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Tags David Hume , empiricism

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Old 19th August 2008, 05:33 PM   #1
Kthulhut Fhtagn
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Inductive Reasoning, Empiricism, Science, and Knowledge.

I've heard some very interesting arguments from numerous people regarding the validity of inductive reasoning and empiricism. Now I've always thought it was perfectly logical to assume that the world exists as we sense it because I have absolutely no reason to believe that it doesn't. It seems perfectly reasonable to assume that a stool is a stool and that a kitten is not an F-22 Raptor but according to the problem of induction this could happen at any given moment. Hume may be right and we may be in fact begging the question when we assume that if we see an apple fall three hundred times we assume that the apple will fall to the ground the 301st time. But it seems spectacularly unreasonable to wait around for the apple to stop in mid-air and reverse it's course. Or for that matter we might as well starve to death while attempting to reason out whether or not our hunger pains will cease because inductive reasoning begs the question. Maybe the fact that we've never seen an object disobey the inductive reasoning we've observed is good enough reason to believe that inductive reasoning does work.

Hume described the problem of induction in An Enquiry concerning Human Understanding and then turned around and stated it's perectly reasonable to assume inductive reasoning for reasons similiar to those I've given. So then in this case does the problem of induction violate Occam's Razor? And what about empiricism? Is it possible to learn from your senses and observations if we're incapable of using inductive reasoning? And for that matter what practical problem does that cause for science and knowledge? Is there such a thing as absolute certainty or is it simply a state of mind?
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Old 19th August 2008, 05:41 PM   #2
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You ought to check out the difference between induction and deduction.
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Old 19th August 2008, 05:53 PM   #3
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I have no problem assuming induction works for the same reason that I assume that the laws of deductive logic work: If they really don't work than it doesn't matter. If induction really doesn't work and the sun turns into a grapefruit tomorrow and everything falls speedily upward, I doubt that my last thoughts are going to be, "well, there goes my epistemology..."

Some people are quite shaken when they learn that human knowledge is forever imperfect, and yet life goes on. "Good enough" is indeed good enough.
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Old 19th August 2008, 06:07 PM   #4
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Originally Posted by Kthulhut Fhtagn View Post
Is there such a thing as absolute certainty or is it simply a state of mind?
Knowledge is probabilistic.
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Old 19th August 2008, 09:00 PM   #5
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Originally Posted by Kthulhut Fhtagn View Post
I've heard some very interesting arguments from numerous people regarding the validity of inductive reasoning and empiricism. Now I've always thought it was perfectly logical to assume that the world exists as we sense it because I have absolutely no reason to believe that it doesn't. It seems perfectly reasonable to assume that a stool is a stool and that a kitten is not an F-22 Raptor but according to the problem of induction this could happen at any given moment. Hume may be right and we may be in fact begging the question when we assume that if we see an apple fall three hundred times we assume that the apple will fall to the ground the 301st time. But it seems spectacularly unreasonable to wait around for the apple to stop in mid-air and reverse it's course. Or for that matter we might as well starve to death while attempting to reason out whether or not our hunger pains will cease because inductive reasoning begs the question. Maybe the fact that we've never seen an object disobey the inductive reasoning we've observed is good enough reason to believe that inductive reasoning does work.

Hume described the problem of induction in An Enquiry concerning Human Understanding and then turned around and stated it's perectly reasonable to assume inductive reasoning for reasons similiar to those I've given. So then in this case does the problem of induction violate Occam's Razor? And what about empiricism? Is it possible to learn from your senses and observations if we're incapable of using inductive reasoning? And for that matter what practical problem does that cause for science and knowledge? Is there such a thing as absolute certainty or is it simply a state of mind?
Don't forget that we now have the extra criterion of falsifiability to address the problem of induction.
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Old 19th August 2008, 09:10 PM   #6
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Originally Posted by Kthulhut Fhtagn View Post
I've heard some very interesting arguments from numerous people regarding the validity of inductive reasoning and empiricism. Now I've always thought it was perfectly logical to assume that the world exists as we sense it because I have absolutely no reason to believe that it doesn't.
Also, there is no assumption in empiricism that the world exists as we sense it - don't confuse empiricism with Materialism.

