The n-Category Café

> Or if you feel it needs an applied discipline for useful interpretative work, why is so little done on topics from computer science

I’m trying to get a handle on what exactly ‘interpretative’ might mean in these contexts. It seems to me that writings in these areas come with their interpretation. What more interpretation could there be? What kind of interpretation are you thinking of?

In fact, maybe you could point to some non-Anglophone work that illustrates what you mean. (In English translation, or maybe I could muddle by in French.)

> One might argue that the concept of ‘time’ has merely split.

Funny you pick the example of time. I’ve been trying (with the emphasis on trying) to read some Heidegger in recent weeks. The path from “non-scientific” time to “scientific” time is one of his main topics, if not the main topic. But I’m not confident to actually say anything about what he says.

I have, at several secondary and post-secondary schools, been caught in the middle of a turf battle between Math departments and Philosophy Departments.

The ostensible prize is: who gets to teach Introduction to Logic? It seems to usually be decided by historical precedent: whichever department first taught it.

I had taken courses in Propositional and and Predicate Calculus at Stuyvesant High School, using university textbooks.

At Caltech, I continued with Infinitary Logic and with Model Theory, despite lacking the formal prerequisites. I simply insisted “but I am POST!” and the professor let me in, and not until mid-semester asked exactly how I was related to Emil Post. I said that I was not; and that he had been fooled by illogic.

When I was an Adjunct Prof of Math at Woodbury University, I expanded the Logic component of Intermediate Algebra as taught, using Lewis Carroll puzzles, which the students loved.

But the administration would not let me expand this further, as the Philosophy Department traditionally taught Intro Logic, and taught it quite badly.

I repurposed the Lewis Carroll worksheets I’d typed when I taught remedial algebra in a Pasadena High School. But they would not entertain a full course on the subject. After all, what do mathematicians with degrees also in Computer Science, and publications in Physics and Biology, know about Logic?

The battle raged one way in Great Britain, with my teachers’teachers’ teachers’ and their teachers in several branches.

Briefly:

John McTaggart Ellis McTaggart [1866-1925] was a Fellow of Trinity College, Lecturer in Moral Sciences, and a Nonreductionist. He was the author of “Studies in Hegelian Cosmology. The Philosophy of Hegel”
[Dissertation, 1898; 1901; Garland, 1984].

This work explored application of a priori conclusions derived from the investigation of pure thought to
empirically-known subject matter; human immortality; the absolute; the supreme good and the moral criticism; punishment; sin; and the conception of society as an organism. McTaggart was controversial for claiming that time was unreal: “The Nature of Existence” [Cambridge University Press, 1921]; “The Unreality of Time” [Mind, vol. XVII].

G. E. Moore (George Edward Moore) [4 Nov 1873-24 Oct 1958] was an English Realist Philosopher, and a leading anti-Idealist. His major publications include “Principia Ethica” [Cambridge, 1903; 1993];
“Ethics” [London, 1912]; Philosophical Studies [London, 1922];
“Some Main Problems of Philosophy” [London, 1953]; Philosophical Papers”
[London, 1959]; and various posthumously edited volumes.

Bertrand Russell [1872-1970] was the great Philosopher/Logician who studied with Wittgenstein and G. E. Moore, wrote “Principia Mathematica” with Alfred North Whitehead, had a major impact on Analytic Philosophy, was a best-selling popular author, was jailed for anti-war protests,
and won the Nobel Prize (1950, Literature).

Norbert Wiener [1897-March 1964] was the creator of Cybernetics, who studied under G. H. Hardy and Bertrand Russell by fellowship. He received his Ph.D. in the Philosophy of Mathematics at Harvard at age 18, under Josiah Royce [1855-1916] – the foremost American Idealist; under
Philosopher/Poet George Santayana [1863-1952]. Norbert Wiener then studied at Gottingen under David Hilbert [23 Jan 1862-14 Feb 1943].

I am a student of a student of Norbert Wiener, the intermediate link being a huckster palgiarist whom I prefer not to discuss in open forum.

In some other threads of n-Category cafe I have alluded to the importance of the work of

See today’s preprint:

Paraconsistent First-Order Logic LP# with infinite hierarchy levels of contradiction
Authors: Jaykov Foukzon
Subjects: Logic (math.LO)

In this paper paraconsistent first-order logic LP# with infinite hierarchy levels of contradiction is proposed. Corresponding paraconsistent set theory KSth# is discussed.

The text of the paper begins:

“The real history of non-Aristotelian logic begins on May 18,1910 when N.A. Vasiliev presented to the Kazan University faculty a lecture ”On Partial Judgements,
the Triangle of Opposition, the Law of Excluded Fourth” [Vasiliev 1910] to satisfy the requirements for obtaining the title of privat-dozent. In this lecture
Vasiliev expounded for the first time the key principles of non-Aristotelian, imaginary, logic.”

David Corfield wrote:
“Something which may experience a similar
fate is ‘causality’. If Judea Pearl wins
out, it will become another scientific
topic treated via the apparatus of
graphical models and the ‘do’ calculus.
But we may also retain a more
phenomenological study.”

Judea Pearl wrote:
“Considering the organization of scientific
knowledge, it makes prefect sense that we
permit scientists to articulate what they
know in plain causal expressions, and not
force them to compromise reliability by
converting to the “higher level” language
of prior probabilities, conditional
independence and other cognitively
unfriendly terminology.”

Stephen wrote:
Pearl’s description seems compatible with the goal of pragmatically minimizing “Pernicious Symbolization”. In your book I didn’t notice a criticism of Pearl, although Jon Williamson, your co-editor, pushes epistemic causality elsewhere. I’m not sure what the scope of your “phenomenological study” encompasses. Just what you mean by that? I did find what appears to be a related philosophical question:

“A crucial question for those interested
in the semantic and metaphysical
foundations of the structural equations
framework is the status of the
counterfactuals encoded by the structural
equations. Are they semantically and
metaphysically primitive so that the
structural equations are simply a summary
of the more basic counterfactuals? Or are
the structural equations themselves to be
taken as the conceptual and metaphysical
primitives, with the counterfactuals
having a secondary, derivative status?”
(Woodward and Hitchcock adaption of Pearl)