Manuscript  Posted 21/09/2014
Peirce, Charles S. (nd). Notes on B. Peirce's Linear Associative Algebra. MS [R] 78
Robin Catalogue:
A. MS., n.p., n.d., pp. 15.
A defense of Benjamin Peirce’s definition of “mathematics”: Six possible objections noted and countered. Cf. G188110 and MS. 18...


Manuscript  Posted 21/09/2014
Peirce, Charles S. (1912 [c.]). Secundal Computation. MS [R] 53
Robin Catalogue:
A. MS., n.p., [c.1912?], pp. 16, with 2 other attempts to write p. 2.
The notion of “elegance” in mathematics. The secundal system. Modes of reality.


Manuscript  Posted 21/09/2014
Peirce, Charles S. (1910 [c.]). Notes on Numerical Notation. MS [R] 52
Robin Catalogue:
A. MS., n.p., [c.1910?], pp. 110, plus a rejected p. 2.
The notion of “elegance” in mathematics. The secundal system.


Manuscript  Posted 15/09/2014
Peirce, Charles S. (1904). Second Definition of Ordinals [R]. MS [R] 45
Robin Catalogue:
A. MS., n.p., [1904], pp. 46; 1922; and 1 p. (the number of which is missing).
Parenthetically: “As for the whole existing race of philosophers, say John...
Ordinal Number, Appurtenance, Comparative Fulfillment, Exclusively Existential Relation, Suilation, Past, Future, Definiteness, Generality, Vagueness, Principle of Excluded Middle, Principle of Contradiction, Fiction, Real, Possible, Mathematics, Actuality, Existence, John Dewey, Royce, Denumerable Collection, First Abnumerable Collection, Collection, Abstraction, Essence, Thought, Counting


Manuscript  Posted 11/09/2014
Peirce, Charles S. (1897 [c.]). On Multitudes [R]. MS [R] 28
Robin Catalogue:
A. MS., n.p., [c.1897?], pp. 2348.
Abnumeral collection; first, second, and third denumeral multitude; princi, secundo, and tertio postnumeral multitude....
Denumerable Collection, Fermatian Inference, Georg Cantor, First Abnumeral Multitude, Second Abnumeral Multitude, Mathematics, Third Abnumeral Multitude, Supermultitudinous Collection, Continuity, Order of Magnitude, Arithm, Infinity, Number, Limit, Assignable Quantity, Primipostnumeral Collection, Simon Newcomb, Euclid, Primipostnumeral Multitude, Secundipostnumeral Multitude, Tertiopostnumeral Multitude, Continuum, Pedagogy, Line


Manuscript  Posted 10/09/2014
Peirce, Charles S. (190507 [c.]). Considerations concerning the Doctrine of Multitude. MS [R] 27
Robin Catalogue:
A. MS., n.p., [c.190507?], pp. 15; 23, 24, 27, 29, 30.
The nature of definition; “collection” defined; first and secondintentional collection.
Doctrine of Multitude, Mathematics, Georg Cantor, Bernard Bolzano, Whitehead, Definition, Mathematical Definition, Collection, Dyadic Relation, Triadic Relation, Multitude, Whole, Integral Whole, Member, Identity, Nothing, Thought, Purpose, Counting, Essence, Existence, Second Intention


Dictionary Entry  Posted 09/09/2014
Quote from "On Multitude"
Mathematics is a study of exact hypotheses, in so far as consequences can be deduced from them. To limit mathematics to the deduction of those consequences would be...


Manuscript  Posted 09/09/2014
Peirce, Charles S. (1897 [c.]). On Multitude. MS [R] 26
Mathematics, Logica Utens, Logica Docens, Collection, Sui Generis Relation, Indefinable Relation, Postulate, Axiom, Corollary, Dyadic Relation, Relate, Correlate, Negative Relation, Principle of Contradiction, Principle of Excluded Middle, Universal Quantification, Particular Quantification, Quantifier, Arithmetical Relation, Deductio Ad Absurdum, Algebra of Dyadic Relatives, General Algebra of Logic, Complementary Collection, Theorem, Problem, Universe of Discourse, Boolian Notation, Peircian Notation, Anonyman Notation, Quantification, Vagueness, Universally Quantified Index, Particularly Quantified Index


Manuscript  Posted 08/09/2014
Peirce, Charles S. (1895 [c.]). Logic of Quantity. MS [R] 18
Robin Catalogue:
A. MS., n.p., n.d., pp. 34.
Defense of a modified version of Benjamin Peirce’s definition of “mathematics.” Cf. MS. 78.


Manuscript  Posted 08/09/2014
Peirce, Charles S. (1895 [c.]). On the Logic of Quantity. MS [R] 17
Robin Catalogue:
A. MS., n.p., [c.1895], pp. 19; 710 of another draft.
This manuscript should be compared with MS. 16, to which it bears a special similarity. See also MS. 250...
Quantity, Mathematics, Hypothesis, Diagram, Scale of Quantity, Aristotle, Augustus De Morgan, William Hamilton, Euclid, Time, Space, Kant, Benjamin Peirce, George Chrystal, Perfect Knowledge, Definition, Science, Experience, Mathematical Hypothesis, Physical Hypothesis, Deductive Reasoning, Cognitive Experience, Emotional Experience, Probability, Feeling, Sensation, Precept, Observation, Relation, Intuition, Vividness, Instantaneous Photograph, Index, Assertion, Intuitional Diagram


Dictionary Entry  Posted 08/09/2014
Quote from "On the Logic of Quantity, and especially of Infinity"
Mathematics may be defined as the study of the substance of exact hypotheses. It comprehends
1st, the framing of hypotheses, and
2nd, the deduction of...


