Types, Tokens, and Logical Form

Black text by London Ed; my comments in blue.

Consider:

This parcel of land on the Thames is a bank.
A bank contains money.
*This parcel of land on the Thames contains money.

The two tokens of ‘bank’ are tokens of the same type, if I understand you correctly. So does the Thames argument above instantiate the following valid form?

This is an F
Every F is G
This F is G

Let's start with a Moorean fact:  the argument is bad!  But why is it bad?  (Now we begin to philosophize.) Is it because one of the premises is false?  Or because the reasoning is incorrect?  That distinction, the one between truth/falsity of propositions and correctness/incorrectness of reasoning, would also seem to be Moorean, or damned near.

There are two approaches.  One is to say that the Thames argument is valid because it it instantiates the valid form depicted, but that it is nevertheless unsound because the first premise is false.  The other approach is to say that the argument involves an equivocation on 'bank' such that the argument falls afoul of quaternio terminorum, which is of course a formal fallacy.  Thus on the second approach, the argument is invalid (because it instantiates an invalid form), but both premises are true.

Either way, the Thames argument is unsound.  On the first approach it is unsound because it sports a false premise; on the second, because it has an invalid form.

'Unsound' is a terminus technicus; a term of the logician's art.  'Bad' is from ordinary language.  But if we are talking about deductive arguments, the former term is a very close exegesis or exfoliation if you will of the Joe Sixpack word.

You seem to hold that if we substitute concrete tokens of the same type, then the resulting argument instantiates the form. And you also hold that to be a token of the same type means having the same spelling, and no more than that.

It’s the ‘and no more than that’ that I am having a problem with. I hold, and this is hardly an extreme or unorthodox position, that identically-spelled tokens can have (and often do have) different meanings, because meaning is a matter of convention. Sameness of spelling is never enough.

This forces me to think hard.  We enter deep and troubled waters below the Moorean surface.  Suppose Poindexter's (weak!) password at the money bank is kzw9*.  Now consider this array:

kzw9*
kzw9*
kzw9*

How many passwords?  One or three?  A simple solution to this puzzle is to say that there are three tokens of the same type.  (Note that a password need not be a word, though it can be ('password' is one dumbassed password): the above passwords are not words of any natural language.)  The type in question here is not a word-type: it has no linguistic meaning.  No token of this type has sense or reference.

It is like a key that unlocks a door.  A token of a key-type has neither sense nor reference.  it is just a little piece of metal that fits into the lock, etc.  It has no semantic properties. Its properties are geometrical, metallurgical, and the like.

Now a word-token has a physical side, a body if you will.  Thus 'bank' -- that particular string of marks -- has geometrical properties, color, etc.  But it is not a word in virtue of being a physical item.  It is a word only when animated by sense.  Perhaps we could say that the sense is the soul of the word whose body is the physical sign.

So we need to distinguish two types.  There is the physical type a token of which is the string of marks, 'bank.'  And there is the word-type a token of which is the word, 'bank.' 

Now I can answer Ed.  He wrote,

You seem to hold that if we substitute concrete tokens of the same type, then the resulting argument instantiates the form. And you also hold that to be a token of the same type means having the same spelling, and no more than that.

That is not my view. For two words to be tokens of the same word-type it does not suffice that they have the same spelling.  In fact, it is not even necessary: 'tire' and 'tyre' are (arguably) tokens of the same English word-type even though they are spelled differently. 

Spelling pertains to the physical side of a word. For two tokens to be of the same word-type they must be animated by the same meaning. 

Returning to the Thames argument, it is clear that there are two tokens of the 'bank' string-of-marks type.  But whether there are two tokens of the same word-type or not depends on what the speaker intended. 

We cannot extract the logical form of an argument be examining its physical features.  We have to understand what the constituent sentences mean, and to understand what they mean, we have to understand what their constituent terms mean.

Meaning cannot be reduced to anything physical or to anything merely syntactical.  Meaning brings mind into the picture.  No mind, no meaning.  This is why I insist that linguistic reference cannot be understood unless we understand what underlies it, mental reference, i.e., intentionality.

Related articles

Abbreviations, Place-Holders, and Logical Form

On Philosophical Denials of the Obvious

Validity and Semantics: Will the Real Frodo Baggins Please Stand Up?

On the Enforcing and Permitting of Coreferentiality by Argument-Forms

Comments on London Ed's "Towards a Positive Theory"

The Stromboli Puzzle Revisited

Against Ostrich Nominalism

Comments

[Ed]

>>
We cannot extract the logical form of an argument be examining its physical features. We have to understand what the constituent sentences mean, and to understand what they mean, we have to understand what their constituent terms mean.
<<

We are entirely agreed then. Shock.

[David Brightly]

Bill,

We can't say that an argument is invalid because it instantiates an invalid form. The argument Socrates is a man; all men are mortal; ergo Socrates is mortal instantiates the invalid form a is F; all Hs are G; ergo a is G, but modulo equivocation, it is truth-preserving. Instantiation of form is just pattern-matching, and the argument does match the pattern of the invalid form.

