Problems In Philosophy • 4

Re: R.J. Lipton and K.W. ReganDid 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 clear from Aristotle and places in Plato that the good of reasoning from fair samples and freely chosen examples was bound up with notions of probability, which in the Greek idiom meant likeness, likelihood, and likely stories, the question being how much the passing image could tell us of the original idea.

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

Problems In Philosophy • 3

Re: R.D. Mounce

Making reality our friend is necessary to survival and finding good descriptions of reality is the better part of doing that, so I don’t imagine we have any less interest in truth than the Ancients.  From what I remember of him, Plato had specific objections to specific styles of art, poetry, or their interpretation, and hardly painted art in general with a broad brush.  Indeed, there is a Pythagorean tradition that reads The Republic as a metaphorical treatise on musical theory, applied no doubt to achieving harmony in society.  Truth in fiction and myth is a matter of interpretation, and come to think of it, that’s not essentially different from truth in more literal forms of expression.

Posted in Aesthetics, Computation, Computer Science, Ethics, Heap Problem, Logic, Mathematics, Model Theory, Normative Science, Paradox, Peirce, Philosophy, Pragmatism, Problem Solving, Proof Theory, Sorites | Tagged , , , , , , , , , , , , , , , | Leave a comment

Problems In Philosophy • 2

Re: R.J. Lipton and K.W. ReganYou Think We Have Problems

One classical tradition views logic as a normative science, the one whose object is truth.  This puts it on a par with ethics, whose object is justice or morality in action, and aesthetics, whose object is beauty or the admirable in itself.

The pragmatic spin on this line of thinking views logic, ethics, and aesthetics as a concentric series of normative sciences, each a subdiscipline of the next.  Logic tells us how we ought to conduct our reasoning in order to achieve the goals of reasoning in general.  Thus logic is a special application of ethics.  Ethics tells us how we ought to conduct our activities in general in order to achieve the good appropriate to each enterprise.  What makes the difference between a normative science and a prescriptive dogma is whether this telling is based on actual inquiry into the relationship of conduct to result, or not.

Here’s a bit more I wrote on this a long time ago in a galaxy not far away —

Logic, Ethics, Aesthetics

Posted in Aesthetics, Computation, Computer Science, Ethics, Heap Problem, Logic, Mathematics, Model Theory, Normative Science, Paradox, Peirce, Philosophy, Pragmatism, Problem Solving, Proof Theory, Sorites | Tagged , , , , , , , , , , , , , , , | 3 Comments

Problems In Philosophy • 1

Re: R.J. Lipton and K.W. ReganYou Think We Have Problems

I used to think about the heap problem a lot when I was programming and I decided the heap quits being a heap as soon as you remove one grain because then it becomes two heaps.

The Pascal sorting of the sorites played on moves between heaps and stacks, but I’ve forgotten the details of that epiphany.  The whole-systems point is clear enough though — the system as a whole makes a discrete transition from one state of organization to another.

Posted in Computation, Computer Science, Heap Problem, Paradox, Philosophy, Sorites | Tagged , , , , , | Leave a comment

Riffs and Rotes : 3

Re: R.J. LiptonFailure 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 doubly recursive factorizations of whole numbers, ending up with two species of graph-theoretic structures that I dubbed Riffs and Rotes.  See the following links for more discussion:

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

Supple Agony

A lack of knowing, my lack of knowing
How to supply either lack of knowing.
Complemental and supplemental ∠s.

Posted in Anamnesis, Communication, Learning, Maieusis, Mantra, Meditation, Memo, Meno, Teaching | Tagged , , , , , , , , | Leave a comment

Prospects for Inquiry Driven Systems • 1

I finally finished retyping the bibliography to my systems engineering project prospectus that had gotten lost in a move between computers, so here is a link to the InterSciWiki copy:

This may be of interest to people working toward applications of Peirce’s theory of inquiry.

Posted in Adaptive Systems, Artificial Intelligence, Automated Research Tools, Cactus Graphs, Constraint Satisfaction Problems, Cybernetics, Differential Logic, Dynamical Systems, Educational Systems Design, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems Engineering, Learning, Logic, Logic of Science, Logical Graphs, Machine Learning, Peirce, Reasoning, Scientific Method, Semiotics, Sign Relations, Theorem Proving | Tagged , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment