Peircelets

Icons are so completely substituted for their objects as hardly to be distinguished from them.

2012-02-16T12:06:00.000-08:00

Joseph Ransdell, "On Peirce's Conception of the Iconic Sign" at ARISBE: THE PEIRCE GATEWAY: "Icons are so completely substituted for their objects as hardly to be distinguished from them. Such are the diagrams of geometry. A diagram, indeed, so far as it has a general signification, is not a pure icon; but in the middle part of our reasonings we forget that abstractness in great measure, and the diagram is for us the very thing. So in contemplating a painting, there is a moment when we lose the consciousness that it is not the thing, the distinction of the real and the copy disappears, and it is for the moment a pure dream--not any particular existence, and yet not general. At that moment we are contemplating an icon. (Collected Papers, 3.362)"

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Charles Sanders Peirce - Thinking in Threes

Peirce Deals with Spurious "Metaphysical" Distinctions

2012-02-16T11:52:00.000-08:00

The Use and Abuse of the Immediate/Dynamical Object Distinction:

This is perhaps what Peirce himself was alluding to -- at least in part -- in that gnomic passage in "The Fixation of Belief" where he says:

"... the importance of what may be deduced from the assumptions involved in the logical question turns out to be greater than might be supposed, and this for reasons which it is difficult to exhibit at the outset. The only one which I shall here mention is, that conceptions which are really products of logical reflection, without being readily seen to be so, mingle with our ordinary thoughts, and are frequently the causes of great confusion. ... The truth is, that common-sense, or thought as it first emerges above the level of the narrowly practical, is deeply imbued with that bad logical quality to which the epithet metaphysical is commonly applied; and nothing can clear it up but a severe course of logic. (CP 5.369 or W3, 246, 1877)"

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Charles Sanders Peirce - Thinking in Threes

Charles Sanders Peirce on how scientists come to agree

2012-01-29T13:13:00.000-08:00

Charles Sanders Peirce on how scientists come to agree
[Quoting Peirce] "One man may investigate the velocity of light by studying the transit of Venus and the aberration of the stars; another by the oppositions of Mars and the eclipses of Jupiter’s satellites; a third by the method of Fizeau; a fourth by that of Foucault; a fifth by the motions of the curves of Lissajoux; a sixth, a seventh, an eighth, and a ninth, may follow the different method of comparing the measures of statical and dynamical electricity. They may at first obtain different results, but, as each perfects his method and his processes, the results are found to move steadily together toward a destined center. So with all scientific research. Different minds may set out with the most antagonistic views, but the progress of investigation carries them by a force outside themselves to one and the same conclusion. (Collected Papers, 5.407)”
Cap tip Peter
Charles Sanders Peirce - Thinking in Threes

Derrida on Peirce on Symbols and Signs a Five Step Progression - Yahoo! Voices - voices.yahoo.com

2012-01-28T13:56:00.000-08:00

Derrida on Peirce on Symbols and Signs a Five Step Progression - Yahoo! Voices - voices.yahoo.com:

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Charles Sanders Peirce - Thinking in Threes

Charles Sanders Peirce on Thought as Melody - Yahoo! Voices - voices.yahoo.com

2012-01-28T13:37:00.000-08:00

Charles Sanders Peirce on Thought as Melody - Yahoo! Voices - voices.yahoo.com: "Applying ideas of Charles Sanders Peirce to our living. Text is drawn from Charles Sanders Peirce as cited in James K Feibleman's remarkable, largely ignored "An Introduction to The Philosophy of Charles S. Peirce" MIT 1969 (1946)"

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Charles Sanders Peirce - Thinking in Threes

ShortFormContent at Blogger: Charles Sanders Peirce - A Collection of Threes

2012-01-27T12:19:00.000-08:00

ShortFormContent at Blogger: Charles Sanders Peirce - A Collection of Threes:

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I have posted this key piece at the link above. It is a useful means of applying one's mind to several fruitful thought processes.