Empiricism deals with the senses and the mathematical relationships that can be detected in sense data - nothing else.
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Old 20th August 2008, 11:14 AM   #7
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Originally Posted by gentlehorse View Post
Knowledge is probabilistic.
No. Inductive knowledge is probabilistic; deductive knowledge can indeed be certain. That's the defining difference between inductive and deductive reasoning (although of the distinction itself predates modern probability theory).

But that's basically the answer to the OP. If you believe and accept that knowledge can be probabilistic, then there is no problem of induction. If you get all hardcore and insist that knowledge cannot be probabilistic, then what we have are a number of extremely good, extremely well-supported wild guesses.

If you take the traditional definition of "knowledge" as a "justified true belief" apart, you will quickly find the following things:
  1. "Justification" is not proof; we are justified to believe all sorts of things about which we are not certain.
  2. Our belief that something is true is a belief, as is our belief that "our belief that something is true" is true.
  3. We can never have better than a belief that something is true; our belief about it still might be wrong.
  4. We don't have any reliable way from sorting justified false beliefs from justified true beliefs. Sucks to be us, I guess.
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Old 20th August 2008, 01:24 PM   #8
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Originally Posted by drkitten View Post
No. Inductive knowledge is probabilistic; deductive knowledge can indeed be certain. That's the defining difference between inductive and deductive reasoning (although of the distinction itself predates modern probability theory).
Well, as certain as your premises are, at least.
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Old 20th August 2008, 07:32 PM   #9
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Originally Posted by Theophage View Post
Well, as certain as your premises are, at least.
Which, in a final stabbing irony, cannot be established through deductive logic.
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Old 20th August 2008, 07:56 PM   #10
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Inductive logic just works, which can be proven inductively.
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Old 21st August 2008, 12:43 PM   #11
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Originally Posted by Mobyseven View Post
Which, in a final stabbing irony, cannot be established through deductive logic.
Didn't pay a lot of attention in math class, did you?
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Old 21st August 2008, 04:03 PM   #12
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Originally Posted by drkitten View Post
Didn't pay a lot of attention in math class, did you?
Even math requires a set of postulates that must be assumed, and cannot be proven. The postulates can be chosen randomly, and changing those postulates creates a different set of mathematical truths. (Peano axiomsWP, Non-Euclidean geometryWP,etc.) Normally, those postulates are chosen such that they make intuitive sense (if two numbers both result in the same number when incremented, then the original numbers must have been the same number), but intuitiveness is not the same a correctness.
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Old 21st August 2008, 07:37 PM   #13
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Originally Posted by GodMark2 View Post
Even math requires a set of postulates that must be assumed, and cannot be proven.
That would be a "no, I didn't," then.

The theorems of mathematics are generally conditional upon the choice of postulates, and conditional upon the choice of logic systems as well.

But this does not mean that math dooesn't produce universal truths. In particular, let's say that I assume P (as a postulate) and conclude Q (using predicate logic). Does this mean Q is universally true? No. But it does mean that the statement "If P is true and if the axioms of predicate logic is true, then Q is also true" is a universally valid statement.

There are no postulates for you to negate here. It's a simple description of the system. If it follows certain rules, then certain things are consequences of certain other things.

This is true outside of logic as well. For example, the statement "All bachelors are unmarried" is true, simply because the word "bachelor" has a meaning that includes "unmarried." The statement "All felons have committed at least one felony" is similarly (universally) true by virtue of what the word 'felon' means. The statement "if a building is in Des Moines, IA, it is in North America" is (universally) true because an authority has defined the extent of Des Moines (and another has defined the extent of North America), and their definition precludes being in the first but not the second.

This, of course, is well known to logicians and philosophers. Deductive logic can only make explicit what is already implicit in the premises. But the act of explication can both be surprising and interesting (which is why mathematics, as an almost purely deductive science, is as well-funded as it is) precisely because people don't know all the consequences of their definitions and beliefs. Legal philosophy is another deductive area that explores the consequences of formal definitions (and will often recommend changes to definitions precisely to avoid being forced to draw unpalatable conclusions -- precisely because the conclusion is unavoidably implicit in the premise/definition). More generally, deductive reasoning is an exploration of the universal relationships of premises to conclusions. Some philosophers have claimed that it's an empty sterile discipline because "it can't tell you anything you don't already know." But this is obviously false, because most people don't know explicitly what what they "already know" implicitly until you chart out the actual deductive reasoning.
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Old 21st August 2008, 08:15 PM   #14
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Of course even mathematicians use non mathematical induction - informally at least.

