[Inquiry] Re: Kaina Stoicheia

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

KS.  Note 16

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| Without stopping here to discuss this large question,
| I will say that psychology is a science which makes
| special observations;  and its whole business is
| to make the phenomena so observed (along with
| familiar facts allied to those things),
| definite and comprehensible.
|
| Logic is a science little removed from pure mathematics.
| It cannot be said to make any positive phenomena known,
| although it takes account and rests upon phenomena of
| daily and hourly experience, which it so analyzes as
| to bring out recondite truths about them.
|
| One might think that a pure mathematician might assume these
| things as an initial hypothesis and deduce logic from these;
| but this turns out, upon trial, not to be the case.
|
| The logician has to be recurring to reexamination of the
| phenomena all along the course of his investigations.
| But logic is all but as far remote from psychology
| as is pure mathematics.
|
| Logic is the study of the eesential nature of signs.
|
| A sign is something that exists in replicas.  Whether the sign "it is raining"
| or "all pairs of particles of matter have component accelerations toward one
| another inversely proportional to the square of the distance" happens to have
| a replica in writing, in oral speech, or in silent thought, is a distinction
| of the very minutest interest to logic, which is a study, not of replicas,
| but of signs.
|
| But this is not the only, nor the most serious error involved in making logic
| treat of "judgments" in place of propositions.  It involves confounding two
| things which must be distinguished if a real comprehension of logic is to
| be attained.
|
| A 'proposition', as I have just intimated, is not to be understood as the
| lingual expression of a judgment.  It is, on the contrary, that sign of
| which the judgment is one replica and the lingual expression another.
| But a judgment is distinctly 'more' than the mere mental replica of
| a proposition.  It not merely 'expresses' the proposition, but it
| goes further and 'accepts' it.
|
| I grant that the normal use of a proposition is to affirm it;  and its
| chief logical properties relate to what would result in reference to its
| affirmation.  It is, therefore, convenient in logic to express propositions
| in most cases in the indicative mood.  But the proposition in the sentence,
| "Socrates est sapiens", strictly expressed, is "Socratem sapientum esse".
| The defence of this position is that in this way we distinguish between
| a proposition and the assertion of it;  and without such distinction it
| is impossible to get a distinct notion of the nature of the proposition.
|
| One and the same proposition may be affirmed, denied, judged,
| doubted, inwardly inquired into, put as a question, wished,
| asked for, effectively commanded, taught, or merely expressed,
| and does not thereby become a different proposition.  What is
| the nature of these operations?  The only one that need detain
| us is affirmation, including judgment, or affirmation to oneself.
|
| As an aid in dissecting the constitution of affirmation I shall employ
| a certain logical magnifying-glass that I have often found efficient
| in such business.  Imagine, then, that I write a proposition on a
| piece of paper, perhaps a number of times, simply as a calligraphic
| exercise.  It is not likely to prove a dangerous amusement.  But
| suppose I afterwards carry the paper before a notary public and
| make affidavit to its contents.  That may prove to be a horse
| of another color.  The reason is that this affidavit may be
| used to determine an assent to the proposition it contains
| in the minds of judge and jury; -- an effect that the paper
| would not have had if I had not sworn to it.  For certain
| penalties here and hereafter are attached to swearing to
| a false proposition;  and consequently the fact that
| I have sworn to it will be taken as a negative index
| that it is not false.  This assent in judge and jury's
| minds may effect in the minds of sheriff and posse a
| determination to an act of force to the detriment of
| some innocent man's liberty or property.  Now certain
| ideas of justice and good order are so powerful that
| the ultimate result may be very bad for me.
|
| This is the way that affirmation looks under the microscope;  for the only
| difference between swearing to a proposition and an ordinary affirmation of
| it, such as logic contemplates, is that in the latter case the penalties
| are less and even less certain than those of the law.  The reason there
| are any penalties is, as before, that the affirmation may determine a
| judgment to the same effect in the mind of the interpreter to his cost.
| It cannot be that the sole cause of his believing it is that there are
| such penalties, since two events cannot cause one another, unless they
| are simultaneous.  There must have been, and we well know that there is,
| a sort of hypnotic disposition to believe what one is told with an air [of]
| command.  It is Grimes's credenciveness, which is the essence of hypnotism.
| This disposition produced belief;  belief produced the penalties;  and the
| knowledge of these strengthens the disposition to believe.
|
| C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 248-249
|
| C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by
| Charles S. Peirce, Volume 4, Mathematical Philosophy',
| Mouton, The Hague, 1976.
|
| Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)',
| Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o