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Perhaps "Fregean Revolution" needs some revision

2012-01-27T04:49:00.000-08:00

Abstract. The historiography of logic conceives of a Fregean revolution in which modern mathematical logic (also called symbolic logic) has replaced Aristotelian logic. The preeminent expositors of this conception are Jean van Heijenoort (1912–1986) and Donald Angus Gillies. The innovations and characteristics that comprise mathematical logic and distinguish it from Aristotelian logic, according to this conception, created ex nihlo by Gottlob Frege (1848–1925) in his Begriffsschrift of 1879, and with Bertrand Russell (1872–1970) as its chief This position likewise understands the algebraic logic of Augustus De Morgan (1806–1871), George Boole (1815–1864), Charles Sanders Peirce (1838–1914), and Ernst Schröder (1841–1902) as belonging to the Aristotelian tradition. The “Booleans” are understood, from this vantage point, to merely have rewritten Aristotelian syllogistic in algebraic guise.

The most detailed listing and elaboration of Frege’s innovations, and the characteristics that distinguish mathematical logic from Aristotelian logic, were set forth by van Heijenoort. I consider each of the elements of van Heijenoort’s list and note the extent to which Peirce had also developed each of these aspects of logic. I also consider the extent to which Peirce and Frege were aware of, and may have influenced, one another’s logical writings. Thus, the work in logic of Charles Peirce is surveyed in light of the characteristics enumerated by historian of logic J. van Heijenoort as defining the original innovations in logic of Frege and which together are said to be the basis of what has come to be called the “Fregean revolution” in logic and which are said to constitute the elements of Frege’s Begriffsschrift of 1879 as the “founding” document of modern logic. - Irving Anellis

SOURCE (PDF)

A sign stands for something to the idea which it produces, or modifies.

2012-01-19T03:55:00.000-08:00

Peirce's Arisbe: R. Marty's 76 DEFINITIONS OF THE SIGN BY C.S. PEIRCE: "61- C.P. 1-339 - unidentified fragment1.

The easiest of those which are of philosophical interest is the idea of a sign, or representation. A sign stands for something to the idea which it produces, or modifies. Or, it is a vehicle conveying into the mind something from without. That for which it stands is called its object; that which it conveys, its meaning; and the idea to which it gives rise, its interpretant. The object of representation can be nothing but a representation of which the first representation is the interpretant. But an endless series of representations, each representing the one behind it, may be conceived to have an absolute object at its limit. The meaning of a representation can be nothing but a representation. In fact, it is nothing but the representation itself conceived as stripped of irrelevant clothing. But this clothing never can be completely stripped off; it is only changed for something more diaphanous. So there is an infinite regression here. Finally, the interpretant is nothing but another representation to which the torch of truth is handed along; and as representation, it has its interpretant again. Lo, another infinite series."

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I take it to be part of Peirce's realism (opposing nominalism) that he takes the sign itself to be being or reality that is only defined by its interpretant,

A Sop To Cerberus - Charles Sanders Peirce

2012-01-19T03:44:00.000-08:00

Commens Peirce Dictionary: Sign: ""I define a Sign as anything which is so determined by something else, called its Object, and so determines an effect upon a person, which effect I call its Interpretant, that the latter is thereby mediately determined by the former. My insertion of "upon a person" is a sop to Cerberus, because I despair of making my own broader conception understood." (A Letter to Lady Welby, SS 80-81, 1908)"

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A late stab at sign. The referenced page contains other stabs and leads to still others. It is part of a quite comprehensive Peirce glossary of many terms.

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What practical consequences might conceivably result

2011-12-24T03:36:00.000-08:00

Pragmatic Maxim – Jon Awbrey:

"Such reasonings and all reasonings turn upon the idea that if one exerts certain kinds of volition, one will undergo in return certain compulsory perceptions. Now this sort of consideration, namely, that certain lines of conduct will entail certain kinds of inevitable experiences is what is called a “practical consideration”. Hence is justified the maxim, belief in which constitutes pragmatism; namely:

"In order to ascertain the meaning of an intellectual conception one should consider what practical consequences might conceivably result by necessity from the truth of that conception; and the sum of these consequences will constitute the entire meaning of the conception. (Peirce, CP 5.9, 1905)."

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Other forms of the pragmatic maxim are noted at the Pragmatic Maxim link above.

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A simple but persistent mistake on the part of one of the pilots

2011-12-19T06:17:00.000-08:00

Air France 447 Flight-Data Recorder Transcript - What Really Happened Aboard Air France 447 - Popular Mechanics: "We now understand that, indeed, AF447 passed into clouds associated with a large system of thunderstorms, its speed sensors became iced over, and the autopilot disengaged. In the ensuing confusion, the pilots lost control of the airplane because they reacted incorrectly to the loss of instrumentation and then seemed unable to comprehend the nature of the problems they had caused. Neither weather nor malfunction doomed AF447, nor a complex chain of error, but a simple but persistent mistake on the part of one of the pilots. "

Cap tip Ben

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If God's self is love, that which he loves must be defect of love.

