BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px; }John, list
Interesting suggestions about the hierarchies of ontologies What about Peirce's Six Categorical modes: - which makes the world a rather complex place. There's 3-3 [Thirdness as Thirdness] which is a pure aspatial, atemporal mode. Pure Mind. That would be Pure Mathematics. 3-2 and 3-1 are two different types of Habit; i.e., they are spatial and temporal laws. And there's pure Secondness [2-2] which is simple physical actuality regardless of laws. But- there's 2-1 - which is a dependent actuality. And - pure Firstness [1-1] which is spatial and temporal BUT without any connections, either physical [as in Secondness] or lawful [as in Thirdness]. Edwina On Wed 22/08/18 11:22 PM , John F Sowa s...@bestweb.net sent: Edwina, Gary R, and Jon AS, I agree with your points and with the quotations by Peirce. The challenge is to find a systematic terminology that is consistent with Peirce, with modern conventions in logic, and with the following constraints: 1. Logic allows a variable x in ∃x to refer to refer to anything mathematical. That implies that any x that refers to anything in pure mathematics can be said to "exist" in some sense. 2. But what sense is that? Is it some "Platonic Heaven" for all mathematical entities -- including the infinities of integers, real numbers, and Cantor's hierarchies of infinity? 3. Those people who deny that anything nonphysical can exist, claim that mathematical things "depend" on physical things for their existence. Frege, for example, identified the number 5 with the totality of all sets of five things in the universe. But if the universe is finite, there must be an upper bound on the integers that can exist. And that construction fails completely for real numbers, functions, and higher orders of infinity. 4. Some logicians (e.g., Lesniewski, Goodman, Quine...) tried to eliminate sets because they are abstract, and they allow new sets to be constructed from iterations of the empty set. For example: {}; {{}}; {{},{{}}.{{{}}}}; {{{}},{{{{}}}}}; ... But Quine relented because he realized that sets or something similar would be necessary to define all of mathematics. 5. In his classification of the sciences, Peirce claimed that pure mathematics is the only independent science. Every other science, including metaphysics, depends on mathematics. That rules out the option of claiming that mathematics has some kind of dependency on what happens to exist in the universe. 6. For his process ontology, Whitehead considered all physical entities to be processes and physical objects to be slowly moving processes. He considered all processes to be situated in a four-dimensional space time, and mathematical entities to be "eternal objects" in the sense that they are outside space and time. 7. Interesting option: John Wilkins (1668), the first secretary of the British Royal Society, developed an ontology with the help of other members of the society. See the attached Wilkins.png. For a copy of his book, see https://archive.org/details/AnEssayTowardsARealCharacterAndAPhilosophicalLanguage [1] Wilkins' top-level distinction is Transcendental/Special. He characterized the transcendental branch as "knowing" and the special branch as "being". Under Transcendental, he placed language, logic, numbers, and metaphysics. Suggestion: Suppose we name the two branches at the top of any ontology transcendental/physical: Transcendental would include all abstractions that are independent of space-time: mathematical entities, sign types, and laws of nature. Does anyone have any preferences for or against the pair Transcendental/Physical instead of Mathematical/Physical? John Links: ------ [1] http://webmail.primus.ca/parse.php?redirect=https%3A%2F%2Farchive.org%2Fdetails%2FAnEssayTowardsARealCharacterAndAPhilosophicalLanguage
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