Monday, March 28, 2016

What I say

"What she said" in the vernacular is a way of expressing or agreeing with what the speaker just said. We can extend this useful idea in all kinds of ways. E.g.

(1) we can apply a negation operator. Thus 'not what she said'.

(2) we can apply it recursively. Thus

A: Snow is white
B:what A said
C:what B said

and so on. Note that all three are statements, each of them says something. Thus to say something is either (i) to say something without reference to another statement. This is the boundary condition. (ii) to reference some other statement which also says something. This is the recursive case.

(3) We can use other pronouns than the third person. E.g. to saying to C, 'not what you said', thus disagreeing with C, and thus disagreeing that snow is white. In the first person 'what I said', emphasising again what you said before, 'not what I said', changing your mind, as we do. And finally 'not what I am saying'. Does this say anything? No. It is a recursive case that has no boundary condition.

(4) Finally, we can ask a question. Thus 'what C says?', to which the answer could be 'what C says', or just 'Snow is white', or 'not what C says', thus 'Snow is not white'. As for 'not what I am saying?', there is no appropriate answer, given that 'not what I am saying' has no boundary condition, as in case (3) above.

Tuesday, March 15, 2016

Truth and conspiracy

A nice companion to my 2010 post:
For the simple truth is that truth is often hard to come by, and that once found it may easily be lost again. Erroneous beliefs may have an astonishing power to survive, for thousands of years, in defiance of experience, with or without the aid of any conspiracy. The history of science, and especially of medicine, could furnish us with a number of good examples. One example is, indeed, the general conspiracy theory itself I mean the erroneous view that whenever something evil happens it must be due to the evil will of an evil power. Various forms of this view have survived down to our own day.

(Karl Popper, from the Annual Philosophical Lecture read before the British Academy on January 20th, 1960. First published in the Proceedings of the British Academy, 46, 1960, and separately by Oxford University Press, 1961).

Thursday, March 03, 2016

Signification and assertion

Every departmental science has a subject, and its literature talks about or refers to that subject. Physics talks about heavy bodies and momentum and energy, chemistry talks about compounds, biology talks about flora and fauna etc. What does semantics, the science of meaning, talk about?

And there is the problem. Sometimes we cannot refer to what we signify.

Frege recognised this problem in 1892, in his essay ‘On Concept and Object’. A sentence consists of words, each of which has a signification or sense. What the whole sentence signifies is thus a compound of the senses corresponding to the words. (See e.g. his undated letter to Jourdain, in Frege’s Philosophical and Mathematical Correspondence, ed Gabriel and Hermes, 1980). The possibility of understanding a sentence we have never heard before depends on this property. What the sentence signifies is something new and perhaps previously unknown to us, but the signification of the words of which it is composed must be known, otherwise we would be incapable of understanding the sentence. For example ‘Socrates is a man’ is composed of the expressions ‘Socrates’ and ‘is a man’, both of which we know and understand.

The problem that Frege grapples with in ‘On Concept and Object’ is that while we can talk about what ‘Socrates’ signifies, namely Socrates himself, we can’t talk about what ‘is a man’ signifies. Or suppose we can. Let’s refer to it by the expression ‘The signification of “is a man”’. Will that do? No, because that expression is what Frege calls an Object term, an expression that refers to an object like Socrates. Thus the sentence ‘The signification of “is a man” is an Object’ is true. But it cannot signify an object, otherwise the sentence ‘Socrates is a man’ would be composed of two terms for objects. But two such terms cannot compose a sentence, any more than ‘Socrates Plato’ can. The sentence would be a mere list of words. Frege says, enigmatically ‘the concept horse is not a concept’, and attributes it to ‘an awkwardness of language’.

There is a similar problem regarding what I call signs of assertion. Consider
It is false that Socrates is a horse
I have not asserted that Socrates is a horse. On the contrary, I have denied it. Yet the four words ‘Socrates is a horse’ occur inside the eight word sentence ‘It is false that Socrates is a horse’. Perhaps we can explain this as follows. The eight word sentence can be split into ‘It is false’ and ‘that Socrates is a horse’. The latter is what Frege calls an object term. It refers to something a mad person might assert as true, the very thing I stand in the relation of denying to. So the meaning of the eight word sentence is changed by putting ‘It is false’ in front, and so if the meaning of the whole sentence is a composite of the meaning of ‘it is false’ and ‘that Socrates is a horse’, the composite is what ‘It is false that Socrates is a horse’ signifies. But of course that can’t be so, for the very fact that we could signify that Socrates was not a horse, would require that Socrates not being a horse was a fact. Worse, ‘It is true that Socrates is a horse’ would signify Socrates being a horse, so would require the existence of Socrates being a horse. Both those contradictory facts would have to exist in order for the contradictory sentences to be significant. Impossible!