2011-12-19T06:08:00.000-08:00

"Philosophy, when just escaping from its golden pupa-skin, mythology, proclaimed the great evolutionary agency of the universe to be Love. Or, since this pirate-lingo, English, is poor in such-like words, let us say Eros, the exuberance-love. Afterwards, Empedocles set up passionate love and hate as the two coordinate powers of the universe. In some passages, kindness is the word. But certainly, in any sense in which it has an opposite, to be senior partner of that opposite, is the highest position that love can attain. Nevertheless, the ontological gospeller, in whose days those views were familiar topics, made the One Supreme Being, by whom all things have been made out of nothing, to be cherishing-love. What, then, can he say to hate? Never mind, at this time, what the scribe of the Apocalypse, if he were John, stung at length by persecution into a rage, unable to distinguish suggestions of evil from visions of heaven, and so become the Slanderer of God to men, may have dreamed. The question is rather what the sane John thought, or ought to have thought, in order to carry out his idea consistently. His statement that God is love seems aimed at that saying of Ecclesiastes that we cannot tell whether God bears us love or hatred. "Nay," says John, "we can tell, and very simply! We know and have trusted the love which God hath in us. God is love." There is no logic in this, unless it means that God loves all men. In the preceding paragraph, he had said, "God is light and in him is no darkness at all." We are to understand, then, that as darkness is merely the defect of light, so hatred and evil are mere imperfect stages of agapę and agathon, love and loveliness.

"This concords with that utterance reported in John's Gospel: "God sent not the Son into the world to judge the world; but that the world should through him be saved. He that believeth on him is not judged: he that believeth not hath been judged already. . . . And this is the judgment, that the light is come into the world, and that men loved darkness rather than the light." That is to say, God visits no punishment on them; they punish themselves, by their natural affinity for the defective. Thus, the love that God is, is not a love of which hatred is the contrary; otherwise Satan would be a coordinate power; but it is a love which embraces hatred as an imperfect stage of it, an Anteros -- yea, even needs hatred and hatefulness as its object. For self-love is no love; so if God's self is love, that which he loves must be defect of love; just as a luminary can light up only that which otherwise would be dark."

From Charles Sanders Peirce, "Evolutionary Love".

Cap tip Gary R.

How often do we think of the thing in algebra?

2011-12-19T05:58:00.000-08:00

"How often do we think of the thing in algebra? When we use the symbol of multiplication we do not even think out the conception of multiplication, we think merely of the laws of that symbol, which coincide with the laws of the conception, and what is more to the purpose coincide with the laws of multiplication in the object. Now, I ask, how is it that anything can be done with a symbol, without reflecting upon the conception, much less imagining the object that belongs to it? It is simply because the symbol has acquired a nature, which may be described thus, that when it is brought before the mind certain principles of its use -- whether reflected on or not -- by association immediately regulate the action of the mind; and these may be regarded as laws of the symbol itself which it cannot 'as a symbol' transgress."

- C.S. Peirce, 'Chronological Edition', CE 1, p. 173. Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865), Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

Cap tip Jon

From Charles Sanders Peirce, "Evolutionary Love"

2011-12-18T10:47:00.000-08:00

Charles Peirce, "Evolutionary Love", at ARISBE: THE PEIRCE GATEWAY: "Undoubtedly the external circumstance, which more than all others at first inclined men to accept Christianity in its loveliness and tenderness, was the fearful extent to which society was broken up into units by the unmitigated greed and hard-heartedness into which the Romans had seduced the world. And yet it was that very same fact, more than any other external circumstance, that fostered that bitterness against the wicked world of which the primitive gospel of Mark contains not a single trace."

