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This is pure skepticism. Your position is: "We don't know anything about the real world." That is absolute hokum. The Earth orbits the Sun, living things need

by javert 12y ago

This is pure skepticism. Your position is: "We don't know anything about the real world." That is absolute hokum. The Earth orbits the Sun, living things need fuel to survive, two units combined with two units sums to four units. I could go on and on. You need good epistemology to explain why this is, since while it's common sense, I agree that common sense is not sufficient when we're talking about philosophy. Clearly you have not discovered good epistemology.

gshubert17 12y ago
Isn't his position that mathematical (2+2=4) and logical (!T=F) knowledge is a different kind of knowledge than empirical (temp=20C) or scientific (F=ma)? I took this to be similar to what Einstein [1] said: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." [1] http://www-groups.dcs.st-and.ac.uk/history/Extras/Einstein_geometry.html http://www-groups.dcs.st-and.ac.uk/history/Extras/Einstein_g...
- pron 12y ago
  Thanks for the Einstein reference. I wasn't familiar with it. However, my comment expressed little more than well established principles in epistemology and the philosophy of science. Einstein in his essay discusses the same general issue. My favorite demonstration of the difficulty of defining (non-mathematical) knowledge is the Gettier problem. The coolest thing about it is that if we try to come up with a definition of knowledge that is always agreed upon by everybody -- one that fully reconciles what we can intuitively and "logically" consider to be knowledge with all forms of the Gettier problem[1] -- we find ourselves with such a narrow definition that hardly covers anything we consider to be "known". This means that in science, as with everything else, we must adopt more lenient -- or pragmatic -- definitions of knowledge, but those definitions are not rigorous in any mathematical sense, and are always lacking. [1]: http://en.wikipedia.org/wiki/Gettier_problem http://en.wikipedia.org/wiki/Gettier_problem Also, see: http://en.wikipedia.org/wiki/Philosophy_of_science http://en.wikipedia.org/wiki/Philosophy_of_science http://en.wikipedia.org/wiki/Epistemology http://en.wikipedia.org/wiki/Epistemology
- javert 12y ago
  Yes, that is his position, but it's a false dichotomy.
pron 12y ago
> Your position is: "We don't know anything about the real world." This is absolutely not my "position". The word know requires definition, which is a very hard thing to do, and is the subject of the whole of epistemology. All I'm saying is that "know" in the real world and "know" in logic are not -- and can never be -- the same. We cannot "know" something about the physical universe in the same sense that we "know" something to be true in mathematics (but we can certainly know a lot about the physical universe, if only we would define knowledge differently than in math, which is pretty much what every philosophy does). The point I was making is that you can't blindly overlay mathematical concepts on the real world merely because they use similar terminology. Particularly, the definition of "truth" is inevitably different in math and in science, if only because science does not have the concept of the axiom, which is a core principle in the definition of mathematical truth. You cannot directly apply your notion of truth from logic to the physical universe and vice versa. Even in your examples you're confusing two different notions of truth. We do not know that the earth orbits the sun in the same sense that we know that 2 + 2 = 4. The latter is simply an algebraic axiom of the field of real numbers, while the former is an application of scientific assumptions to observations. We can be content with both types of knowledge, but we cannot equate them. We can treat both as true, but they are not true in the same sense.
- javert 12y ago
  > This is absolutely not my "position". I didn't just say that to take a cheap whack at you. I'm not interested in that kind of low-brow discussion. But I see why you don't agree with that characterization. So I'll back off on that point. I do think you're making a very serious error (albeit common in philosphers and mathematicians). What you are saying is that mathematics is derived from a set of axioms, and therefore is true "by definition," whereas truth about the real world is something else. And you have a harder time in various ways) with non-mathematical truth. The foundations there are shakier. However, the foundations actually are not shakier. They just aren't as widely known among philosophers (or common people). I'm not going to try to explain it here. That would be ridiculous. But to say one important thing that most people miss: You have to realize that knowledge is only valid in its context. It is contextual. So it is true to say, for example, that Earth orbits the Sun. It could turn out that we all live in the Matrix and that Earth doesn't orbit the Sun, but that claim would still have been true in the current context (where we have no reason to assume we live in the Matrix). Likewise, Newtonian mechanics can never be invalidated by later discoveries, because it is true in its context, i.e. at a macro scale. I don't know if this point will help you, but it is one barrier to getting scientific knowledge on a non-shaky foundation. A separate point: while it's true that you can have a mathematical system with arbitrary axioms, you can also have a mathematical system that describes reality that is developed using philosophical (as opposed to mathematical) induction (just like all "scientific" truths), and thus that is actual true in a scienfic sense, and which is NOT based on axioms. For instance, you can define a mathematics where 1 + 1 is 2, but you can also induce this rule from reality by looking at objects. You can define a mathematics where 1 + 1 is 1, but you can't induce that from reality, because it isn't true in reality. Really, the point of mathematics is to improve human life, not to be an idle pasttime for professors that don't have moral qualms with getting paid by taxpayers yet not rendering them a service. So the point of mathematics should be to look at mathematics as it can be induced from reality, and figure out things that are not only true in what you call a mathematical sense, but also true in reality. It's also fine to look at made-up mathematics, but only in that that sometimes turns into useful discoveries for real mathematics.
mreiland 12y ago
As someone with a pretty strong Math background, I certainly didn't take that from his comment. I took it to mean he understands Math fairly strongly as well, and that most of your grievances with him have more to do with your lack of familiarity with the deeper underpinnings of Mathematics.

