Which is exactly why it works so well as a morality mis-en-scene — a context for free-will.
A triangle is a mathematical abstraction. Certain physical objects approximate triangularity.
True, true. And those crude approximations crudely drawn on a sheet of paper clearly illustrated Euclid’s proof of the Pythagorean Theorm.
In fact all of the geometric proofs were done by means of such approximate drawings.
At first I was thinking Hoodoo has a good point because our math is based on an abstract perfection that probably does not really exist in the “real” world (I know, I’m playing with fire using the term “real”).
But as I consider it a little longer, it seems that we are bound to find 3 “somethings” somewhere in the universe at some point in time that happen to fall into the precise configuration for a right triangle, and at that point the mathematical relationship is no longer an abstract idea in our mind.
Now I just have to find those 3 particles.
Your left toenail. Did I not exist before I came onto the straight dope? You never knew about me, you never heard of me before, and yet I knew I existed. If we change your question to “can any human name anything that exists that they don’t know about” then what about an alien species that knows about a different part of the univserse? I can’t say it exists, but they are pretty sure they exist. Ok, so then I guess everything must have a sentient being to know about it so that it exists. The only possible conclusion I can see to explain everything exists even though I don’t know about it? An omnipotent being that can know about everything, so that everything exists.
I think you’re on the right track. Countless perfect geometric shapes exist in the real world. Pick any three cities and you can make a triangle between them. Identify the distance between two pairs and the triangle yields the distance between the final pairing. (Well, the earth isn’t flat, but it’s close.)
If beings can not differentiate one thing from another then how does a snake know prey from non-prey? And why do only humans know of the convept of “two”? Do the dinosaurs in a field not comprehend tha difference betwwen one or two or ten dinosaurs standing there? And how do you know whether humans or other beings know of such concepts?
The problem is that they don’t know. There is no such thing as a perfect triangle or circle that exists in the world. This leads me to conclude that the only things that are perfect are creations in and of themselves.
A piece of art, like any mental creation is perfect in and of itself or per se. We as humans have been given the power of interpretation for whatever reason and this has granted us the ability to create. Those creations may be flawed but they are perfect in and of themselves. By this I mean that Hendrix at Monterey gave a perfect performance. It may have been flawed, no concert is perfect (trust me), but to the Hendrix fan or a person who was caught up in the moment, it was perfect. The statue of David by Michelangelo might be flawed but it is perfect as an expression of an artistic concept. In other words the irregularities in form or presentation in a creation add to the character of the artistic expression. Mathematics like these is an art and in and of itself it is perfect.
Exactly. Existence is an epistemic assertion. If we insist on making it a metaphysical assertion, then we must deal with possibilities of existence.
Substitute “essence” for “existence” in the above sentence. Still true?
I didn’t say that beings cannot differentiate. I said that their differentiation is arbitrary. We differentiate a tree from the ground, a limb from the trunk, and even a twig from a limb. At what exact point does a twig become a limb? Consider the creature Abstractius, who, instead of a tree and the ground, sees a cylinder and a plane. Taxonomical classifications are always arbitrary. If you’ve ever participated in the classification of an inventory for a large wholesale distributor of, say, industrial tools, then you’ve seen the madness of how to classify a drill bit. Should it be under cutting tools (which is more typical) or under accessories? And in different contexts, the same item might be classified differently. A pointed spade? Lawn and garden at the Wal-Mart, but digging tools at Contractors Supply. With respect to snakes, according to a peer reviewed study published in Functional Ecology, snakes differentiate prey based on size, movement, and temperature.
Because they invented it. And in fact, not all humans are aware of the concept of “two”. Yumbri, for example, is one language with no numbers. Jabuti is another. In languages like these, the only concepts understood are one and many.
Probably not. In fact, one good way for a group of people to put off the charge of a wild animal is to stand together as one. Size is what puts off the animal. If you decide to spread out in order to wow him with your superior numbers, one of you will be like a gazelle from the herd in the mouth of a lion.
I just read a lot.
Well, obviously, essence not a metaphysical (ontological) assertion. Treating it as epistemic is problematic on account of analytic a priori baggage. Essence is an assertion of aesthetics. It is a matter of what is valued.
Thanks, Lib. That helps me make some sense of your view of things. Goes to show there are no stupid questions.
There’s nothing quite so fulfilling as being understood. Thanks for letting me know that, Hoodoo.
Concepts cannot exist without brains[sup]1[/sup]: Ok.
Nonetheless, I assert that if 2 dinosaurs enter a field that contains 2 other dinosaurs, the result will be 4 dinos. To that extent, mathematics (here, counting) is not only a mental concept; it’s also a property, analogous to gravity.
Permit me to characterize R. Penrose’s argument[sup]2[/sup]. Math is either invented or discovered (see ExTank’s post, btw). Those who believe that it is invented will have difficulty accounting for fractiles, for example the Mandelbrot set.
But wait. If math isn’t invented, it must be discovered. How can that be? Penrose posits three worlds: they are the physical world, the mental world and “The Platonic Mathematical World”: the latter exists without a spatial position or a particular point in time. The 3 worlds are tied together is some mysterious way.
Bizarre, to my way of thinking: I admit that I had thought that Platonic idealism was so much hocus-pocus. At the same time, I have difficulty accounting for the example of fractals without some sort of idealist framework. Those particular pictures are created by the algorithm; their origin differs markedly from your typical museum print or creative work.
A disturbing prospect, for this empiricist.
[sup]1[/sup]Brains, here, don’t have to be organic.
[sup]2[/sup]Not original to him, I’d guess. Roger Penrose is a noted physicist, mathematician and author currently at Oxford University.