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C. S. Peirce on A Definition of Logic

2011-12-18T09:17:00.000-08:00

Some reasons having now been given for adopting the unpsychological conception of the science, let us now seek to make this conception sufficiently distinct to serve for a definition of logic. For this purpose we must bring our 'logos' from the abstract to the concrete, from the absolute to the dependent. There is no science of absolutes. The metaphysical logos is no more to us than the metaphysical soul or the metaphysical matter. To the absolute Idea or Logos, the dependent or relative 'word' corresponds. The word 'horse', is thought of as being a word though it be unwritten, unsaid, and unthought. It is true, it must be considered as having been thought; but it need not have been thought by the same mind which regards it as being a word. I can think of a word in Feejee, though I can attach no definite articulation to it, and do not guess what it would be like. Such a word, abstract but not absolute, is no more than the genus of all symbols having the same meaning. We can also think of the higher genus which contains words of all meanings. A first approximation to a definition, then, will be that logic is the science of representations in general, whether
mental or material. This definition coincides with Locke's. It is however too wide for logic does not treat of all kinds of representations. The resemblance of a portrait to its object, for example, is not logical truth. It is necessary, therefore, to divide the genus representation according to the different ways in which it may accord with its object.

The first and simplest kind of truth is the resemblance of a copy. It may be roughly stated to consist in a sameness of predicates. Leibniz would say that carried to its highest point, it would destroy itself by becoming identity. Whether that is true or not, all known resemblance has a limit. Hence, resemblance is always partial truth. On the other hand, no two things are so different as to resemble each other in no particular. Such a case is supposed in the proverb that Dreams go by contraries, -- an absurd notion, since concretes have no contraries. A false copy is one which claims to resemble an object which it does not resemble. But this never fully occurs, for two reasons; in the first place, the falsehood does not lie in the copy itself but in the 'claim' which is made for it, in the 'superscription' for instance; in the second place, as there must be 'some' resemblance between the copy and its object, this falsehood cannot be entire. Hence, there is no absolute truth or falsehood of copies. Now logical representations have absolute truth and falsehood as we know 'à posteriori' from the law of excluded middle. Hence, logic does not treat of copies.

The second kind of truth, is the denotation of a sign, according to a previous convention. A child's name, for example, by a convention made at baptism, denotes that person. Signs may be plural but they cannot have genuine generality because each of the objects to which they refer must have been fixed upon by convention. It is true that we may agree that a certain sign shall denote a certain individual conception, an individual act of an individual mind, and that conception may stand for all conceptions resembling it; but in this case, the generality belongs to the 'conception' and not to the sign. Signs, therefore, in this narrow sense are not treated of in logic, because logic deals only with general terms.

The third kind of truth or accordance of a representation with its object, is that which inheres in the very nature of the representation whether that nature be original or acquired. Such a representation I name a 'symbol'.

- C.S. Peirce, 'Chronological Edition', CE 1, pp. 169-170. Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

Cap tip Jon

Logic is an analysis of forms not a study of the mind.

2011-12-17T05:32:00.000-08:00

Logic is an analysis of forms not a study of the mind. It tells 'why' an inference follows not 'how' it arises in the mind. It is the business therefore of the logician to break up complicated inferences from numerous premisses into the simplest possible parts and not to leave them as they are.

C.S. Peirce, 'Chronological Edition', CE 1, p. 217. Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865), 'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866', Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

Cap tip Jon

Charles Sanders Peirce on Logic as Semiotic

2011-12-17T05:14:00.000-08:00

Logic, in its general sense, is, as I believe I have shown, only another name for 'semiotic' (Greek 'semeiotike'), the quasi-necessary, or formal, doctrine of signs. By describing the doctrine as "quasi-necessary", or formal, I mean that we observe the characters of such signs as we know, and from such an observation, by a process which I will not object to naming Abstraction, we are led to statements, eminently fallible, and therefore in one sense by no means necessary, as to what 'must be' the characters of all signs used by a "scientific" intelligence, that is to say, by an intelligence capable of learning by experience. As to that process of abstraction, it is itself a sort of observation.

The faculty which I call abstractive observation is one which ordinary people perfectly recognize, but for which the theories of philosophers sometimes hardly leave room. It is a familiar experience to every human being to wish for something quite beyond his present means, and to follow that wish by the question, "Should I wish for that thing just the same, if I had ample means to gratify it?" To answer that question, he searches his heart, and in doing so makes what I term an abstractive observation. He makes in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what modifications the hypothetical state of things would
require to be made in that picture, and then examines it, that is, 'observes' what he has imagined, to see whether
the same ardent desire is there to be discerned. By such a process, which is at bottom very much like mathematical reasoning, we can reach conclusions as to what 'would be' true of signs in all cases, so long as the intelligence using them was scientific.

- Charles Sanders Peirce, 'Collected Papers', CP 2.227. Eds. Note. "From an unidentified fragment, c. 1897".

