Not quite obviously. Is the Pentagon a pentagon? or simply a pentagonally-shaped building?
The “core” concept, as I see it, is the geometric and therefore all other (correct) uses of the word are metaphors.
(It’s HE, by the way)
Man, if there is ONE f**cking place in the whole internet where I can ask a question like this, it is the SDMB.
A philosphically themed question coming as an offshoot of an SSM thread, what is there not to like?
The question can be moronic, but a question where Plato, Samuel L. Jackson and Cthulhu can be parts of the answers is a good question in my book.
It would be interesting to see if the word “triangle” (or its equivalent in the appropriate language) was used first to describe the concept or the reality of triangular-shaped pbjects.
I see it as the exact opposite. Real-world triangles are the core, and the mathematical construct is an abstraction that attempts to formalise the concept, but is dependent on the RW examples for inspiration.
In other words, I do not see the “ideal” triangle as the model, with the RW triangles as approximations, I see the RW triangles as the models, with the “ideal” as a( very huma)n attempt to extract meaning from what we’re seeing.
Or, to put it in a simpler form, existence precedes essence.
I’d love to know, but I doubt there’d be any way of telling. But IANAPhilologist.
Not exactly this question, but the question “What does the reality of triangles consist in,” has been an important philosophical question for millenia.
If it is legitimate to ask “What does the reality of triangles consist in” I can’t see how it is foolish to ask “do triangles actually exist?”
Another way to put the question is “How could triangles possibly exist?” For as mgtman points out previously in this thread, nothing in the actual physical world can possibly fit the definition of triangle. So if triangles exist, there’s something mysterious about that.
A perfectly sensible (if wrong) response to this mystery is to reject the premise that triangles exist. Since nothing physical can fit the definition, and since everything that exists exists physically, there are no triangles.
I don’t buy this argument myself but there’s nothing fundamentally stupid about it. If I had a better memory for names, I’d probably be able to tell you which names or movements gave basically this very argument about geometrical objects. I’d guess* that Quine and other nominalists hold to something like this line.
-FrL-
*Would someone more familiar with Phil of Math please rescue me here?
From what I have learned from playing computer games is that not only do triangles exist, they are the basis for every other form in the known and unknown universe. Apparently we are made up of nothing but thousands upon thousands of tiny triangles.
Not only that, but if you should happen to go into our completely hollow interiors, you would find that those triangles are only visible from one side. I also have it on good authority that motion is actually just a series of discrete updates happening very quickly, there are only three real colors, and depth is a massive fraud perpetrated for nefarious purposes.
It was in the same school that I learned that the moment you begin feel comfortable puttering around a nice little village, waves upon waves of triangle people in blue loinclothes will come and kick the shit out of you with rocks and spears.
Although I have no proof, I’d be surprised that it was the case.
I don’t see how “natural” triangles became the mother of “geometric” ones. (I may still be the case, though).
Even obvious things like colours are not as evident to everybody, the “border” between colors is different in differetn languages, so even though there is a real physical event going on (reflection and absortion) we may separate how we name the different wavelengths.
Because they predate human consciousness & extelligence, which is the only place the geometric or abstract triangle exists.
Humans had to observe real triangles and develop the abstract concepts of “straight line”, “angle”, “internal”, “sum” etc before being able to develop the abstract mathematical concept of “triangle”. Even then, something like “Σ[sub]angles[/sub]=180°” is not something that is axiomatic to that concept, either, but something that has to be proved using other concepts like parallel lines.
But (IMO) all that abstraction is in service to one goal - adding to our internal world model, which is the way we process and interact with the real world - it is part of a toolset for cognition, and as such arises out of our innate need to model the world around us, internally. So: no real world to model, no need for abstractions. Clearly, then, it is the real world that inspires the abstractions, not vice versa.