ONT Re: Ontology as Math or Metaphysics?
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Note 4
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BU = Benjamin Udell
BU: That’s some pretty interesting stuff you’ve been sending out.
JA, citing MK, diagramming JR, reconstructing CSP:
| 3. Logic
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| (Formal Semiotic, or the science of self-controlled or deliberate thought;
| considers those things whose end is to represent something)
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| a. Philosophical Grammar
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| (Speculative Grammar, or the Theory of Meaning)
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| b. Critical Logic
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| (Theory of Inference)
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| i. Abduction (logic of hypothesis).
| ii. Induction (logic of sampling).
| iii. Deduction (formal logic).
BU: This tears it. I don’t care what it does to my budget,
I’ve got to get the Peirce CD. I’ve just got to know
what he thought the mathematics of logic consisted in.
I suggested that it consisted in the mathematics that
is specially useful to logic. But looking at some of
your excepts, maybe the answer is, the logic which is
specially useful to mathematics (as in the case of
reasoning about infinities & continuity). Maybe,
or maybe not, since he follows a discussion of that
straightaway with a discussion of logic as a branch
of philosophy. Well, I won’t speculate at length on
that which for you is just one of a number of issues
that you’re pursuing here.
I feel like I've collected almost enough data to risk a hypothesis --
there's Spice Racks A Priori and Spice Racks A Posteriori, and it's
precisely because of my predilections for the former that I must be
diligent toward the disciplines of the latter -- but we experienced
a bit more heat than light in this kitchen at our last get-together
on these premisses, so I am trying to be careful, and keep the fire
distinguisher at the ready.
I think that we need to sift out the ways that
Mathematics and Phenomenology are alike or not:
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| o Metaphysics |
| /| |
| / | |
| / | |
| Normative Science o | |
| / \ | |
| / \ | |
| / \| |
| Mathematics o o Phenomenology |
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| Normative science rests largely on phenomenology and on mathematics;|
| metaphysics on phenomenology and on normative science. |
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| Charles Sanders Peirce, 'Collected Papers', CP 1.186 (1903) |
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In the wise that Mathematics is kin to Phenomenology,
the operator "mathematics of" suggests a "survey of".
So "Math of Logic" intimates a descriptive survey of
a normative science of how to conduct one's thought
in signs with a due regard to the objects thereof.
But my intellectual taste buds are now piqued enough
that I'm off to reconnoiter in the wild woods of NEM,
to seek out some leaf more sage or salient than that.
Jon Awbrey
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