As I said, “proof” by “a bunch of people say it”, is not proof. So, like me, you have not proven anything. Gosh, we’re on an equal footing, how about that?
Ah, of course, silly me, more of your semantic hair-splitting. My sincere apologies for not seeing that right off.
Absolute baloney, I have meant everything that I’ve said in this thread, you have nothing to indicate otherwise. I have never implied that you’re stupid, anything you’ve gotten in that direction has been made up from your own mind. I have never said that you aren’t worth my time or that I don’t want to waste time on you. Jeez, guy, try to play by your own rules and accord my words their meaning, rather than adjusting them to some other meaning. I never referred to you, I referred to your arguments. Understand the distinction? I have indicated that your arguments and your style of debate and your apparent basic belief system are sufficiently different from my own that we have no common ground to serve as the basis for any semblence of a rational discussion. Everything you post just keeps establishing that as true.
Ok, I’ll play this one game. If we take that as a given, then there is nothing that fits that defintion of “real”. Therefore, the entire concept of “objective” is meaningless. Therefore, any attempted distinction between subjective and objective is meaningless. Therefore, everything is subjective. Therefore, any meaningful discussion or interaction between any two supposedly sentient beings is pointless because, after all, your subjectivity and mine are unrelated, so we have no common ground for any interaction.
Mildly interesting, but doesn’t really get you anywhere, does it?
Yes rocks exist. People exist. Water exists. And all the other physical objects that we sense in any fashion exist independently of whether or not anyone is around to sense them.
However mathematics is not a rock or a person or water or any other physical object that we sense. It is a concept in the human brain and that concept exists, I suppose, as a set of patterns of electrical activity in the brain. If there is no brain to have that electrical activity I can’t see how there can be any mathematics.
Mathematics is also not quite like the idea of gravitation or chemisty. Rocks and rain fall, astronomical objects circle each other whether or not there is a human around to see it. Wood burns, acid corrodes, etc. even in the absence of a human to observe. But, being only the presence of an electrical impulse in a human brain, mathematics doesn’t exist without that brain. And I think that is true whether or not mathematics is defined operationally or as a structure of numerical concepts. I regard those numerical concepts again as just electricity in a brain.
One more time. Come hell or high water, mathematics is a construct of the human brain, viz an invention.
It sure likes like we are going to have to go down separate roads until the end of time on this. In that case I suppose you will prevail because I suspect your time will run out after mine does.
And a comet 1000 A.U.'s from the sun will be orbiting at a different velocity than a comet 500 A.U.'s from the sun whether or not there is a human to see it, even if the only difference is the magnitude of the distance from the sun. And Uranium-235 has different physical properties than Uranium-238, even in the absence of a human to observe, even though the difference is only the number of neutrons in the nucleus.
I thought Dennett did a decent job of quining qualia back in the 80s.
Regarding the tangents in this thread, some of them make no sense to me. Numbers didn’t exist before humans became smart enough to discover/invent them? Is that a stated position in this thread, or am I misreading? If so, does that mean that a million years ago, the earth was not the third planet from the sun, but instead was embroiled in an amorphous undefined numerological dispersement cloud or somesuch? Because in my worldview, the earth was exactly three planets out from the sun long before humans evolved. Just because nobody was around to conceive of the number 3 doesn’t mean it didn’t exist.
I mean, if I dig up a rock with 10 fossils in it from hundreds of millions of years ago, doesn’t that prove (or at least demonstrate) that 1) stuff existed long before any intelligence was around to perceive it, and 2) there was such a thing as “10”, in whatever form, because there was a group of 10 fossils in a rock long before man stood up and learned to count?
To the OP, years ago I got into a similar debate with a friend of mine. His favorite argument was that “science used to tell us the earth was flat.” I convinced him of the core of the debate as outlined in the OP with the assertion that no matter what alien species lands on our planet to say hello – even if 1000 such species stop by during the next million years – every single one of them will agree that 1+1=2, allowances given for different notations.
The universal truths we’ve uncovered are just that: universally true. I don’t know that I’d put all of mathematics under that umbrella, but certainly much of math (and physics) belong there. Before humans existed, gravity still worked.
Personally, I view math the same as I view evolution. Evolution is a fact, independent of human ideas, just as basic math is fact, independent of human ideas. The theory of evolution, ie natural selection, is a manmade effort to model the pre-existing fact. In a similar way, formal mathematics is a manmade effort to model the pre-existing fact.
