Relatives Of Second Intention • Comment 5

Re: C.S. Peirce • Relatives of Second Intention
Re: Peirce List (1) (2) • John Sowa (1) (2)
Re: Peirce ListJon Alan Schmidt

JAS:
Thanks for providing a longer excerpt of that passage than I did, including Peirce’s statement about “the lower animals.”  I see now that I was wrong when I said on Tuesday, “Peirce makes no claim in the relevant texts about non-human animals at all.”  What I should have said is that he makes no claim in the relevant texts about whether non-human animals can “learn to recognize negations.”  He merely expresses doubt that they “have any clear and steady conception of falsehood,” and adds that “without a knowledge of falsehood no development of discursive reason can take place.”
In other words, it is not reasoning per se that distinguishes humans from other animals, since no notion of falsity is required for that — only a capacity for drawing inferences, which in “non-relative formal logic” corresponds to the relation of implication such that one proposition necessarily (i.e., deductively) follows from another.  Instead, what distinguishes humans from other animals is discursive reasoning, which does require “a knowledge of falsehood” and the more sophisticated “logic of relatives.”
In accordance with Peirce’s own words, it is important to keep in mind that these points all have to do with logic, not psychology or linguistics.  His thesis is that we acquire the notion of falsity and associate it with the formal relation of negation through “the avenue of experience and logical reflexion,” when reality confronts us with surprising observations that call for explanation, thus compelling us to initiate the process of inquiry by which we eventually revise our previous beliefs that grounded our incorrect expectations.

Dear Jon Alan,

Thanks for your comments, which I look forward to studying further.  Earlier I mentioned CP 3.488–490 as one of “the very doors I first walked through into the wonderland of logic à la Peirce”.  That is because, just the other side of that door, at CP 3.491, Peirce introduces a triadic relative term signifying with reference to three elements $A, B, C$ in the universe of discourse that $A$ is neither $B$ nor $C.$

Now, a relation among three elements of an arbitrary universe of discourse is more general than a relation among three logical values but they are kin enough to connect the passage with Peirce’s marking of the amphecks Nand and Nnor and their sole sufficiency among boolean operations.

What flashed me back this time, though, was John Sowa raising the topic of reflection on visual diagrams, those being forms of expression and calling to mind what Peirce wrote about “logical reflexion” being “the observation of thoughts in their expressions”.

I’m now going to hold off further commentary on this passage and stand back to take in a broader view of its context, Peirce’s 1897 Logic of Relatives, as I’m seeing many issues I did not appreciate, much less understand in times past.  This looks like it will take me no little time …

Regards,

Jon

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