on history, poetry, and philosophy.

“The difference between the historian and the poet is not merely that one writes verse and the other prose…the essential difference is that the one tells us what happened and the other the sort of thing that would happen. This is why poetry is at once more like philosophy and more worth while than history, since poetry tends to make general statements, while those of history are particular. A ‘general statement’ means one that tells us what sort of man would, probably or necessarily, say or do what sort of things, and this is what poetry aims at, though it attaches proper names; a particular statement on the other hand tells us what Alcibiades, for instance, did or what happened to him.”

Aristotle, Poetics 1451b3-1

I like how Aristotle likens the poet to the philosopher—so much for the alleged war between them. However, I’m puzzled by Aristotle’s reason for thinking that the poet is more like the philosopher than the historian. Is it really the case that the poet’s business is to tell us what a certain sort of person would do? Is this what the philosopher is in the business of doing? Furthermore, the historian does tell us what has happened, as opposed to what would happen, but the historian also gives us an account of what happened—viz. an explanation. And isn’t part of the point of learning history is to know what we would most likely do in similar circumstances?

on whether every thought can be expressed.

It’s obvious that some thoughts are not expressible in English. Of course, ex hypothesi, I can’t give you any examples. And there’s no inconsistency whatever in expressing this fact in English, for even if their genus is expressible in English (viz. the thoughts which are not expressible in English), it doesn’t follow that their specific difference is thereby expressible in English.

not either, not both, and not even between.

Let ‘T’ abbreviate ‘true’; consider:

(1)         (x)(Tx v ~Tx)

(1) says that everything is either true or not true. I say (1) is false for an infinite number or reasons.  Here are five: it’s not true that my cat is either true or not true. It’s not true that my nostril is either true or not true. It’s not true that a banana is true or not true.  It’s not true that this italicized sentence is either true or not true. If you’re not convinced that (1) is not true, I suggest that you consider each and every natural number n, and you’ll see that it’s not true that n is either true or not true.

    But here’s my problem. If I deny (1) by affirming

(2)      ~(x)(Tx v ~Tx)

I thereby affirm

(3)       (∃x)(~Tx • Tx)

for (2) and (3) are logically equivalent if quantifier negation and De Morgan’s law are valid, which they are. So here’s my dilemma: affirm (1) or affirm a contradiction. Because (1) itself will eventually lead to a contradiction, my choice is really between affirming a contradiction now or affirming one later. I choose never. So I say that though (1) and (2) appear to be more than a string of symbols, they are not.

on whether a string of bananas may refer to itself.

The following sentence may express a truth when you use it:

This string of symbols per se does not refer to itself.

But if you proceed to mention the previous sentence and affirm that at it is true, the previous sentence is no longer being used but rather is being referred to, in which case you are, in effect, declaring that a string of symbols is true. But how can a string of symbols not only express a truth, but also be true? I understand, for example, how an arrangement of bananas may express a truth, but what does it mean to say that the arrangement of bananas would thereby itself be true?

That * is bananas.

on whether every thesis should be examined.

“Not every problem, or every thesis, should be examined, but only one which might puzzle one of those who need argument, not punishment or perception. For people who are puzzled to know whether one ought to honor the gods and love one’s parents or not need punishment, while those who are puzzled to know whether snow is white or not need perception.”

Aristotle, Topics I, 11, 105a2-8

on the purpose of words.

“…But it should make no difference whichever description is used; for our object in thus distinguishing them has not been to create a new terminology, but to recognize what differences actually exists between them.”

Aristotle, Topics I, 11, 104a137ish

Quine is right only if Quine is wrong.

“…necessity resides in the way in which we say things, and not in the things we talk about.”

–  W.V. Quine, “Three grades of modal involvement”

(note: in what follows I use single-quotation marks to name words and ignore their meaning and double-quotation marks to name a word with emphasis on its meaning.)

Suppose I ask you if the statement

(1)           Brutus killed Caesar.

could have been false, and you say: “Yes, for the word ‘killed’ could have meant “married”, and since Brutus did not marry Caesar, had (1) meant “Brutus married Caesar”, (1) would have been false.”

            Utterly dumbfounded by your response, I present you with the following statement

(2)             7 is prime. 

and ask if (2) could have been false, and you respond in kind: “Yes, for the word ‘7’ could have meant “6”, and since 6 is not prime, had (2) meant “6 is prime”, (2) would have been false.”

            At this point exactly half of my dumbfoundery has vanished because I see that when I asked you whether (1) and (2) could have been false, you responded by mentioning the words I used when I was using those words to talk about things.

            Suppose I make the semantic ascent to your level and ask you if you think it’s true that:

(3)             The word ‘killed’ could have meant “married”. 

and

(4)             The word ‘7’ could have meant “6”.

If you answer “no”, then you’re being inconsistent.  If you answer “yes”, then you disagree with Quine, for (3) and (4) are true only if necessity resides in at least some of things we talk about, for (3) and (4) are equivalent to

(3’)       The word ‘killed’ possibly means “married”.

and

   (4’)        The word ‘7’ possibly means “6”.

and (3’) and (4’) are equivalent to

(3’’)      The word ‘killed’ doesn’t necessarily not mean “married”.