Witness all the computational attempts to test the Riemann Hypothesis. Chaitin has even suggested that non mathematical induction be formally accepted as a valid form of mathematics.
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Old 21st August 2008, 10:34 PM   #15
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Originally Posted by drkitten View Post
Didn't pay a lot of attention in math class, did you?
I'm sorry, I must have missed that part of the course. Remind me again how we can form a useful* sound argument that tells us about the world without going outside of deductive logic?

*Tautologies aren't useful, nor is using a contradiction in the premise to 'prove' the conclusion (yes, there really was a guy who presented a talk insisting that as contradictions can be logically formed, everything is true...even the negation of his thesis).
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Old 22nd August 2008, 07:55 AM   #16
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Originally Posted by Mobyseven View Post
I'm sorry, I must have missed that part of the course. Remind me again how we can form a useful* sound argument that tells us about the world without going outside of deductive logic?
I dunno. Ever hear of Rivest, Shamir, and Adelman? They used mathematics to develop (deductively) a method of keeping communications secure that's used worldwide, gave them the Turing Award, and incidentally made them multimillionaires.

Claude Shannon was able to establish (deductively) limits on the amount of information that can be transferred across a noisy channel regardless of the technology employed, and established not only the entire discipline of information theory, but revolutionized the analysis of actual data transmission by giving the phone company goals to shoot for (empirically) in their construction and deployment of wires.

Similarly, Newton developed (deductively) this technique called the "method of fluxions" that allowed people to talk about things like the area under a curve instead of under a polygon, or about the instantaneous rate of speed (and therefore resolve Zeno's paradox.) I believe these "fluxions" are a standard part of every undergraduate mathematics curriculum today, albeit under a different name.

Even before that, Archimedes was able to use deductive reasoning to establish a useful value for pi as the limit of a set of polygons, which was of tremendous use to geometers, architects, surveyors, and engineers.

Sounds like someone found this stuff useful.

Quote:
*Tautologies aren't useful,
That's a common misconception, yes. In actual fact, tautologies can be quite useful, simply because no one is aware of all the implications of a given statement.

If the statement X -> Y is a tautology, but you don't know it, then finding out (via deductive reasoning) that is it is a tautology is very useful.

Quote:
nor is using a contradiction in the premise to 'prove' the conclusion .
Proof by contradiction is a very useful way to establish the truth of a proposition. One of the problems cryptographers have faced in DES, for example, is that there simply aren't enough keys (we're now at the point where a moderately large computer can brute-force DES by exhausting the keyspace). AES has a larger keyspace, so it avoids the problem for a while --- but we know that the keyspace will eventually be exhausted if computers get big enough.

We know, however, that the RSA keyspace will never be exhausted. Why? Because we know (deductively) that there are infinitely many prime numbers. Therefore, we know the useful fact that we can always enlarge the size of the keys and make the keyspace as large as we like. It is not possible to exhaust the RSA keyspace, a useful fact -- even though it's tautological.
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Old 22nd August 2008, 05:10 PM   #17
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Originally Posted by drkitten View Post
That would be a "no, I didn't," then.

The theorems of mathematics are generally conditional upon the choice of postulates, and conditional upon the choice of logic systems as well.

But this does not mean that math dooesn't produce universal truths. In particular, let's say that I assume P (as a postulate) and conclude Q (using predicate logic). Does this mean Q is universally true? No. But it does mean that the statement "If P is true and if the axioms of predicate logic is true, then Q is also true" is a universally valid statement.

There are no postulates for you to negate here.
Well, no postulates except "if the axioms of predicate logic is true", which is exactly the sort of postulates I was referring to. The axioms of predicate logic, interestingly, cannot be proven by predicate logic. They must be assumed.

Quote:
If it follows certain rules, then certain things are consequences of certain other things.
That's exactly the 'if' that can't be determined, except experimentally/inductively.

