How do you reckon a world would work out, if 2 did not, in fact, equal 2, of if 9 was less than 7? — Wayfarer
Why can you assume in some universe beyond our imagination our brand of logic must hold? — jgill
Logic is in the mind, but not [o]f it. It’s not our invention but what we are able to discover through reason. I really don’t think that the idea of a world where there are no necessary facts is even an hypothesis. — Wayfarer
Logic is in the mind, but not of it. It’s not our invention but what we are able to discover through reason. I really don’t think that the idea of a world where there are no necessary facts is even an hypothesis — Wayfarer
And it doesn't make much sense to say "what does the world look like without eyes," or "how would we think about the world without minds." — Count Timothy von Icarus
In this view, only the higher, noumenal realm can be causally efficacious, or at least there is only downwards causality from the noumenal onto the phenomenal, not the other way around. To my mind, this creates an arbitrary division in nature that many don't really want to defend, but which it is nonetheless easy to accidentally fall into. — Count Timothy von Icarus
Objectivity then is about descriptions that smooth out the differences that arise from variances in subjects' phenomenal experience. You view the same phenomena in many different ways, using tools, experiments, etc., and identify the morphisms between all perspectives. — Count Timothy von Icarus
there is a strong tendency for the mathematical patterns "at work in," or "describing" natural phenomena to be similar at very different levels of scale — Count Timothy von Icarus
the observation of mathematical patterns that describe and predict the world are among the very best established empirical facts. — Count Timothy von Icarus
it seems obvious that living things must incorporate within themselves descriptions of nature that are isomorphic to nature. Such descriptions might be highly compressed, based on heuristics that make them prone to error, etc., but this doesn't preclude the fact that they are to some extent accurate descriptions of nature — Count Timothy von Icarus
This is how we end up fooling ourselves into believing that mathematical structures are embedded in the world. What is embedded in the world is human discursive interactions, not the abstract forms that we fabricate out of these relationships. — Joshs
That’s the point. To understand the origin of mathematicalWhat a happy coincidence how well the products of mathematical science work! We should all thank our lucky stars. — Wayfarer
As you say, the products of mathematical science work well. I would add that they work precisely, accurately in the sense dictated by the demands of formal logic. — Joshs
"Husserl was interested in the psychological origin of number concepts. He explored how individuals move from concrete individual experiences to abstract generalizations that constitute numerical understanding. For Husserl, numbers aren't just abstract entities; they have their roots in our lived experiences and acts of grouping and collecting. — Wayfarer
I think the sciences are slowly moving away from the idea, exemplified by the periodic table, of pre-existing forms that reappear throughout nature. They are coming to realize that such abstractions cover over the fact that no entity pre-exists its interaction with other entities within a configuration of relations. — Joshs
s this thumbnail sketch of Husserl's philosophy of math any good? — Wayfarer
It is no different than saying that "tree" is a generic concept, abstracted from actual trees. — Janus
As an abstract concept, it's a universal. More to the point, per my earlier posts in this thread, is that mathematics can be used to make discoveries hitherto unknown about nature herself, thereby demonstrating that they are something more than simply 'mental constructs'. — Wayfarer
What is the difference between a universal concept and a generic concept? — Janus
Can you give me an example of pure math being used to discover anything about nature? — Janus
Do you think any discoveries about nature are about nature as it is in itself or merely as it appears to us? — Janus
What he was trying to do was avoid psychologism (which he was accused of in Philosophy of Arithmetic) by grounding mathematical principles in transcendental
phenomenology. — Joshs
Good question. In the context of Aristotle's philosophy, as well as in biological classification and other systems of categorization, a "genus" is a class or group that includes different species. Note however its ultimate source in Aristotle. — Wayfarer
This equation incorporated both the principles of quantum mechanics and the theory of special relativity, describing electron behavior at relativistic speeds. — Wayfarer
I'm incllined to agree with Bohr's aphorism 'It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature.' Also Heisenberg's 'What we observe is not nature in itself but nature exposed to our method of questioning.' — Wayfarer
This is an equation belonging to quantum physics and relativity theory, not pure math. — Janus
You are allowing yourself to be fooled by your invented grammar. Mathematics, and the logic it is based on, rests on a peculiar way humans decided at a certain point in their history ( actually, as a gradual process of development) to formulate the idea of the persistingly present, self-identical object. Doing so led to subsequent assumptions such as the law of identity, the law of non-contradiction, geometrical forms such as lines and magnitudes, and propositional statements binding or separating a subject and predicate. Mathematical structures are only ‘embedded’ in the world to the extent that we force the world into such odd forms. But such processes of objectivation are derived modes of thinking which hide within themselves what gives them their sense and intelligibly. Put differently, a persisting object only persists for us in its meaning by continuing to be the same differently. — Joshs
Nevertheless it could never have been discovered without mathematics. — Wayfarer
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