The universe is inherently quantitative. When elements burn they give off radiation at specific wavelengths. Gravity is proportional to the inverse of the square of the distance between objects. Light travels at a specific speed c.

What a load of philosophical bullshit. Do you deny that the moon exists?

But regardless, all those divisions actually exist, whether they are useful to any organism, or not.

So what? The world exists regardless of what any of us happens to be thinking about at any particular moment. When I look at a glass of water, I'm not thinking about the individual water molecules or the hydrogen bonds that between them, but so what, they're there.

Ridiculous. Tell that to Hawking.

None of that is under dispute.


No. And not bullshit; I think this is pretty much an unavoidable consequence of the theory of evolution.


They exist now. Lots of things exist now that didn't before complex organisms evolved. Consciousness, for example.

None of that is under dispute.

Light can be slowed down in a super-atomic cloud to around 38 mph. Other methods allow light to be slowed while remaining in phase.

That's not even relevant to the irrelevant side topic.

Jay

Sure, but not the wavelengths of the emissions from the combustion of strontium, the number of planets revolving around the sun, Planck's constant, and the speed of light.

Your earlier point was that numbers are inherently metaphors; mine is that they are not. They are inherent to the Universe.

I don't disagree. (I thought I already said that.)

... Let me see if I can lay this out as clearly as possible. (Also I'll mention that it'd really help if you employ the principle of charity: try to understand before trying to refute.)

When we look back at the history of the universe, including the history before our own existence, and describe it, we are doing so using the features of the brain that we've evolved to have. (Again: not a disputable point, or at least not by appeal to Hawking; you might try Michael Behe if you're desperate.)

What this means is that we can (and do) say there were eight planets in our solar system 3.5 billion years ago, and we mean the same thing we mean when we say there are eight planets in our solar system now. And there are (and were) eight planets in our solar system: it's a fact. However (and as a direct result of the theory of natural selection), what it means to say that---what it means for that to be a fact---is slightly different from what we have traditionally taken it to mean. It is a claim about reality, yes, but it is also a claim partially about a particular type of primate brain (which is, of course, now part of reality).

Division of the universe into separate "objects" can be done in any number of ways. Some ways are interesting to organisms like us, and some aren't. My position is not the same as saying objects don't exist (I'm neither an object- nor a number-eliminativist), but it is also false to say that objects are part of reality in a mind-independent way (whatever you want to call that). What I'm saying is that they are useful fictions---they are theoretical creations used by minds to reason about things more efficiently. They exist, just like numbers and colors, but you have to look at things the right way in order to see them.

Since there are so many ways to divide the universe into objects, prior to the evolution of minds either nothing could have been meaningfully "said" regarding the number of planets in our solar system, or pretty much anything could be said (based on the near-infinite number of possible object-division methods that could, however slim the chances, be used by some future organism with a mind); but as long as the same idea is meant, it doesn't really matter which way you want to describe it. (Your statement above that "all those divisions exist" could jive with the latter, if you want.) This issue isn't particularly important, except that it can be used to help in understanding what it means now for it to be true that "there are (and were) eight planets in our solar system". (And yes, I know it is also obvious that nothing could've actually been said, regardless of what could hypothetically "meaningfully" be said: no minds existed either to do the saying or to grok the meaning.)

More about color might help, since it is a lot less fundamental in our thinking than objects. Color-vision and color evolved at the same time (organisms became flashier as other organisms developed ways to detect that flashiness). It is inherently organism-relative, and it is much easier to explain why than it is with numbers or object-division or "folk psychology" stuff: different organisms have different types of cells in their retinas. For example, we have trichromatic vision-systems, while pigeons detect color using a tetra-chromatic system.

So does red exist? Well, yes. It exists in a way similar to centers of gravity or numbers. And when we think about red as if it were a property of a surface (or as a property of light), we are engaging in a form of metaphorical reasoning that uses fictional concepts to make its deductions. It isn't sensical to call it "false" reasoning, because the deductions are made in a (mostly) inference-preserving way---in this situation (a brain evolved by natural selection), the results are what matter, not the shortcuts used to compute them. So the "property of redness" does "exist" (there's no denying everyday sentences like "red exists" or "that ball is red"), but it exists metaphorically (as a useful fiction---an abstract way to think about something more complex).


What does that mean? (If you're saying numbers are extremely useful for describing the Universe, I agree.)

I don't disagree. (I thought I already said that.)

...

Division of the universe into separate "objects" can be done in any number of ways. Some ways are interesting to organisms like us, and some aren't. My position is not the same as saying objects don't exist (I'm neither an object- nor a number-eliminativist), but it is also false to say that objects are part of reality in a mind-independent way (whatever you want to call that). What I'm saying is that they are useful fictions---they are theoretical creations used by minds to reason about things more efficiently. They exist, just like numbers and colors, but you have to look at things the right way in order to see them.

More about color might help, since it is a lot less fundamental in our thinking than objects. Color-vision and color evolved at the same time (organisms became flashier as other organisms developed ways to detect that flashiness). It is inherently organism-relative...

And when we think about red as if it were a property of a surface (or as a property of light), we are engaging in a form of metaphorical reasoning that uses fictional concepts to make its deductions.

What does that mean? (If you're saying numbers are extremely useful for describing the Universe, I agree.)

