can analyze our various uses of 'true' in ways that do not commit us to a property of truth, then we will have succeeded in deflating the topic of truth and showing it to be metaphysically insubstantial or 'lightweight.' The most radical approach would be one that tries to dispense with the predicate 'true' by showing that everything we say with its help can be said without its help (and without the help of any obvious synonym such as 'correct.') The idea here is not merely that truth is not a genuine property, but that 'true' is not even a genuine predicate.

Consider two assertions. I first assert that snow is white, and then I assert that it is true that snow is white. The two assertions have the same content. They convey the same meaning to the audience. This suggests that the sentential operator  'It is true that ___' adds nothing to the content of what is asserted. And the same goes for the predicate '___ is true.' Whether we think of 'true' as an operator or as a predicate, it seems redundant, or logically superfluous. In "Facts and Propositions" (1927), Frank Ramsey sketches a redundancy or logical superfluity theory of truth. This may be the first such theory in the Anglosphere. (Is there an historian in the house?)

For Ramsey, "there really is no separate problem of truth but merely a linguistic muddle." Ramsey tells us that ". . . 'It is true that Caesar was murdered' means no more than that Caesar was murdered, and 'It is false that Caesar was murdered' means that Caesar was not murdered." (F. P. Ramsey, Philosophical Papers, Cambridge UP, 1990, ed. D. H. Mellor, p. 38) But what about a case in which a proposition is not explicitly given, but is merely described, as in 'He is always right'? In this example, 'right' has the sense of 'true.' 'He is always' right means that whatever he asserts is true. As a means of getting rid of 'true' in this sort of case, Ramsey suggests:

1. For all p, if he asserts p, then p is true.

But since "the propositional function p is true is the same as p, as e.g., its value 'Caesar was murdered is true' is the same as 'Caesar was murdered,'" Ramsey thinks he can move from (1) to

2. For all p, if he asserts p, then p.

If the move to (2) is kosher, then 'true' will have been eliminated. Unfortunately, (2) is unintelligible. To see this, try to apply Universal Instantiation to (2). If the variable 'p' ranges over sentences, we get

3. If he asserts 'Snow is white,' then 'Snow is white.'

This is nonsense, because "'Snow is white'" in both occurrences is a name, whence it follows that the consequent of the conditional is not a proposition, as it must be if the conditional is to be well-formed. If, on the other hand, the variable 'p' is taken to range over propositions, then we get the same result:

4. If he asserts the proposition that snow is white, then the proposition that snow is white

which is also nonsense. Unless I am missing something, it looks as if Ramsey's redundancy theory cannot succeed in eliminating 'true.' It looks as if 'true' is an indispensable predicate, and thus a genuine predicate. This does not, however, show that truth is a genuine property.   It merely shows that we cannot get rid of 'true.'

Geach on Assertion

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.  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.

What bearing does this have on recent discussions?  I am not sure I understand William of Woking's position, but he seems to be denying something that Geach plausibly maintains, namely, that "there is no expression in ordinary language that regularly conveys assertoric force." (261)  Suppose I want to assert that Tom is drunk.  Then I would use the indicative sentence 'Tom is drunk.'  But there is nothing intrinsically assertoric about that sentence.  If there were, then prefixing 'if' to it would not remove its assertoric force as it does.    As I have already explained, an assertive utterance of 'If Tom is drunk, then he is unfit to drive'  does not amount to an assertive utterance of 'Tom is drunk.'  'If' cancels the assertoric force.  And yet the same proposition occurs in both assertions, the assertion that Tom is drunk and the assertion that if Tom is drunk, then he is unfit to drive.  I conclude that there is nothing intrinsically assertoric about indicative sentences.  If so, there is no semantic component of an indicative sentence that can be called the assertoric component.

'If' prefixed to an indicative sentence does not alter its content: it neither augments it nor diminishes it.  But it does subtract assertoric force.  Given that the meaning of an indicative sentence is its content, and the semantics has to do with meaning, then there is no semantic assertoric component of an indicative sentence or of the proposition it expresses.  Assertion and assertoric force do not belong in semantics; they belong in pragmatics.  Or so it seems to me.

Sentence, Linguistic Meaning, Proposition

I maintain that we must distinguish among declarative sentences, their linguistic meanings, and the propositions expressed by tokenings of declarative sentences by speakers in definite contexts. Furthermore, I maintain that propositions, not linguistic meanings, are the vehicles of the truth-values. Here are four declarative sentences in four different languages, English, German, Turkish, and Latin:  I love you; Ich liebe dich; Seni seviyorum; Te amo. 

Clearly, each of these sentences can be used to express many different thoughts or propositions. If Jack says 'I love you' to Jill, the proposition expressed is different from the proposition expressed if Bill says 'I love you' to Hill. Since one and the same sentence type can be used to express different propositions, it follows that sentence types are distinct from propositions.