(4’’)      The word ‘7’ doesn’t necessarily not mean “6”.

Ergo, etc.

on the usefulness of a quine.

quine, n. a razor-sharp machete often used to shave beards and clear jungles. Usually too blunt for either task, but quite effective for precision trimming and stunting overgrowth.

you may use one but don't mention it.

            At t₁, I come into existence and say nothing. At t₂ I say, “the cat is on mat” and nothing else. But, at t₂, the cat is not on the mat. At t₃, I say, “I never tell the truth” and nothing else.  What exactly am I saying? Here are some options:

(1)  What I said at t₂ is true.

(2)  What I said at t₂ is not true.

(3)  What I said at t₂ is true and what I am saying at t₃ is true.

(4)  What I said at t₂ is true and what I am saying at t₃ is not true.

(5)  What I said at t₂ is not true and what I am saying at t₃ is true.

(6)  What I said at t₂ is not true and what I am saying at t₃ is not true.

If (1), then what I say is false, full stop.

If (2), then what I say is true, full stop.

If (3), then what I say is false, full stop.

If (4), then what I say is false, full stop.

If (5), then what I say is true, full stop.

If (6), then what I say is false, full stop.

Are there any other options?  If not, whatever it is I say at t₃, it is not both true and false. Ergo, etc.

at least two formally valid arguments are not valid.

Here’s a formal proof of the liar:

1.  (x)(p)((Cx • S_x(p)) ⊃ ~p)

2.  Cc • S_c((x)(Cx • S_x(p) ⊃ ~p))  ∴  ~(x)(p)((Cx • S_x(p)) ⊃ ~p)

3.  Cc • S_c((x)(p)((Cx • S_x(p)) ⊃ ~p) ⊃ ~(x)(p)((Cx • S_x(p)) ⊃ ~p 1, UI

4.  ~(x)(p)((Cx • S_x(p)) ⊃ ~p)   2, 3, MP

In English:

1. for any x and any p if x is a Cretan and x says p then ~p.

2. Chris is a Cretan and Chris says for any x and any p if x is a Cretan and x says p then ~p.

3. If Chris is a Cretan and Chris says for any x and any p if x is a Cretan and x says p then ~p then it’s not the case that for any x and any p if x is a Cretan and x says p then ~p. (From 1 and universal instantiation)

4. it’s not the case that for any x and any p if x is a Cretan and x says p then ~p. (from 2, 3, and modus ponens)

Here might be a way out:

The argument’s form is valid, but there is no time in which the string of symbols which compose lines 1 and 2 express a proposition. Since strings of symbols which fail to express propositions eo ipso fail to express premises, any instance of lines 1 and 2 will fail to constitute an argument.  Since only arguments may be valid and lines 1 and 2 fail to constitute an argument, nothing follows from lines 1 and 2.  Ergo, there is no liar’s paradox.

Objection:  Wow. Way to be ad hoc.

Reply: False. I have independent reasons for saying that some strings of symbols which appear to express propositions don’t actually express propositions. For example, here’s a formal proof of Zeus’ existence:

1. (x)x = x      ∴  (∃x)x = z

2. z = z              1, UI

3. (∃x)x = z      2, EG

In English:

1. Everything is identical to itself.

2. Zeus is Zeus.  (from 1 and universal instantiation)

3. There is something such that it is Zeus.  (from 2, and existential generalization)

I think that this argument’s form is valid, and I also think that its one and only premise is true. However, I don’t think the string of symbols in line 2 expresses a proposition because in order for it to express a proposition, the letter ‘z’ must refer to Zeus. Since Zeus doesn’t exist,  ‘z’ doesn’t name anything, and therefore line 2 is not even false. Since the proof only goes through if each line expresses a proposition, lines 1, 2, and 3 fail to constitute a proof. 

on dubious business.

W.V. Quine (1974, p. 187f) says that quantifying into intensional contexts is dubious business, and he offers the following as a case in point. Ralph suspects that the man wearing a green hat is a spy. Though they have never met, Ralph has also heard a great deal of good about a fellow by the name of Bernard. Unbeknownst to Ralph, the man in the green hat and Bernard are one and the same person. We ask Ralph about whether he thinks Bernard is a spy, and Ralph replies, “Bernard is no spy!” Thus, it appears that Ralph has contradictory beliefs: Ralph believes that Bernard is a spy and Ralph believes that Bernard is not a spy.

            Wait, what? This isn’t obvious. It seems to me that Ralph believes that someone who wears a green hat is a spy: (let ‘r’ abbreviate ‘Ralph’ and ‘(∃x)B_r(Sx • Gx)’ abbreviate ‘there is something such that Ralph believes it is a spy and it wears a green hat’. Thus:

(1)       (∃x)B_r(Sx • Gx)

Ralph also believes that Bernard (b) is not a spy:

(2)       (∃x)B_r(x = b • ~Sx)

(1) and (2) quantify into Ralph’s beliefs, but their conjunction does not imply that Ralph has contradictory beliefs.  

References

Quine, W.V. (1974) “Quantifiers and Propositional Attitudes”, reprinted in The Ways of Paradox and Other Essays (revised ed.), Cambridge: Harvard University Press.