[Inquiry] Re: Model Theory Unplugged

[Jon Awbrey]

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MTU.  Note 4

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The next part of this is still a bit rough in my mind,
and it will most likely be unavoidable that we advance
in a halting, incremental fashion, with the possibility
of progress being subject to the occasional backtracking.

The task will be to show how the heuristic procedure that is
recommended by the so-called "pragmatic maxim" is tantamount
to what is commonly known as a "representation principle" in
mathematics.  Generally speaking, a "representation theorem"
says something to the effect that any mathematical entity of
a particular abstract sort can be represented in a specified
concrete form.

In the present setting I will show that the pragmatic maxim is aptly interpreted
to say that any abstract concept can be represented in a particular concrete way,
where the concept being true amounts to a constraint on the relationship between
actions and reactions, that is, courses of conduct and consequential experiences.

For future reference, here are seven excerpts that
give different versions of the pragmatic maxim or
that provide explanatory glosses on its meaning:

PM_1

| Pragmatism.  The opinion that metaphysics is to be largely cleared up
| by the application of the following maxim for attaining clearness of
| apprehension:  "Consider what effects, that might conceivably have
| practical bearings, we conceive the object of our conception to have.
| Then, our conception of these effects is the whole of our conception
| of the object."
|
| Peirce, CP 5.2, 1878/1902.

PM_2

| Pragmaticism was originally enounced in the form of a maxim, as follows:
| Consider what effects that might conceivably have practical bearings you
| conceive the objects of your conception to have.  Then, your conception
| of those effects is the whole of your conception of the object.
|
| Peirce, CP 5.438, 1878/1905.

PM_3

| Such reasonings and all reasonings turn upon the idea that if one exerts
| certain kinds of volition, one will undergo in return certain compulsory
| perceptions.  Now this sort of consideration, namely, that certain lines
| of conduct will entail certain kinds of inevitable experiences is what
| is called a "practical consideration".  Hence is justified the maxim,
| belief in which constitutes pragmatism;  namely,
| 
| In order to ascertain the meaning of an intellectual conception one should
| consider what practical consequences might conceivably result by necessity
| from the truth of that conception;  and the sum of these consequences will
| constitute the entire meaning of the conception.
|
| Peirce, CP 5.9, 1905.

PM_4

| Pragmatism is the principle that every theoretical judgment expressible
| in a sentence in the indicative mood is a confused form of thought whose
| only meaning, if it has any, lies in its tendency to enforce a corresponding
| practical maxim expressible as a conditional sentence having its apodosis in
| the imperative mood.
|
| Peirce, CP 5.18, 1903.

PM_5

| The doctrine appears to assume that the end of man is action --
| a stoical axiom which, to the present writer at the age of
| sixty, does not recommend itself so forcibly as it did at
| thirty.  If it be admitted, on the contrary, that action
| wants an end, and that that end must be something of a
| general description, then the spirit of the maxim itself,
| which is that we must look to the upshot of our concepts
| in order rightly to apprehend them, would direct us towards
| something different from practical facts, namely, to general
| ideas, as the true interpreters of our thought.
|
| Peirce, CP 5.3, 1902.

PM_6

| The study of philosophy consists, therefore, in reflexion, and pragmatism
| is that method of reflexion which is guided by constantly holding in view
| its purpose and the purpose of the ideas it analyzes, whether these ends
| be of the nature and uses of action or of thought.  ...
| 
| It will be seen that pragmatism is not a Weltanschauung but is a
| method of reflexion having for its purpose to render ideas clear.
|
| Peirce, CP 5.13 note 1, 1902.

PM_7

| This employment five times over of derivates of 'concipere' must then have
| had a purpose.  In point of fact it had two.  One was to show that I was
| speaking of meaning in no other sense than that of intellectual purport.
| The other was to avoid all danger of being understood as attempting to
| explain a concept by percepts, images, schemata, or by anything but
| concepts.  I did not, therefore, mean to say that acts, which are
| more strictly singular than anything, could constitute the purport,
| or adequate proper interpretation, of any symbol.  I compared action
| to the finale of the symphony of thought, belief being a demicadence.
| Nobody conceives that the few bars at the end of a musical movement
| are the purpose of the movement.  They may be called its upshot.
|
| Peirce, CP 5.402 note 3, 1906.

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