Frege alludes to this problem in a much later essay (‘Negation’) published in 1918. He distinguishes between a question (my example is ‘is Socrates a horse’) from the thought corresponding to an answer like ‘yes’ or ‘no’. For if the sense of the question contained the sense of ‘yes’ or ‘no’, then the question would contain its own answer. The question would express a thought ‘whose being consists in its being true’.
Grasping the sense [of the question] would at the same time be an act of judging, and the utterance of the interrogative sentence would at the same time be an assertion, and so an answer to the question. But in an interrogative sentence neither the truth nor the falsity of the sense may be asserted.
Fair enough, but Frege does not see this as a challenge to his compositional semantics. Consider ‘Is Socrates a horse? No’. The first part signifies the question. If adding the sign ‘No’ completes the sense, then what is signified by the whole thing, namely question plus answer, must indeed be something whose being consists in being true, which Frege apparently denies.

In summary, if the signification of the whole is made up of the signification of the parts, then we should be able to refer to the signification of the whole, if semantics is to be a proper science. But we can’t, otherwise the subject of our science would include items like Socrates not being a horse, as well as Socrates being a horse. Which is impossible. Therefore semantics is not a science, at least not a proper science.

Sunday, February 28, 2016

Necessary beings

We don’t have to buy everything that Frege says about concepts to agree that using a concept expression F we can say things like ‘There are three Fs’ or ‘the number of Fs is n’. We can also say ‘There is at least one F’ which, according to Frege, is equivalent to ‘Fs exist’ or ‘there are Fs’. That seems uncontroversial.

Therefore ‘girls over the age of 17 at Mallory Towers’ is a concept-expression. For we can say that there are three girls over the age of 17 at Mallory Towers, or that the number of girls over the age of 17 at Mallory Towers is three. And we can say that, since there is at least one girl over the age of 17 at Mallory Towers, that there are girls over the age of 17 at Mallory Towers.

But here’s the problem. If it is true that ‘girls over the age of 17 at Mallory Towers’ is the name for a concept, then such a concept is not a necessary being. For in a possible world where there is no such school as Mallory Towers, we cannot specify the content of the concept. The property of being a girl over the age of 17 at Mallory Towers cannot be specified without reference to the actual Mallory Towers.

But that seems impossible. In such a possible world, there are no girls at Mallory Towers, since the school doesn’t exist, hence there are no such girls over 17. Therefore the non-existence of such girls is the non-instantiation of the concept *girl over the age of 17 at Mallory Towers*, and so that concept, in that possible world, has the property of being non-instantiated. But in order to have that property, it must exist. Since this is any possible world, it follows that the concept must exist in every possible world, and so is a necessary being. Yet we just supposed that it wasn’t a necessary being. Contradiction.


Is number a property of an aggregate of things? But what is an aggregate? Can the very same things have the same number once disaggregated? Frege (The Foundations of Arithmetic § 23, translation J.L. Austin) writes:
To the question: What is it that the number belongs to as a property? Mill replies as follows: the name of a number connotes, ‘of course, some property belonging to the agglomeration of things which we call by the name; and that property is the characteristic manner in which the agglomeration is made up of, and may be separated into, parts.’

Here the definite article in the phrase "the characteristic manner" is a mistake right away; for there are very various manners in which an agglomeration can be separated into parts, and we cannot say that one alone would be characteristic. For example, a bundle of straw can be separated into parts by cutting all the straws in half, or by splitting it up into single straws, or by dividing it into two bundles. Further, is a heap of a hundred grains of sand made up of parts in exactly the same way as a bundle of 100 straws? And yet we have the same number. The number word ‘one’, again, in the expression ‘one straw’ signally fails to do justice to the way in which the straw is made up of cells or molecules. Still more difficulty is presented by the number 0. Besides, need the straws form any sort of bundle at all in order to be numbered? Must we literally hold a rally of all the blind in Germany before we can attach any sense to the expression ‘the number of blind in Germany’? Are a thousand grains of wheat, when once they have been scattered by the sower, a thousand grains of wheat no longer? Do such things really exist as agglomerations of proofs of a theorem, or agglomerations of events? And yet these too can be numbered. Nor does it make any difference whether the events occur together or thousands of years apart.

Sunday, February 21, 2016

Number, concepts and existence

The Maverick Philosopher is agonising about number and existence in this post. It would be simpler if we returned to the original text of Frege which started all this (Die Grundlagen der Arithmetik 1884. Page numbers are to the original edition).

Frege claims with a concept the question is always whether anything, and if so what, falls under it. With a proper name such questions make no sense. (§51, p. 64). He also claims that when you add the definite article to a concept word, it ceases to function as a concept word, although it still so functions with the indefinite article, or in the plural (ibid).

This is part of a section of the Grundlagen where he develops the thesis that number is a property of concepts, not of things. Thus if I say (§46, p. 59) that ‘the King’s carriage is drawn by four horses’, I am ascribing the number 4 to the concept horse that draws the King’s carriage. The number is not a property of the horses, either individually or collectively, but of a concept.

From these two claims, namely that number is a property of concept words, and that proper names are not concept words, it seems to follow that ‘Socrates exists’ makes no sense. If ‘Socrates’ is not a concept word, then it seems no concept corresponds to it, but existence means that some concept is instantiated, so ‘Socrates exists’cannot express existence. This is the difficulty that Bill is grappling with.