by javert 12y ago

gshubert17 12y ago

Isn't his position that mathematical (2+2=4) and logical (!T=F) knowledge is a different kind of knowledge than empirical (temp=20C) or scientific (F=ma)? I took this to be similar to what Einstein [1] said: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." [1] http://www-groups.dcs.st-and.ac.uk/history/Extras/Einstein_geometry.html http://www-groups.dcs.st-and.ac.uk/history/Extras/Einstein_g...

pron 12y ago
Thanks for the Einstein reference. I wasn't familiar with it. However, my comment expressed little more than well established principles in epistemology and the philosophy of science. Einstein in his essay discusses the same general issue. My favorite demonstration of the difficulty of defining (non-mathematical) knowledge is the Gettier problem. The coolest thing about it is that if we try to come up with a definition of knowledge that is always agreed upon by everybody -- one that fully reconciles what we can intuitively and "logically" consider to be knowledge with all forms of the Gettier problem[1] -- we find ourselves with such a narrow definition that hardly covers anything we consider to be "known". This means that in science, as with everything else, we must adopt more lenient -- or pragmatic -- definitions of knowledge, but those definitions are not rigorous in any mathematical sense, and are always lacking. [1]: http://en.wikipedia.org/wiki/Gettier_problem http://en.wikipedia.org/wiki/Gettier_problem Also, see: http://en.wikipedia.org/wiki/Philosophy_of_science http://en.wikipedia.org/wiki/Philosophy_of_science http://en.wikipedia.org/wiki/Epistemology http://en.wikipedia.org/wiki/Epistemology
javert 12y ago
Yes, that is his position, but it's a false dichotomy.

pron 12y ago

> Your position is: "We don't know anything about the real world." This is absolutely not my "position". The word know requires definition, which is a very hard thing to do, and is the subject of the whole of epistemology. All I'm saying is that "know" in the real world and "know" in logic are not -- and can never be -- the same. We cannot "know" something about the physical universe in the same sense that we "know" something to be true in mathematics (but we can certainly know a lot about the physical universe, if only we would define knowledge differently than in math, which is pretty much what every philosophy does). The point I was making is that you can't blindly overlay mathematical concepts on the real world merely because they use similar terminology. Particularly, the definition of "truth" is inevitably different in math and in science, if only because science does not have the concept of the axiom, which is a core principle in the definition of mathematical truth. You cannot directly apply your notion of truth from logic to the physical universe and vice versa. Even in your examples you're confusing two different notions of truth. We do not know that the earth orbits the sun in the same sense that we know that 2 + 2 = 4. The latter is simply an algebraic axiom of the field of real numbers, while the former is an application of scientific assumptions to observations. We can be content with both types of knowledge, but we cannot equate them. We can treat both as true, but they are not true in the same sense.

javert 12y ago
> This is absolutely not my "position". I didn't just say that to take a cheap whack at you. I'm not interested in that kind of low-brow discussion. But I see why you don't agree with that characterization. So I'll back off on that point. I do think you're making a very serious error (albeit common in philosphers and mathematicians). What you are saying is that mathematics is derived from a set of axioms, and therefore is true "by definition," whereas truth about the real world is something else. And you have a harder time in various ways) with non-mathematical truth. The foundations there are shakier. However, the foundations actually are not shakier. They just aren't as widely known among philosophers (or common people). I'm not going to try to explain it here. That would be ridiculous. But to say one important thing that most people miss: You have to realize that knowledge is only valid in its context. It is contextual. So it is true to say, for example, that Earth orbits the Sun. It could turn out that we all live in the Matrix and that Earth doesn't orbit the Sun, but that claim would still have been true in the current context (where we have no reason to assume we live in the Matrix). Likewise, Newtonian mechanics can never be invalidated by later discoveries, because it is true in its context, i.e. at a macro scale. I don't know if this point will help you, but it is one barrier to getting scientific knowledge on a non-shaky foundation. A separate point: while it's true that you can have a mathematical system with arbitrary axioms, you can also have a mathematical system that describes reality that is developed using philosophical (as opposed to mathematical) induction (just like all "scientific" truths), and thus that is actual true in a scienfic sense, and which is NOT based on axioms. For instance, you can define a mathematics where 1 + 1 is 2, but you can also induce this rule from reality by looking at objects. You can define a mathematics where 1 + 1 is 1, but you can't induce that from reality, because it isn't true in reality. Really, the point of mathematics is to improve human life, not to be an idle pasttime for professors that don't have moral qualms with getting paid by taxpayers yet not rendering them a service. So the point of mathematics should be to look at mathematics as it can be induced from reality, and figure out things that are not only true in what you call a mathematical sense, but also true in reality. It's also fine to look at made-up mathematics, but only in that that sometimes turns into useful discoveries for real mathematics.

mreiland 12y ago

As someone with a pretty strong Math background, I certainly didn't take that from his comment. I took it to mean he understands Math fairly strongly as well, and that most of your grievances with him have more to do with your lack of familiarity with the deeper underpinnings of Mathematics.