The symbolism seems to me entirely irrelevant. The idea 2+2=4 can be represented in Roman numerals, binary notation, the Babylonian number system, etc. — Art48
So, in my view, I directly experience sensations: i.e., the five physical senses, emotions, and thoughts. Everything else is an idea that makes sense of my perceptions.
Therefore, my sensations have a more secure epistemological status than a theoretical construct I create to explain my sensations. My ideas certainly have reality and existence. Matter, maybe, maybe not. — Art48
:up:it's a concession to both reductionism and reification to accept that only physical objects exist. — Jamal
partly what motivated Markus Gabriel's ontology, in which tables, quarks, numbers, nations, and ideas all exist. — Jamal
It's also hard to make sense of the claim that only such objects exist, — green flag
I wouldn't even say they are so different. — green flag
There is a difference between phenomenal objects which are temporally delimited and composed of parts, and the objects of thought. — Wayfarer
The static ontology of medium-size dry goods doesn’t feel right. — Jamal
Some would say that s static ontology doesn’t even work for them either, which I suppose is process metaphysics. — Jamal
But numbers are more thingy than thoughts, while at the same time being not or less mind-dependent, and not situated in space and time. — Jamal
So there’s a scale of thingyness and an independent scale of abstactness. — Jamal
I agree that we can discursively break the world up and think about the category or concept of a dog as apart from any particular dog. We indeed have that sort of metacognition. — green flag
Neoplatonic mathematics is governed by a fundamental distiction which is indeed inherent in Greek science in general, but is here most strongly formulated. According to this distinction, one branch of mathematics participates in the contemplation of that which is in no way subject to change, or to becoming and passing away. This branch contemplates that which is always such as it is and which alone is capable of being known: for that which is known in the act of knowing, being a communicable and teachable possession, must be something that is once and for all fixed. — Jacob Klein, Greek Mathematical Thought and the Origin of Algebra.
I think instead of saying math isn't in space and time we should say that math methodically ignores the actual, local spatial and temporal situation — green flag
The Pythagoreans were shocked to discover that the square root of 2 was irrational.It is an eternal fact that the square root of 2 cannot be expressed as a ratio of two whole numbers. That fact was true before the Pythagoreans discovered it and it will be true for all eternity. You seemed to be taking the Mathemetical Formalism route, which is a minority position among working mathematicians, most of whom accept Mathematical Platonism. — Art48
why worry? — Jamal
Thomists and other critics of Ockham have tended to present traditional [i.e. 'scholastic'] realism with its forms or natures, as the solution to the modern problem of knowledge. It seems to me that it does not quite get to the heart of the matter. A genuine realist should see “forms” not merely as a solution to a distinctly modern problem of knowledge, but as part of an alternative conception of knowledge, a conception that is not so much desired and awaiting defense, as forgotten and so no longer desired. Characterized by forms, reality had an intrinsic intelligibility, not just in each of its parts but as a whole. With forms as causes, there are interconnections between different parts of an intelligible world, indeed there are overlapping matrices of intelligibility in the world, making possible an ascent from the more particular, posterior, and mundane to the more universal, primary, and noble.
In short, the appeal to forms or natures does not just help account for the possibility of trustworthy access to facts, it makes possible a notion of wisdom, traditionally conceived as an ordering grasp of reality. — Joshua Hochschild - What's Wrong with Ockham?
So there’s a scale of thingyness and an independent scale of abstractness. — Jamal
I like considering more than one dimension. — green flag
We will probably never stop trying to figure out exactly what an idea is (what we mean by 'idea.'). I think they exist (whatever exactly that means), and I think they are at least like blurry equivalence classes. — green flag
From Wittgenstein's "Remarks on the Foundation of Mathematic"
I 168, "The mathematician is aninventor, not a discoverer."
II 2 "But the mathematician is not a discoverer: he is aninventor." — Richard B
Try shaking harder. :) These questions were discussed long before science existed and are interesting in themselves. P.S. I like your chart of thing/process, abstract/concrete.I can’t shake the thought that the controversies over what exists are motivated by a fear of irrelevance in the face of physical science. — Jamal
These questions were discussed long before science existed and are interesting in themselves. — Art48
... philosophy should seek its contents in the unlimited diversity of its objects. It should become fully receptive to them without looking to any system of coordinates or its so-called postulates for backing. It must not use its objects as the mirrors from which it constantly reads its own image and it must not confuse its own reflection with the true object of cognition. — Adorno, Lectures on Negative Dialectics
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