Cap tip Jon

Key C. S. Peirce Interpretations

2011-12-15T12:43:00.000-08:00

ELISEO FERNÁNDEZ

"Energy, Semiosis and Emergence — The Place of Biosemiotics in an Evolutionary Conception of Nature" (in PDF format)
http://www.lindahall.org/services/reference/papers/fernandez/Energy_semiosis_and_emergence.pdf
"Peircean Habits and the Life of Symbols" (in PDF format)
http://www.lindahall.org/services/reference/papers/fernandez/Peirce_habits.pdf
"Variescence — Cosmic Progress and Contemporary Science" (in PDF format)
http://www.lindahall.org/services/reference/papers/fernandez/variescence.pdf
Also available in the original Spanish:
"Variescencia — Progreso cósmico y ciencia contemporánea" (in PDF format)
http://www.lindahall.org/services/reference/papers/fernandez/variescence_spanish.pdf
"Living is Surviving: Causation, Reproduction and Semiosis" (in PDF format)
http://www.lindahall.org/services/reference/papers/fernandez/survive.pdf
"Life, Temporality and Semiosis: The Place of Biosemiotics within General Semiotics" (in PDF format)
http://www.lindahall.org/services/reference/papers/fernandez/semiotics.pdf
"Biosemiotics and the Relational Turn in Biology" (in PDF format)
http://www.lindahall.org/services/reference/papers/fernandez/biosemiotics_and_the_relational_turn_in_biology.pdf
"Peirce in 21st Century Science and Philosophy: New Prospects" (in PDF format)
http://www.lindahall.org/services/reference/papers/fernandez/P_en_A_English.pdf
Also available in the original Spanish:
"Peirce en la Ciencia y la Filosofía del Siglo XXI: Nuevas Oportunidades" (in PDF format)
http://www.lindahall.org/services/reference/papers/fernandez/P_en_A_Espanol.pdf
"Biosemiotics from Peirce to Rosen" (in PDF format)
http://www.lindahall.org/services/reference/papers/fernandez/PRfinal.pdf
"Signs, Instruments and Self-Reference in Biosemiotics" (in PDF format)
http://www.lindahall.org/services/reference/papers/fernandez/signs.pdf

From On Small Differences in Sensation By Charles Sanders Peirce & Joseph Jastrow (1885)

2011-12-08T03:49:00.000-08:00

Classics in the History of Psychology: " This happened in cases where the judgments were so much affected by the difference of pressures as to be correct three times out of five. The general fact has highly important practical bearings, since it gives new reason for believing that we gather what is passing in one another's minds in large measure from sensations so faint that we are not fairly aware of having them, and can give no account of how we reach our conclusions about such matters. The insight of females as well as certain "telepathic" phenomena may be explained in this way. Such faint sensations ought to be fully studied by the psychologist and assiduously cultivated by every man." - from On Small Differences in Sensation By Charles Sanders Peirce & Joseph Jastrow (1885)

Cap tips Jon, Jonathan

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The faculty which I call abstractive observation

2011-12-07T17:38:00.001-08:00

The faculty which I call abstractive observation is one which ordinary people perfectly recognize, but for which the theories of philosophers sometimes hardly leave room. It is a familiar experience to every human being to wish for something quite beyond his present means, and to follow that wish by the question, "Should I wish for that thing just the same, if I had ample means to gratify it?" To answer that question, he searches his heart, and in doing so makes what I term an abstractive observation. He makes in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what modifications the hypothetical state of things would require to be made in that picture, and then examines it, that is, 'observes' what he has imagined, to see whether the same ardent desire is there to be discerned. By such a process, which is at bottom very much like mathematical reasoning, we can reach conclusions as to what 'would be' true of signs in all cases, so long as the intelligence using them was scientific.

- Charles Sanders Peirce, 'Collected Papers', CP 2.227. Eds. Note. "From an unidentified fragment, c. 1897".

Cap tip Jon

Semeiotic theory is necessarily first among sciences

2011-12-06T04:52:00.001-08:00

"For "semiotics" to be an effective unifying discipline it must not isolate itself. Unfortunately, it's too late. By a series of missteps, related cross-discipline confusions, and plain term usage, "semiotics" *is* isolated.

"The irony is that semeiotic theory is necessarily first among sciences. Yet its current position is worse than last. If you surveyed most scientists today that understand the discipline I suspect they would consider it irrelevant, many more have never heard of it.