I don't think there is anything organism-dependent, fictional, or theoretical about the existence of the planet Mars. It's there. We've landed things on it.


I can agree that color is inherently organism-dependent. The cup of coffee I'm drinking, however, is not.


Again, I disagree. There is nothing metaphorical or fictional about the color of an object, even if we agree that not all organisms perceive the object as red.


I'm saying that the speed of light is c, that the hydrogen ion does have a line in its emission spectrum at a wavelength of 12,818 Angstroms. These are quantitative properties of the Universe.

What's he metaphor for the number e raised to the power i ?

Jay

I can agree that color is inherently organism-dependent. The cup of coffee I'm drinking, however, is not.

Again, I disagree. There is nothing metaphorical or fictional about the color of an object, even if we agree that not all organisms perceive the object as red.

I'm saying that the speed of light is c, that the hydrogen ion does have a line in its emission spectrum at a wavelength of 12,818 Angstroms. These are quantitative properties of the Universe.

What's he metaphor for the number e raised to the power i ?

If I take your words at face value, I'd be remiss if I didn't retort that the cup of coffee you're drinking is actually part of the (extended) human phenotype. Claiming it is organism-independent would be like claiming your pinkie-finger is organism-independent.

However, maybe you mean something a little different. If what you're saying is that the matter currently serving to function as that particular cup of coffee, whatever it happens to be, and regardless of how it got there, exists in an organism-independent sense, then I agree 100%. But the fact that it is currently being a "cup of coffee" (which is a verifiable fact; "objective" in any important sense) is a fact which is intrinsically tied to a class of observers (us). I'm sure you'll agree that the notion of a "cup of coffee" is organism-dependent.

I can't tell what you're saying here. (But maybe it's because you apparently didn't say anything, except that you think I'm wrong.)

Maybe you can make your position clearer by answering some questions:

Prior to the evolution of color-vision systems, did the "color of an object" exist? If, in 2050, every human who is not red-green color-blind is mass-murdered in the weirdest genocide ever, would red and green still exist as independent "colors of objects"? What if (a few centuries later) every organism with eyes is mercilessly slaughtered (by a new race of super-intelligent, eyeless machines)? What if eyes had never evolved?

And what other color-like properties do we need admit the existence of? Suppose that one day, organisms will evolve another sense organ, which can detect the folor of something: do folors-of-objects exist today, despite the lack of an observer, or do we have to wait?

I don't disagree with either of those statements (unless there's something special hidden in the italics). If that's really all you mean by saying numbers are "inherent to the universe" (and I'd be surprised if it is), then I agree.

...and I'll reply: numbers are metaphorical and "inherent to the universe", the latter point having no relation to the former.

Not "the".

In the particular (scientific, falsifiable) theory I was mentioning earlier, there's a couple dozen conceptual metaphors and metaphorical blends involved. I can't really just sum it up here; if you're interested, you might check out the book Where Mathematics Comes From by Lakoff and Nuñez. (It ends with a "case study" of e^(pi * i) + 1, which I think also should address your question.)

Well, the cup and the coffee in it were made by an organism. But once they are made, they have an objective physical existence. Their function, though, is clearly organism-dependent.

I'd say that the simple answer to the questions is "no," but the simpler argument that color is organism dependent is simply that there are organisms that perceive the color differently, or not at all.

I don't understand that statement.

That's funny because (1) I ordered that book a couple days ago, and (2) it addresses for all intents and purposes the very question I asked (e^i).

From what I gather, most mathematicians think Lakoff is nuts, although mathematics educators think his work has more merit.

I've also read bits of Lakoff's earlier book (from '79 I think, and I don't recall the title), and I thought that his theory was on pretty shaky ground. His "time is money" metaphor seemed especially off the mark. Furthermore, it was difficult to deduce what his methodology was. Bad science (uncontrolled observations) combined with philosophy was my best guess. I think the authors did generate some interesting, testable hypotheses, and apparently some recent results from neuro-something-or-other are consistent their hypotheses.

Sure. Light moves at speed c.... but I move at speed v. As great as it sounds... c isn't constant just like v isn't constant. That is all.

7) Math jokes are NOT funny.

Did you just make that up on the spot or that part of your repertoire? Either way, i laughed, so you win the math joke argument.

Did you just make that up on the spot or that part of your repertoire? Either way, i laughed, so you win the math joke argument.

The entire concept of an "object" is organism-relative. Organisms with complex nervous systems often model their environment by dividing it into "objects" (sometimes in multiple ways) because it is useful to do so; what granularity of this division is maximally useful is going to depend on the details of the organism (it's size, method of locomotion, primary sense-organs, what it eats, what eats it, and any number of other details).

Prior to the evolution of color-vision systems, did the "color of an object" exist? If, in 2050, every human who is not red-green color-blind is mass-murdered in the weirdest genocide ever, would red and green still exist as independent "colors of objects"? What if (a few centuries later) every organism with eyes is mercilessly slaughtered (by a new race of super-intelligent, eyeless machines)? What if eyes had never evolved?

And what other color-like properties do we need admit the existence of? Suppose that one day, organisms will evolve another sense organ, which can detect the folor of something: do folors-of-objects exist today, despite the lack of an observer, or do we have to wait?