Quote:
This is true outside of logic as well. For example, the statement "All bachelors are unmarried" is true, simply because the word "bachelor" has a meaning that includes "unmarried." The statement "All felons have committed at least one felony" is similarly (universally) true by virtue of what the word 'felon' means. The statement "if a building is in Des Moines, IA, it is in North America" is (universally) true because an authority has defined the extent of Des Moines (and another has defined the extent of North America), and their definition precludes being in the first but not the second.
Ignoring all the felons that were convicted of a felony, but were innocent of the action.

If "A bachelor is a man who does not have a wife", are married gay men therefore bachelors? They each have a husband, but neither has a wife. But they're both married. If instead "A bachelor is an unmarried man" then widowers become bachelors. Which axiom/definition do I use?

If a building is in Washington DC, and Washington DC is in the United States of America, does that necessarily mean that the building is in The United States of America? Not if that building is a foreign embassy. Then the building is considered an extension of it's mother land, and specifically not the USA.

Your definition of "Universal Truth" seems a bit different from mine.

Quote:
This, of course, is well known to logicians and philosophers. Deductive logic can only make explicit what is already implicit in the premises. But the act of explication can both be surprising and interesting (which is why mathematics, as an almost purely deductive science, is as well-funded as it is) precisely because people don't know all the consequences of their definitions and beliefs. Legal philosophy is another deductive area that explores the consequences of formal definitions (and will often recommend changes to definitions precisely to avoid being forced to draw unpalatable conclusions -- precisely because the conclusion is unavoidably implicit in the premise/definition). More generally, deductive reasoning is an exploration of the universal relationships of premises to conclusions. Some philosophers have claimed that it's an empty sterile discipline because "it can't tell you anything you don't already know." But this is obviously false, because most people don't know explicitly what what they "already know" implicitly until you chart out the actual deductive reasoning.
I would never claim "it can't tell you anything you don't already know". Deductive logic can indeed show you previously unknown necessary results of your assumed axioms, but not anything about the axioms themselves. The best it can hope for in that regard is to either show that the axioms do not contain any inherent contradictions, or that they do.
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Old 22nd August 2008, 08:39 PM   #18
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Originally Posted by drkitten View Post
I dunno. Ever hear of Rivest, Shamir, and Adelman? They used mathematics to develop (deductively) a method of keeping communications secure that's used worldwide, gave them the Turing Award, and incidentally made them multimillionaires.

Claude Shannon was able to establish (deductively) limits on the amount of information that can be transferred across a noisy channel regardless of the technology employed, and established not only the entire discipline of information theory, but revolutionized the analysis of actual data transmission by giving the phone company goals to shoot for (empirically) in their construction and deployment of wires.

Similarly, Newton developed (deductively) this technique called the "method of fluxions" that allowed people to talk about things like the area under a curve instead of under a polygon, or about the instantaneous rate of speed (and therefore resolve Zeno's paradox.) I believe these "fluxions" are a standard part of every undergraduate mathematics curriculum today, albeit under a different name.

Even before that, Archimedes was able to use deductive reasoning to establish a useful value for pi as the limit of a set of polygons, which was of tremendous use to geometers, architects, surveyors, and engineers.

Sounds like someone found this stuff useful.
Ah, I see where we're having a bit of a disconnect here.

Yes, these things were deductively proven and are useful in the real world. But those two things aren't necessarily connected all the time. It is entirely conceivable that Newton could have developed calculus, and then found it had absolutely no application to the real world, instead making it a mathematical curiousity and not much more.

That is does have (many) applications to the real world is something that has been established empirically, and that's where the issue is here - something can be established using deductive reasoning, but to establish that the thing we've just deduced is useful in the real world, we have to check it in the real world...and that involves reaching outside of deductive logic.

Originally Posted by drkitten View Post
That's a common misconception, yes. In actual fact, tautologies can be quite useful, simply because no one is aware of all the implications of a given statement.

If the statement X -> Y is a tautology, but you don't know it, then finding out (via deductive reasoning) that is it is a tautology is very useful.
True. I'll concede that.

Originally Posted by drkitten View Post
Proof by contradiction is a very useful way to establish the truth of a proposition.
Haha...sorry, that was my little joke - I wasn't sure if it'd come across well. I didn't mean that proof by contradiction isn't useful. It was a reference to a guy who, in all seriousness, presented a talk on how because we can make an argument trivially sound simply by making the premises a contradiction, that meant that every proposition really is true, including contradictory propositions.
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