But why, from the fact that ‘Socrates’ is not a concept word, does it follow that there is no corresponding concept? Frege has already told us that a concept word ceases to be such when we attach the definite article to it. So while ‘teacher of Plato’ signifies a concept, ‘the teacher of Plato does not. Why can’t the definite noun phrase ‘Socrates’ be the same, except that the definiteness is built into the proper name, rather than a syntactical compound of definite article and concept word. Why can’t ‘Socrates’ be semantically compound? So that it embeds a concept like person identical with Socrates, which with the definite article appended gives us ‘Socrates’?

As I argued in one of the comments, the following three concepts all have a number

C1: {any man at all}
C2: {any man besides Socrates}
C3: {satisfies C1 but not C2}

If the number corresponding to C1 is n, then the number of C2 is n-1. And the number of C3 is of course 1, and if C3 is satisfied, then Socrates exists. Simple.

Saturday, February 13, 2016

Metaphysical monstrosities

I have been looking at ‘Van Inwagen on Fiction, Existence, Properties, Particulars, and Method’, by Bill Vallicella (Studia Neoaristotelica Review Article 12 (2015) / 2). Bill is the famous Maverick Philosopher.

Section 3 deals with haecceity. A haecceity property is one which, unlike man or white cannot be multiply instantiated, or as Scotus said, not-predicable of several things (indicibilis de pluribus). For example, being Socrates (Socrateity) is a property which, if instantiated, is instantiated by Socrates alone in the actual world and by nothing distinct from Socrates in any possible world.

It is necessary to posit such properties, Bill argues, to support the semantic thesis of the univocity of ‘exists’ and ‘is’, and its ontological counterpart, that there are no modes of being/existence. It is essential to the thesis that number-words are univocal, and that ‘exists’ is a number-word. But it is not a number-word, for we can say of certain individual things that they exist, using referring terms.
Consider my cat Max Black. I joyously exclaim, ‘Max exists!’. My exclamation expresses a truth. Compare ‘Cats exist’. Now I agree with van Inwagen that the general ‘Cats exist’ is equivalent to ‘The number of cats is one or more’. But it is perfectly plain that the singular ‘Max exists’ is not equivalent to ‘The number of Max is one or more’. For the right-hand-side of the equivalence is nonsense, hence necessarily neither true nor false.
Right, but can’t a proper name N signify a property N* which can be instantiated, but by only one individual, and always and necessarily by the same individual? Then it makes sense to state there is only one object possessing N*, a statement which is false only if there are no (i.e. zero) objects possessing N*. Bill considers this, but thinks it a heavy price to pay for univocity across general and singular existentials.

‘Haecceity properties are metaphysical monstrosities’.

Why? His argument is that being properties, haecceities are necessary beings, and so exist at all possible times in all possible worlds. But how, before Socrates came into existence, could there have been any such property as the property of being identical to him. There would have been simply nothing to give content to the proposition that it is Socrates.

Now I agree that a haecceity predicate is essential to save the univocity of ‘exists’. And I agree, for the reasons given by Bill, that a haecceity property is absurd. But can there not be predicates, i.e. grammatical items, which have no properties corresponding to them?

More later.

Monday, February 08, 2016

Intentional Identity

Peter Geach (“Intentional Identity.” Journal of Philosophy 64, 627-32, reprinted in Logic Matters. Oxford: Blackwell, 1972) argues that the following sentence can be true even if there are no witches, yet can only be true if Hob and Nob are, as it were, thinking of the same witch.
Hob thinks that a witch has blighted Bob’s mare, and Nob wonders whether she killed Cob’s sow.
But how it could be true? If we read it in the opaque way of reading indirect speech clauses then each that-clause must stand on its own syntactically, but there is no way of interpreting the pronoun ‘she’ as a bound variable. The two thoughts add up, as it were, to ‘for some x, x has blighted Bob’s mare, and x killed Cob’s sow. But we can’t split them up into two separate thoughts, because of the second part of the conjunction. I.e. the following is not well-formed.
* Hob thinks that for some x, x has blighted Bob’s mare, and Nob wonders whether x killed Cob’s sow.
On the other hand, if we render the original sentence in the transparent way, we have to presume the existence of a real witch, i.e. some witch such that Hob thinks that she has blighted Bob’s mare, and Nob wonders whether she killed Cob’s sow. Neither of these are satisfactory. I don’t propose any answer yet, but I will start by noticing that the same problem attaches to saying what sentences say, rather than what people think.
(1) A witch has blighted Bob’s mare.
(2) She killed Cob’s sow.
(3) Sentence (1) says that a witch has blighted Bob’s mare.
(4) Sentence (2) says that she (or the witch) has blighted Bob’s mare.
Clearly sentences (3) and (4) are true, even though sentences (1) and (2) are false. Yet the problem is exactly the same as the problem involving different thoughts. Thus we have simplified the problem. We don’t have to worry about explaining thoughts in different minds, but only how we express the meaning of different sentences. Meanings are a little easier than thoughts.