Laws of gravity in physics
2. Engineering/Design formulas for; compressive forces, tensile strength, torsional forces, etc.
3. Musical notation — 3017amen
That doesn't entail independent existence apart from the things that relate in that way. — Relativist
Musical notation isn't an abstraction, it's a semantics that maps to various aspects of sound. — Relativist
Now we get to infinity. The arguments I've seen for its existence — Relativist
In mathematics and logic, we use the existential quantifier(∃) in a way inconsistent with the above — Relativist
reject its existence — Relativist
That sounds like Platonism. My problem with ontologies that include platonic objects is that they seem unnecessary. Why posit an independent existence for triangles, when triangles can be accounted for as constituents of triangular objects? Further, how do triangles exist independently? How do they get connected to objects? Can the connection be severed? This makes it even more unnecessarily complex? Can they replaced with squares simply by replacing the connection?If a given abstract does not exist for the sole purposes of the creation of a particular concrete thing, by definition, it would then be something independent of the thing itself. — 3017amen
The notation is interpreted by a musician, analogously to a reader interpreting print words. Words refer to objects, concepts, actions etc, while musical notations refer to the various aspects of sounds you mention. The sounds can be reproduced on an instrument, or merely interpreted within the musician's mind.. I don't see the difference, or even how semantics would play a role. — 3017amen
Both ways are consistent with the way of abstraction. We mentally consider a set of attributes common to all triangles to form the abstraction in our minds, then reverse the process, adding back concrete elements.Abstracts can work both ways. — 3017amen
Sets are abstractions. Creating abstraction just means conceptualizing. My point is that abstractions don't actually exist except as mental entities. Mathematical abstractions are useful because they entail analyzable properties Does anyone suggest imaginary numbers exist? Nevertheless, they appear in physics equations.Of course, we can hold that there do not exist infinite sets. But then providing a formal axiomatization for the mathematics for the sciences gets a lot more complicated. — GrandMinnow
That sounds like Platonism. My problem with ontologies that include platonic objects is that they seem unnecessary. Why posit an independent existence for triangles, when triangles can be accounted for as constituents of triangular objects? Further, how do triangles exist independently? How do they get connected to objects? Can the connection be severed? This makes it even more unnecessarily complex? Can they replaced with squares simply by replacing the connection? — Relativist
The notation is interpreted by a musician, analogously to a reader interpreting print words. Words refer to objects, concepts, actions etc, while musical notations refer to the various aspects of sounds you mention. The sounds can be reproduced on an instrument, or merely interpreted within the musician's mind. — Relativist
Both ways are consistent with the way of abstraction. We mentally consider a set of attributes common to all triangles to form the abstraction in our minds, then reverse the process, adding back concrete elements. — Relativist
Agreed. The question remains: do immaterial objects exist? If so, what does it mean to exist? Does Spider-Man exist? Do all fictions, past present, and future exist? What about possible fictions that never get authored?Existential quantification is not inconsistent with the claim that abstractions are not material objects. — GrandMinnow
Fair point, although infinites appear in some physics equations, and they are treated ad objects in transfinite math. Regardless, from this viewpoint, the question is: is there something that exists in the real world that maps to an infinite set?There is not an entity called 'infinity' (distinct from a different notion of points on a real extended line or figures of speech such as "as x goes to infinity"). Rather, there is the adjective 'is infinite', and an axiom that entails (with other axioms) that entails certain theorems including the existence of infinite sets. — GrandMinnow
Do all fictions, past present, and future exist? — Relativist
OK, but that's just referring to a concept - a mental object. It is spatially located in your brain, unless dualism is true. Triangular objects exist even if there are no minds to conceptualize triangles. When people speak of the existence of infinity they are not merely referring to the concept that exists in our minds.I don't think it's Platonism because it assumes an independent existence outside of consciousness. The triangulation of a roof truss exists abstractly. The connection can be 'severed' and independent of the concrete thing itself, the roof truss. — 3017amen
Sorry. I agree with that. They are useful fictions.That doesn't answer my point that without infinitistic set theory, axiomatizing the mathematics for the sciences gets a lot more complicated. — GrandMinnow
No, but one shouldn't conflate existential quantification with a statement of ontology. IOW just because we can do some useful math with infinities doesn't entail anything ontic.The presence of such questions doesn't impugn existential quantification. — GrandMinnow
the question is: is there something that exists in the real world that maps to an infinite set? — Relativist
They are useful fictions. — Relativist
Yes, and thus we get into metaphysics. A topic for another day.That raises the question, "What do you mean by 'the real world'"? And what do you mean by "something exists in the real world"? — GrandMinnow
Triangular objects exist even if there are no minds to conceptualize triangles. — Relativist
Time exists a a relation between states of affairs. I don't believe abstraction exist independently of states of affairs. — Relativist
A triangular object has 3 sides that are arranged in a certain general way. It's existence and structure is not dependent on a mind analyzing that structure.Triangular objects exist even if there are no minds to conceptualize triangles.
— Relativist
How is that possible? — 3017amen
Everything that exists is a State of Affairs. It's constituents are; a particular, its attached properties, and its relations to other states of affairs. This acknowlwdges that properties exist only in their instatiations in a state of affairs. — Relativist
A triangular object has 3 sides that are arranged in a certain general way. It's existence and structure is not dependent on a mind analyzing that structure. — Relativist
Not really. The relations between consciousnesses seems indirect.In a humanistic sense, are you saying that we all are an interconnected consciousness? — 3017amen
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