Inquiry Into Inquiry

Re: C.S. Peirce • Relatives of Second Intention
Re: Peirce List (1) (2) • John Sowa (1) (2)
Re: Peirce List • Jon 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 in the universe of discourse that is neither nor

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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Re: C.S. Peirce • Relatives of Second Intention
Re: Laws of Form • Lyle Anderson

LA:

Here Peirce is confusing Truth and Falsity with Good and Evil.  The Creator of the Universe (CotU) created Truth and Falsity when He drew the First Distinction.  The Universe started with Bet (2) not Aleph (1).  What was the First Commandment?  Do NOT eat of the Tree of the Knowledge of Good and Evil.  Good and Evil are many levels of abstraction away from True and False.

Dear Lyle,

Thanks for making that observation.  I had seen what Peirce did there, too, and it’s one reason I saw him as making an allegorical or parabolic use of felix culpa at that point, since I know he knows his Scripture too well to imagine it anything but intentional.  Read in that spirit Peirce is inviting us to contemplate a particular form of distinction — a threshold between an immersive state of being and a reflective stage of critical thought.

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Re: C.S. Peirce • Relatives of Second Intention
Re: FB | Medieval Logic • Kollbjorn Oldtheyn

Dear Kollbjorn,

I used to think I knew what Peirce was talking about in this passage but it looks like it may be time to make a new examination of that.

• Guess 1.  Strictly speaking he’s talking about his earlier system of “entitative graphs” which are logically dual to existential graphs as far as propositional calculus goes.  That may not affect his point, except he did not extend the entitative graphs to cover the logic of relative terms, so he may be talking about the limitations of absolute versus relative terms.
• Guess 2.  He may be alluding to the complex way he treated negation in his 1870 Logic of Relatives, which is very tricky but worth revisiting.
• Guess 3.  He may be talking about the threshold between first intentional and second intentional relatives, which may or may not be the same thing as first order versus second order logic.

At any rate, I’ll be looking further into it …

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Re: C.S. Peirce • Relatives of Second Intention
Re: FB | Medieval Logic • Kollbjorn Oldtheyn

Dear Kollbjorn,

The way I understand Peirce’s parable, he is asking, “How do we arrive at a condition far enough removed from our immersion in a current experience to question it, to reflect on it, and thereby conceive the possibility of something other?”  Until we do that we do not have a concept of “not”.

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Re: C.S. Peirce • Relatives of Second Intention
Re: Paradisaical Logic and the After Math • Comment (1) (2)

I am getting a feeling I occasionally get when discussing Peirce’s work in a group setting — as though we had a grand feast set before us while the dining philosophers wrangle over the amuse-bouche.  With that in mind I’d like to return to the inciting text, the one so exciting me all those years ago, and see what’s truly substantial and tantalizing in it.

Selections from C.S. Peirce, “The Logic of Relatives”, CP 3.456–552

488.   The general method of graphical representation of propositions has now been given in all its essential elements, except, of course, that we have not, as yet, studied any truths concerning special relatives;  for to do so would seem, at first, to be “extralogical”.

Logic in this stage of its development may be called paradisaical logic, because it represents the state of Man’s cognition before the Fall.  For although, with this apparatus, it is easy to write propositions necessarily true, it is absolutely impossible to write any which is necessarily false, or, in any way which that stage of logic affords, to find out that anything is false.  The mind has not as yet eaten of the fruit of the Tree of Knowledge of Truth and Falsity.

Probably it will not be doubted that every child in its mental development necessarily passes through a stage in which he has some ideas, but yet has never recognised that an idea may be erroneous;  and a stage that every child necessarily passes through must have been formerly passed through by the race in its adult development.  It may be doubted whether many of the lower animals have any clear and steady conception of falsehood;  for their instincts work so unerringly that there is little to force it upon their attention.  Yet plainly without a knowledge of falsehood no development of discursive reason can take place.

489.   This paradisaical logic appears in the study of non-relative formal logic.  But there no possible avenue appears by which the knowledge of falsehood could be brought into this Garden of Eden except by the arbitrary and inexplicable introduction of the Serpent in the guise of a proposition necessarily false.  The logic of relatives affords such an avenue, and that, the very avenue by which in actual development, this stage of logic supervenes.  It is the avenue of experience and logical reflexion.

490.   By logical reflexion, I mean the observation of thoughts in their expressions.  Aquinas remarked that this sort of reflexion is requisite to furnish us with those ideas which, from lack of contrast, ordinary external experience fails to bring into prominence.  He called such ideas second intentions.  Is is by means of relatives of second intention that the general method of logical representation is to find completion.

Reference

• Charles S. Peirce, “The Logic of Relatives”, The Monist, vol. 7, 161–217, (1897).  Reprinted, CP 3.456–552.

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