Re: A theorem for agnostics

From: Acme Diagnostics (LFinezapthis_at_partpostmark.net)
Date: 07/26/04 

Date: 26 Jul 2004 01:23:09 -0500

G. Frege <no_spam@aol.com> wrote:
>
>Stewart Shapiro in his article "Classical Logic" [in Stanford
>Encyclopedia of Philosophy]:
>
>"[...] Typically, ordinary reasoning takes place in a
>natural language, or perhaps a natural language augmented with some
>mathematical symbols. So our question begins with the relationship
>between a natural language and a formal language. Without attempting to
>be comprehensive, it may help to sketch several options on this matter.
>
>One view is that the formal languages accurately exhibit actual features
>of certain fragments of a natural language. Some philosophers claim that
>declarative sentences of natural language have underlying logical forms
>and that these forms are displayed by formulas of a formal language.
>Other writers hold that (successful) declarative sentences express
>propositions; and formulas of formal languages somehow display the forms
>of these propositions. On views like this, the components of a logic
>provide the underlying deep structure of correct reasoning. A chunk of
>reasoning in natural language is correct if the forms underlying the
>sentences constitute a valid or deducible argument. See for example,
>Montague [1974], Davidson [1984], Lycan [1984].
>
>Another view, held at least in part by Gottlob Frege and Wilhelm
>Leibniz, is that because natural languages are vague and ambiguous, they
>should be replaced by formal languages. A similar view, held by W. V. O.
>Quine (e.g., [1960], [1986]), is that a natural language should be
>regimented, cleaned up for serious scientific and metaphysical work. One
>desideratum of the enterprise is that the logical structures in the
>regimented language should be transparent. It should be easy to "read
>off" the logical properties of each sentence. A regimented language is
>similar to a formal language regarding, for example, the explicitly
>presented rigor of its syntax and its truth conditions.
>
>On a view like this, deducibility and validity represent idealizations
>of correct reasoning in natural language. A chunk of reasoning is
>correct to the extent that it corresponds to, or can be regimented by, a
>valid or deducible argument in a formal language.
>
>When mathematicians and many philosophers reason, they occasionally
>invoke formulas in a formal language to help disambiguate, or otherwise
>clarify what they mean. In other words, sometimes formulas in a formal
>language are used in ordinary reasoning. This suggests that one might
>think of a formal language as an addendum to a natural language. Then
>our present question concerns the relationship between this addendum and
>the original language. What do deducibility and validity, as sharply
>defined on the addendum, tell us about correct reasoning in general?
>
>Another view is that a formal language is a mathematical model of a
>natural language in roughly the same sense as, say, a collection of
>point masses is a model of a system of physical objects, and the Bohr
>construction is a model of an atom. In other words, a formal language
>displays certain features of natural languages, or idealizations
>thereof, while ignoring or simplifying other features. The purpose of
>mathematical models is to shed light on what they are models of, without
>claiming that the model is accurate in all respects or that the model
>should replace what it is a model of. On a view like this, deducibility
>and validity represent mathematical models of (perhaps different aspects
>of) correct reasoning in natural languages. Correct chunks of reasoning
>correspond, more or less, to valid or deducible arguments; incorrect
>chunks of reasoning roughly correspond to invalid or non-deducible
>arguments. See, for example, Corcoran [1973] or Shapiro [1998].
>
>There is no need to adjudicate this matter here. Perhaps the truth lies
>in a combination of the above options, or maybe some other option is the
>correct, or most illuminating one. I raise the matter only to lend some
>philosophical perspective to the formal treatment that follows."
>
>Source:
>plato.stanford.edu/entries/logic-classical/

Thanks for posting this well-written piece of explanation. But...

Reread just the three summaries of the summaries of the three
supposedly different dogmas. They are all the same!

I excerpt the three for the convenience of readers:

>On views like this, the components of a logic
>provide the underlying deep structure of correct reasoning. A chunk of
>reasoning in natural language is correct if the forms underlying the
>sentences constitute a valid or deducible argument. See for example,
>Montague [1974], Davidson [1984], Lycan [1984].

Is that not essentially the same as (Frege, Quine, etc.):

>On a view like this, deducibility and validity represent idealizations
>of correct reasoning in natural language. A chunk of reasoning is
>correct to the extent that it corresponds to, or can be regimented by, a
>valid or deducible argument in a formal language.

Also which is essentially the same as this?:

>On a view like this, deducibility
>and validity represent mathematical models of (perhaps different aspects
>of) correct reasoning in natural languages. Correct chunks of reasoning
>correspond, more or less, to valid or deducible arguments; incorrect
>chunks of reasoning roughly correspond to invalid or non-deducible
>arguments. See, for example, Corcoran [1973] or Shapiro [1998].

I think that this focus on natural language invokes, at least in large
part, a pragmatic use. In that sense, couldn't one paraphase all three
just by saying:

"You take natural language, then inference (40 names for this including
contextual reasoning) out propositions (called a few things above
including "forms" and "mathematical models") and apply deductive or
inductive logic."

Isn't that nutshell what is essentially done (or attempted) in every
Usenet post? How many tens of thousands of times does one need to see
the same thing over and over before even a simple person like myself
recognizes patterns?

Did any of the above-mentioned authors read tens of thousands of
Usenet messages, and participate in 10,000 themselves? Where did
they get their samples, and what was their sample size? 1000x (or
whatever) the evidence seems to overcome 10x (or whatever, over
average folks like myself) the human-fallible untestable logic, I am
only supposing. Were their samples matters of record, like every Usenet
post, easily available and reproducable to all?

"Philosophy is always the victim of the latest experiment." (Sagan, I
think, at least where I first read it). Does this apply here?

Disclaimer: I understand the above is only a second-hand summary.
Understand all these authors did a lot more than is represented above,
and the "lot more" may be what is really interesting about them.

Larry

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