Gary F, Auke, List,
Before commenting on your notes,
I want to emphasize that Peirce's paragraph about paradisaical logic in
R699 (1911) is a short version of CP 3.488-489, from his Monist article
about entitative graphs (written in 1896, published in 1897). See the
copy attached as CP3_488.txt).
GF> are you seriously
claiming that an infants crying is an instance
of logical
negation?
No, of course not. I was just making the
point that infants are not born into a paradise. They have many negative
experiences about which they express negative thoughts. They learn to use
the words 'no' and 'not' soon after they begin to utter two or three word
sentences. That is long before they begin to say if-then
sentences.
GF> Peirce is using a metaphor to make a
point about logic. He never
approved of basing logical principles on
psychology.
I agree with both sentences. But his
metaphor is weird and unconvincing. In the 19th century, every university
graduate had studied Aristotle's syllogisms. Peirce could just give an
example to remind his readers that negation is important.
AvB> For me Pierce here hints at the distiction between a logica
utens and a logica docens. It marks the difference between semiosis
subject to the normative sciences and semiosis which is not.
That distinction is important. But in both cases (1896 and 1911),
he followed the metaphor with a discussion of negation. He didn't mention
semiosis or the normative sciences.
And by the way, the
fact that Peirce used the same weird metaphor in 1991 that he had
published in 1897 is significant. It shows that he must have reviewed his
earlier publications about entitative and existential graphs shortly
before writing R669.
In any case, I usually find
Peirce's examples and metaphors apt and
convincing. But I have no
idea why Peirce felt the need for that odd
metaphor. Every logic
since Aristotle had negations. Every logic
that Peirce studied since
he was 13 had negations. Why did he feel the need to justify including
negation in his logic? And if so, why did he resurrect an odd metaphor he
had used in a different context 15 years earlier?
Thought for the day: Did Peirce ask himself the same or similar
questions during the five days between ending R669 and beginning R670?
What thoughts led him to make negation a primitive in R670? In R670 and
L231, he didn't feel any need to justify that choice. He just showed
examples that use negations and nested negations.
John
>From Monist on entitative graphs (1897, written in 1896).
CP 3.488. 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.
3.489. This paradisaical logic appears in the study of nonrelative
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.
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