Manuscript  Posted 08/09/2014
Peirce, Charles S. (1895 [c.]). On the Logic of Quantity, and especially of Infinity. MS [R] 16
Robin Catalogue:
A. MS, n.p., [c.1895], pp. 1, 59, 718, 1820.
Several definitions of “mathematics,” including Aristotle’s and CSP’s. Mathematical proof and probable reasoning...
Mathematics, Aristotle, Mathematical Hypothesis, Diagrammatic Embodiment, Diagram, Inherential Diagram, Imputational Diagram, Probable Reasoning, Probability, Experience, Deductive Reasoning, Syllogism, Scale of Quantity, Hume, Contguity, Idea, Vividness, Dimness, Clustering of Ideas, Feeling, Consciousness of Duality, Perception, Imagination, Attention, Desire, Suggestiveness, Inner World, Outer World, Nature, Resemblance, Reason, Evolution of Forms, Metaphysics, Quality, Dual Relation, Mediation, Plural Relation, Sign, Representamen, Icon, Noumenon, Index, Symbol, Assertion, Definition, Familiarity, Clearness, Distinctness, Proper Name, Number, Will, Intuition


Dictionary Entry  Posted 04/09/2014
Quote from "On Quantity, with special reference to Collectional and Mathematical Infinity"
…the mathematician is not concerned with real truth, but only studies the substance of hypotheses. [—] …the mathematician observes nothing but the diagrams he himself constructs; and no occult...


Dictionary Entry  Posted 04/09/2014
Quote from "On Quantity, with special reference to Collectional and Mathematical Infinity"
Mathematics is the study of the substance of hypotheses with a view to the tracing of necessary conclusions from them.


Dictionary Entry  Posted 01/09/2014
Quote from "On Quantity, with special reference to Collectional and Mathematical Infinity"
…the proper definition of mathematics is that it is the study of the substances of hypotheses, which it first frames and then traces to their consequences.


Manuscript  Posted 01/09/2014
Peirce, Charles S. (1895 [c.]). On Quantity, with special reference to Collectional and Mathematical Infinity. MS [R] 14
Robin Catalogue:
The nature of mathematics, pure and applied. In general, mathematics is concerned with the substance of hypotheses, drawing necessary conclusions from them; pure...
Mathematics, Quantity, Continuity, Infinity, Definition, Pure Mathematics, Applied Mathematics, Deductive Reasoning, Transitive Relation, Cyclical Relation, Negation, Singularity, Addition, Rational Quantity, Real Quantity, Endless Series, Direct Convergence, Limit, Imaginary Quantity, Quaternion, Quasicontinuum, Topics, Graphics, Metrics, Multitude, Number, Counting, Cardinal Numerals, Enumerable Collection, Denumerable Collection, Innumerable Collection, Georg Cantor, Abnumeral Collection, General, Individual, Time, Space, Reasoning, Moment, Presence, Continuum


Manuscript  Posted 01/09/2014
Peirce, Charles S. (1896). On the Logic of Quantity. MS [R] 13
Robin Catalogue:
A. MS., n.p., [c.1895], pp. 113; 712, with an alternative p. 8 of another draft.
The principal questions raised are these: Why mathematics always deals with a...
Mathematics, Systems of Quantity, Philosophy, Logic, Metaphysics, Special Observational Sciences, Special Science, Psychical Science, Physical Science, Nomological Science, Classificatory Science, Descriptive Science, Arts, Categories, Quality, Actuality, Law, First, Second, Third, Medium, Otherness, Firstness, Secondness, Thirdness, Idea, Fact, Evolution, Artist, Practical Man, Philosopher, Singular fact, Dual Fact, Relation of Reason, Real Relation, Individual, Identity, Likeness, Plural Fact, Chaldean Metaphysics, Chaos, Partial Determination, Triplicity, Term, Proposition, Mathematics of Logic, Principle of Identity, Falsity, Principle of Contradiction, Principle of Excluded Middle, Function, Equivalence, Copula of Inclusion, Nota Notae, Principle of the Transitiveness of the Copula, Principle of Reasoning from Definition to Definitum, Principle of Hypothetic Syllogism, Principle of the Dilemma


Dictionary Entry  Posted 01/09/2014
Quote from "Lessons of the History of Science"
The most abstract of all the sciences is mathematics. That this is so, has been made manifest in our day; because all mathematicians now see clearly that mathematics is...


Anthology Volume  Posted 31/08/2014
Peirce, Charles S. (2010). Philosophy of Mathematics: Selected Writings


Manuscript  Posted 31/08/2014
Peirce, Charles S. (1904). On the Foundations of Mathematics. MS [R] 7
Robin Catalogue:
A. MS., n.p., [c.1903?], pp. 116, with 3 rejected pages; 1719 of another draft.
Mathematics as dealing essentially with signs. The MSS. below (Nos. 811) are...
Mathematics, Sign, Replica, Interpretant, Consciousness, Real Object, Falsity, Truth, Definition, Imagination, Experimentation, Quality, Ground, Meaning, Icon, Index, Proposition, Information, Symbol, Argument, Argumentation, Schema, Term