"And I do not think the situation can be rescued. Any serious analysis of the situation must, I think, draw this conclusion.

"The right approach I have concluded is to drive a resurgence with renewed interest in logic and its foundations, expanding the scope of the discipline to encompass the concerns that rest within what we call "semeiotic theory." Logic has a role that is better appreciated and can be driven toward a useful expansion and a clarification by semeiotic theory." - Steven Ericsson-Zenith

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Every logical evolution of thought should be dialogic

2011-12-03T14:46:00.001-08:00

CP 4.551 (the 1906 “Prolegomena”):

Admitting that connected Signs must have a Quasi-mind, it may further be declared that there can be no isolated sign. Moreover, signs require at least two Quasi-minds; a Quasi-utterer and a Quasi-interpreter; and although these two are at one (i.e., are one mind) in the sign itself, they must nevertheless be distinct. In the Sign they are, so to say, welded. Accordingly, it is not merely a fact of human Psychology, but a necessity of Logic, that every logical evolution of thought should be dialogic.

Cap tip Gary F.

Of the three Universes of Experience

2011-12-02T14:51:00.001-08:00

"A Neglected Argument" (1908 _Hibbert Journal_, vol. 7, no. 1, pp. 90-112) Section 1

http://en.wikisource.org/wiki/A_Neglected_Argument_for_the_Reality_of_God

http://www.gnusystems.ca/CSPgod.htm#na0

CP 6.455.

Of the three Universes of Experience familiar to us all †1, the first comprises all mere Ideas, those airy nothings to which the mind of poet, pure mathematician, or another _might_ give local habitation and a name within that mind. Their very airy-nothingness, the fact that their Being consists in mere capability of getting thought, not in anybody's Actually thinking them, saves their Reality. The second Universe is that of the Brute Actuality of things and facts. I am confident that their Being consists in reactions against Brute forces, notwithstanding objections redoubtable until they are closely and fairly examined. The third Universe comprises everything whose being consists in active power to establish connections between different objects, especially between objects in different Universes. Such is everything which is essentially a Sign — not the mere body of the Sign, which is not essentially such, but, so to speak, the Sign's Soul, which has its Being in its power of serving as intermediary between its Object and a Mind. Such, too, is a living consciousness, and such the life, the power of growth, of a plant. Such is a living institution — a daily newspaper, a great fortune, a social "movement."

Cap tip Ben

The perfect truth cannot be stated

2011-12-02T14:46:00.001-08:00

From "Truth and Falsity and Error" in _Dictionary of Philosophy and Psychology_ vol. 2 (1902) pp. 718-20.

http://www.gnusystems.ca/BaldwinPeirce.htm#Truth

http://books.google.com/books?id=punn721pFwoC&pg=PA718

CP 5.567.

These characters equally apply to pure mathematics. Projective geometry is not pure mathematics, unless it be recognized that whatever is said of rays holds good of every family of curves of which there is one and one only through any two points, and any two of which have a point in common. But even then it is not pure mathematics until for points we put any complete determinations of any two-dimensional continuum. Nor will that be enough. A proposition is not a statement of perfectly pure mathematics until it is devoid of all definite meaning, and comes to this — that a property of a certain icon is pointed out and is declared to belong to anything like it, of which instances are given. The perfect truth cannot be stated, except in the sense that it confesses its imperfection. The pure mathematician deals exclusively with hypotheses. Whether or not there is any corresponding real thing, he does not care. His hypotheses are creatures of his own imagination; but he discovers in them relations which surprise him sometimes. A metaphysician may hold that this very forcing upon the mathematician's acceptance of propositions for which he was not prepared, proves, or even constitutes, a mode of being independent of the mathematician's thought, and so a _reality_. But whether there is any reality or not, the truth of the pure mathematical proposition is constituted by the impossibility of ever finding a case in which it fails. This, however, is only possible if we confess the impossibility of precisely defining it.

Cap tip Ben

Fallacies in pure mathematics

2011-12-02T14:42:00.001-08:00

From "Reasoning" in _Dictionary of Philosophy and Psychology_, vol. 2 (1902), pp. 426-28

from CP 2.778

Fallacies in pure mathematics have gone undetected for many centuries. It is to ideal states of things alone — or to real states of things as ideally conceived, always more or less departing from the reality — that deduction applies.

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