Category Archives: Number Theory

Problems In Philosophy • 4

Re: R.J. Lipton and K.W. Regan • Did Euclid Really Mean ‘Random’? These are the forms of time, which imitates eternity and revolves according to a law of number. Plato • Timaeus • 38 A Benjamin Jowett (trans.) It is … Continue reading

Posted in Aristotle, Computation, Computer Science, Euclid, Genericity, Geometry, Iconicity, Likelihood, Likely Story, Likeness, Mathematics, Number Theory, Philosophy, Philosophy of Mathematics, Plato, Probability, Socrates | Tagged , , , , , , , , , , , , , , , , | 3 Comments

Riffs and Rotes : 3

Re: R.J. Lipton • Failure Of Unique Factorization My favorite question in this realm is how much of the linear ordering of the natural numbers is purely combinatorial, where we eliminate all the structure that isn’t purely combinatorial via the … Continue reading

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Relations & Their Relatives : 4

Re: Peirce List Discussion • Helmut Raulien The “divisor of” relation signified by is a dyadic relation on the set of positive integers so it can be understood as a subset of the cartesian product   It is an example … Continue reading

Posted in C.S. Peirce, Denotation, Logic, Logic of Relatives, Mathematics, Number Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , | 3 Comments

Relations & Their Relatives : 3

Here are two ways of looking at the divisibility relation, a dyadic relation of fundamental importance in number theory. Table 1 shows the first few ordered pairs of the relation on positive integers that corresponds to the relative term, “divisor … Continue reading

Posted in C.S. Peirce, Denotation, Logic, Logic of Relatives, Mathematics, Number Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , | 3 Comments

Forest Primeval → Riffs & Rotes

Re: Shifting Paradigms? • (1) • (2) • (3) • (4) • (5) • (6) Prompted by the discussion of Catalan numbers on the Foundations Of Math List, I dug up a few pieces of early correspondence and later discussions that … Continue reading

Posted in Algebra, Arithmetic, Combinatorics, Forest Primeval, Graph Theory, Group Theory, Integer Sequences, Lambda Calculus, Logic, Mathematics, Model Theory, Number Theory, Paradigms, Peirce, Programming, Proof Theory, Riffs and Rotes | Tagged , , , , , , , , , , , , , , , , | Leave a comment

¿Shifting Paradigms? • 2

Re: Timothy Chow • Shifting Paradigms? 2014 Jul 31 I can’t remember when I first started playing with Gödel codings of graph-theoretic structures, which arose in logical and computational settings, but I remember being egged on in that direction by … Continue reading

Posted in Algebra, Arithmetic, Combinatorics, Foundations of Mathematics, Graph Theory, Group Theory, Inquiry, Logic, Mathematics, Model Theory, Number Theory, Paradigms, Peirce, Programming, Proof Theory, Riffs and Rotes | Tagged , , , , , , , , , , , , , , , | Leave a comment

Riffs and Rotes : 2

Re: Peter Cameron The interaction between addition and multiplication in the natural numbers has long been an interest of mine, leading to broader questions about the relationship between algebra and combinatorics.  My gropings with these enigmas led me to the … Continue reading

Posted in Algebra, Combinatorics, Graph Theory, Group Theory, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , | Leave a comment