As I mentioned yesterday, I highly recommend everyone in this thread take a look at Where Mathematics Comes From (preferably the book, not just the article about it that I’m linking to). It is exactly on point for this discussion. Whether you agree with the authors or not, they present some interesting arguments. From the Wikipedia article:
I’m still reading and digesting the book, and I don’t know if I’m completely convinced that Ellis Dee is wrong about the relationship of the fossils and the number 10 (or at least that we can’t say Ellis Dee is right), but it’s definitely worth looking into if you find this discussion interesting. Even if you come away completely disagreeing with what the authors have to say, the book is extremely interesting.
I agree with what you say about mathematics, but I disagree with this. Existence is something that you, as a sentient being, define. There is no existence without your conception of it. Look at it this way: can you name anything that exists that you don’t know anything about?
But what if my example of 1000 different alien species landing on earth comes true and they all understood the exact same mathematical fundamentals long before they met us? Wouldn’t that be one way we “scientifically could possibly tell” that math was not solely a human construct?
If the alien hypothetical came to pass, and the new-and-improved theory became that math was simply a sentient-being construct that any (and all) intelligent species eventually figured out on their own, then I would say that the “discovered” camp would be shown to be correct.
Is this conclusion flawed? (I really don’t know; this is an honest question.)
I don’t know either… but I’d agree with you. However, a hypothesis that requires us to meet 1000 different alien species to test it (or even a single species to begin to test it) is pretty much the same as an untestable hypothesis, at least at this time. IF what you talk about occurred, and we were able to communicate mathematical ideas with the aliens, then I think it would prove that Lakoff and Núñez are wrong, unless those aliens are very similar to us.
For example, as I understand what I’ve read so far, Lakoff and Núñez propose that one of the “grounding metaphors” for our mathematics (the things in the real world that we experience and use to build arithmetic and higher math) is “arithmetic is movement on a path,” from which we get the concept of the number line, and most of our understanding of negative numbers. Something that came to mind for me as I read that section of the book was this: If we met a radially symmetrical alien species, which was capable of walking “forward” in five different directions, their arithmetic (if they had something similar to arithmetic, that is) might be completely different from ours, since they might not have a real-world “forward and backward” to map onto “positive numbers and negative numbers”. With that fundamental difference, any system that they devised equivalent to our mathematics might be completely different from ours.
Of course, I haven’t finished the book, and I think it’ll take at least one more read to really grok it, so I might be way off from what they’re trying to say
The point is that it doesn’t make any difference. To be a difference, the difference must make a difference. In all cases, even yours, people act as if there is an external world out there that has the ability to bite down real hard if, for example, you step out of that 33rd floor window. And that determines how we act which is all that really matters…
I swear, amongst all the babble, this guy can be really lucid at times and this is a perfect example of it.
But he is right about another thing. Mathematics was early on associated with philosophy. For example, the Pythagorean Theorem. Pythagoras was a philosopher and, I might add, a musician. The Golden Mean was discovered from observing the harmonics of stringed instruments. Logic was a tool of philosophy before it was married to mathematics considerably later. As you can see, what Liberal stated in this case is not nonsense.
I can understand where Roadfood and the others are coming from. Those who cling to philosophy will always have a trump card when it comes to existence. Our interaction with what we perceive is all we know and we must come to grips with it. But I’m not going to relent and say, “you know what, you’re right, let’s agree to believe in what you and everyone else believes in.” That is where you misunderstand our aim. Our aim is to question something as seemingly concrete as mathematics in order to get at the answers. Think about what Liberal and others are saying and let’s advance this discussion.
Once, you would have been burned at the stake for suggesting that there is no God. Now, you are marginalized, ridiculed, and possibly committed for suggesting that there may be something other than mathematics and science to describe our world. How is this different? We always like to think that we are more “advanced” than people in the past but have you ever stopped to wonder if these people of the past got along just fine without technology?
Was there ever an agreement on the right triangle thing?
It seems like that is a perfect example of a mathematical relationship (the square of the sides to the square of the hypotenuse) that exists (note I said “exists”, not “is real”) even if our minds aren’t around to define the terms involved.
Is math the relationship? If so it seems independent of human thought.
Yes, and a triangle is a physical object. Does a triangle exist if it is only electrical activity in a brain? The electricity exits but I question the triangle.