Returning to the Thames argument, we can split your second approach into two variants:

1. The argument is valid by virtue of instantiating a valid form; the premises are true; but the argument is unsound because of equivocation on 'bank'.
2. Equivocation on 'bank' invalidates the argument.

Which option we choose depends on how we want to extend the notion of validity of form to validity of argument. Both routes are feasible, I think, but we need to be consistent else confusion arises. My inclination is for (1). For me validity is about syntactic form. Soundness brings in truth. For this we have to have meaning, Hence equivocation on meaning falls under soundness.

I can't agree that 'We cannot extract the logical form of an argument be examining its physical features.' The only reason that the Thames argument is put forward as a truth-preserving inference is that its conclusion results from matching its premises to those of a valid inferential pattern. There is no valid argument form with premises This is an F; every H is G and conclusion This F is G. The form of the quoted argument has to be the one given.

[london ed]

Bill: “We cannot extract the logical form of an argument be [sic, = by] examining its physical features. “
I rarely correct your typos but I have a reason this time. More later.

This is just to note that Jan Lukasiewicz would have profoundly disagreed with this statement, holding that it is precisely the physical features, and only the physical features, that logical form is concerned with. Why? He says (see the first chapter of Aristotle's Syllogistic from the Standpoint of Modern Formal Logic, 1951, that logic in the true sense must avoid any kind of psychologism. Logic is not ‘the law of the forms of thought’ or whatever. For thought is a psychological phenomenon and the thoughts of others are not accessible to us ‘unless we are clairvoyants’, which we generally aren’t. Logic should avoid ‘thought’ and ‘meaning’ entirely. The purpose of logic is to assign or categorise valid forms of expression, i.e. the outward manifestations of thought, namely visible signs or spoken words. Such signs are accessible to others. We can agree on their shape and order, we can agree (unless the writing is really poor) whether a letter is a token of ‘a’ or ‘b’ or whatever.

Lukasiewicz concedes that ordinary language is ambiguous, and for that very reason prefers truly ‘formal’ logic, i.e. a logic where the signs and syntax are completely unambiguous, such as predicate calculus or the ghastly Polish logic, which he developed. For him, logical ‘form’ is therefore precisely about the physical, i.e. perceptible features of argumentation. Validity cannot be guaranteed when it depends on partly or wholly unobservable items such as ‘thoughts’ or ‘meanings’ or ‘intentions’.

Returning to the typo. I altered your ‘be’ to ‘by’. Why? ‘Be’ was what you actually typed. However, I made a judgement about your intention. You meant to type ‘by’, correct? But the question is how I knew this. Am I a clairvoyant with access to your private mental states? Surely not. I looked at the sentence and it did not make sense. I found that I could make sense of it by altering the word in that way. So I made the judgment, and changed it. Without clairvoyance or telepathic powers.

Indeed, I could write a crude computer program to pick up typos like that. My word processor already has one. Yet a computer cannot access private mental states either.

In conclusion, perhaps Lukasiewicz is right. Logical form is about the outward manifestation of arguments as expressed in writing or speech. However, a more sophisticated approach would be to understand how we resolve ambiguity without the crude and literal approach advocated by Lukasiewicz. That is a matter for further investigation.

[BV]

Ed,

It looks like Lukasiewicz was deeply confused. Yes, psychologism is to be avoided. But how does it follow that logic is concerned precisely with physical features? The conclusion is absurd. Therefore, any argument to it must have one or more false premises.

Did L. reject psychologism only to fall into 'physicism'? I have argued in these pages that logic cannot be reduced to psychology. But it cannot be reduced to physics either, or to any empirical study of merely material things or processes.

One could study a complex pattern of bird droppings on a wall, noting all sorts of physical, including geometrical, features. But no such pattern expresses a proposition. And without propositions one cannot do logic. Logic is concerned with consistency, inconsistency, and entailment. But these are relations defined over propositions. These relations do not hold between or among merely physical things and processes.

[london ed]

Brightly: “We can't say that an argument is invalid because it instantiates an invalid form.”

I spotted that too.

“equivocation on meaning falls under soundness.” I can’t agree with that, neither I suspect would Bill.

Bill “how does it follow that logic is concerned precisely with physical features?”

L didn’t say that. He said that logical form is concerned with that. That is why it is called ‘form’.

“It looks like Lukasiewicz was deeply confused.”

Well he is a very famous and respected logician, and inventor of Polish logic. Perhaps I misread him. I shall read the chapter again and report back.

Lukasiewicz was quite a character. Someone told me a story about his obsession with the correct use of quotation marks, but I can’t remember it. He also argued that if the schema is ‘every A is a B’, we cannot substitute ‘all As are Bs’, because it is not precisely equiform.

He also fell into the class of ‘rude logicians’. There are some juicy quotes in the chapter which I can send. We were going to discuss this. Are logicians as a group more uncivil and generally more unpleasant than other professions? If so, why? Has anyone done a statistical survey?

[BV]

I love you guys even though we disagree about almost everything. Amazing that you've stuck with me all these years.