We must also distinguish between a sentence type and its linguistic meaning, the meaning it has in virtue of the conventions of the language to which the sentence type belongs. The four sentences displayed above have the same meaning. Since one and the same meaning is possessed by these four different sentence types, it follows that linguistic meanings are distinct from sentence types. It follows from the two points just made that linguistic meanings are distinct from propositions. One proof of this is that one can have a complete understanding of the linguistic meaning of a sentence without knowing any proposition that the sentence has ever expressed. Let me explain.

Suppose a Spanish speaker learning English learns that 'Mary loves Carl' means the same as 'Mary ama a Carl.' The Spanish speaker then fully understands the linguistic meaning of 'Mary loves Carl' but without needing to know any proposition, any truth or falsehood, that the English sentence has ever expressed. (See Castaneda, Thinking and Doing, p. 35) Therefore, the linguistic meaning of a declarative sentence is distinct from the proposition expressed by the sentence on some occasion of the sentence's use. Some, blinded by the nominalist fear of reification, cannot admit this obvious distinction between linguistic meaning and proposition. One nominalist writes, "In summary, the meaning of a sentence is what it says, what it says is true or false, ergo the meaning of a sentence is a 'truth bearer'." The argument is this:

1. The meaning of a sentence is what it says.

2. What a sentence says is either true or false. Therefore,

3. The meaning of a sentence is either true or false.

The argument equivocates on 'what it says.' If premise (2) is true, then what a declarative sentence says is identical to the proposition it expresses. It is important to realize that I am not assuming any particular theory of propositions. Thus I am not assuming that they are Platonic entities. I am simply insisting that we need to distinguish between the linguistic meaning of a sentence (the meaning it has in virtue of the conventions of the language to which it belongs) and the proposition a sentence expresses when the sentence is uttered or otherwise tokened by a person in a definite situation. But in premise (1), the linguistic meaning of a sentence is identified with what it says. Thus 'what it says' is being used in two different ways, which fact destroys the validity of the argument. If a proponent of the argument says I am begging the question against him, I reply that he is failing to admit an obvious distinction. The distinction is not original with me. It ought to be visible to anyone. If an a priori commitment to nominalism blinds one to so obvious a distinction, then so much the worse for an a priori commitment to nominalism.

The Elusive Assertoric Component

William of Woking comments:

 Consider again

(1) Tom runs

(2) that Tom runs

(3) It is true that Tom runs

We have agreed that (1) and (3) are semantically identical. Yes, they express the very same propositional content or thought. They have the very same meaning (Sinn).   We also agree that (2) is verbally more complex than (1), likewise (3) is verbally more complex than (2). Yes, that's obvious. 

Do you agree that it logically follows that in some cases, increasing the verbal complexity can reduce the semantic complexity? I argue as follows. Either (2) is semantically more complex than (1) or less complex. If more complex, then it follows that (2) is semantically more complex than (3), because of the semantic identity we agreed. In which case it logically follows that increasing the verbal complexity (in the move from (2) to (3)) reduces the semantic complexity. Therefore &c. Or (2) is semantically less complex than (1). In which case it logically follows that increasing the verbal complexity (from (1) to (2)) reduces the semantic complexity.

Your argument seems correct: in some cases increasing verbal complexity reduces semantic complexity.  But what exactly do you mean by 'semantic complexity'?  Verbal complexity seems clear: if one expression contains more words than another, then the first expression is verbally more complex.  But you need to explain to us exactly what you mean when you say that one expression is semantically more complex than another.  For example, (1) and (2) are semantically distinct.  The first has a truth-value, the second doesn't.  But which is semantically more complex?  What criterion do you use to decide that?  I don't see that (2) is semantically more complex than (1).  If you think of 'that' as a sentential operator, then you can say that (2) results from (1) when 'that' operates upon (1).  But that is not to say that (2) is semantically more complex than (1).  For 'that' by itself carries no meaning.  It is syncategorematical as opposed to autocaregorematical to use some Medieval lingo.

If you agree to this, then I have a large part of what I propose, for nearly all your negative arguments rest on the observation that a token of the same verbal expression (i.e. with the same verbal complexity) may appear to lack the assertoric component that the other has. My reply here is that this is consistent with 'semantic subtraction' operators. The token of the expression (1) above ('Tom runs') is identical to the token included in the that-clause in (2).   No, they are distinct tokens; they are only type-identical. Yet (2) as a whole appears not to be an assertion. To be precise: (2), by itself, cannot be used to make an assertion.  You would argue, in general, that this is because there is no such thing as a semantic component of assertion. I reply, in general, that this is because of the 'negative effect' of the 'that operator'.

I'm afraid this is still very unclear.  Consider the sentence 'Tom sucks.'  Now consider two tokens of this sentence type.  (T1)  'Tom sucks' uttered by Tanya to express contempt for Tom. (T2) 'Tom sucks' uttered by Tony to describe how Tom is ingesting his cola.  From the point of view of grammar, both tokens are in the indicative mood.  But only one is being used to make an assertion.  Therefore, there cannot be an assertoric component in indicative sentence types.  And whether there is anything assertoric about a token depends on how it is used in a concrete situation.

In any case, what is the wider relevance of all this?  What's at stake here?  Where are you going with this?