Bibliography

The Bed-Rock Beneath Pragmaticism

…the Actual, – the simple unmodalized Fact, – is that ingredient of the Truth the acknowledgement of which may be forced on the mind by experience, but can never receive a definite rational explanation free from any arbitrary element…

Very ignorant persons confound doubt with disbelief. Many others think simple unbelief constitutes doubt. What “doubt” really denotes is to be insupportably discontent to dispose for oneself of the proposition that is said to be “doubted,” in any suggestible way whatever, whether it be to affirm it to oneself, or to deny it, or yet to leave the question of its truth unsettled. The abstract definition is easily apprehended; but an intimate, pillow-sharing acquaintance with the thing must come when living experience brings it.

…in speaking […] of a “generalized” icon, I used the qualification in a sense of “generalize” common among designers, especially among cartographers, as well as in vernacular talk, though it is not the proper logical sense of the verb, since it does not signify the removal of any constituent of logical depth from a condition, nor confers any liberty on the interpreter, but implies some almost microscopic items that are, really falsifications committed in the interest of simplification. Thus, a map “generalizes” its image of a river in representing the latter as not making sundry small windings that it really does make. So recollection may be said to “generalize” the remembered perception in representing this to be without many insignificant details that really did belong to it; and although an icon is not, properly speaking, general, so far as it is a pure icon, yet every icon must “generalize,” more or less, in this peculiar sense. Even a photograph does so.

…the Necessary […] is that which tends to govern both Thought and real Fact, even should it never become absolute in either sway.

…the principle that logicians call “the Nota notae,” that the sign of a sign of anything, X, is itself a sign of the very same X…

...the Possible is an ingredient of the Truth which, in consequence of its vagueness, must remain a thought and can never be more than an idea except by taking on a definiteness that does belong to it in itself…

…I define a pseudo-continuum as that which modern writers on the theory of functions call a continuum. But this is fully represented by, and according to G. Cantor stands in one-to-one correspondence with, the totality of real values, rational and irrational; and these are iconized, in their turn, according to these writers [by the] entire body of decimal expressions carried out to the right to all finite powers of 1/10 without going on to Cantor’s ωth place of decimals.

For it is a principle continually employed in the reasoning of the universally accepted “doctrine of limits” that two values, that differ at all, differ by a finite value, which would not be true if the ωth place of decimals were supposed to be included in their exact expressions; and indeed the whole purpose of the doctrine of limits is to avoid acknowledging that that place is concerned. Consequently the denumeral rows of figures which, by virtue of a simple general principle, are in one-to-one correspondence with the values, have relations among themselves, quite regardless of their denoting those values that perfectly agree in form with the relations between the values; and consequently these unlimited decimal fractions themselves, apart from their significations, constitute a pseudo-continuum. This consideration renders it easy to define a pseudo-continuum. It is in the first place a collection of objects absolutely distinct from one another. Now from the fact that Cantor and others call it a “continuum,” as well as from other things they say about it, I am led to suspect that they do not regard the pseudo-continuum of unlimited decimal expressions as [having members] all absolutely distinct from any other, for the reason that, taking any one of them, it does not possess any one elementary and definite non-relative character which is not possessed by any other of them. But this is not what I mean, nor what is generally meant, by a collection of absolutely independent members. What I mean by that expression is that every member is distinguished from every other by possessing some one or another elementary and definite non-relative character which that other does not possess; and that this is the usual acceptation of the expression is evidenced by the fact that the majority of logicians are in the habit of conceiving of a universe of absolutely distinct individual objects, by which they only mean that every individual is in every respect, of a certain universe of respects, determined in one or other of two ways and that every individual is differently determined from every other in some of those respects; and they do not generally conceive that every individual object has a determination in any one elementary and definite respect, while all the other individuals are determined in the opposite way.

…a relative, or relative term, is a word, phrase, or sign fit to be the predicate of an assertion but requiring the affixion of more than one subject in order to complete the fully explicit expression of the matter of an assertion, a dyadic relative requiring two subjects, etc.

…the Phemic Sheet iconizes the Universe of Discourse, since it more immediately represents a field of Thought, or Mental Experience, which is itself directed to the Universe of Discourse, and considered as a sign, denotes that Universe. Moreover, it [is because it must be understood] as being directed to that Universe, that it is iconized by the Phemic Sheet. So, on the principle that logicians call “the Nota notae” that the sign of anything, X, is itself a sign of the very same X, the Phemic Sheet, in representing the field of attention, represents the general object of that attention, the Universe of Discourse.