Volandum (![[info]](http://l-stat.livejournal.com/img/userinfo.gif){kind=small} volandum) wrote,@ 2007-03-29 15:37:00 |
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Argh, amateur philosophy
I'm ignorant, and would appreciate correction - though often it might be easier and more helpful to cite something which corrects me (I've found a few myself that I'll look up when I get back, but more don't hurt.).
me: Hello.
Gregory: Hello, Vol.
me: How are you?
Do you know much about philosophy of mathematics or science? I don't.
Gregory: I'm fairly well. Life has been keeping me incredibly busy by throwing opportunities into my path that I have been 'carpe'-ing as best as I can.
And about the philosophy of mathematics and science... that sounds a lot like late 18th and early 19th century science.
When scientists were called 'natural philosophers'
and science was seen as some way of trying to discern a set of natural laws through reason.
me: I had a rather frustrating conversation, and on further thought I'd like a critique of my own statements, at least a few of which were probably suspect.
Gregory: Okay.
I don't have to be out of here for about 2 hours, and so long as I get a bit more reading done at some point in there I can do other stuff too.
That's the advantage to getting up early, really.
me: Okay, thanks!
Gregory: Hmm. Interesting claim there, midway through.
Your debatee says that he prefers facts over assumptions and therefore wouldn't like philosophy.
I think his definition of 'fact' is rather different than yours.
me: Her - please, tell me more.
Gregory: Ah. Excuse me. Her definition.
Well, you say that maths would be better than chemistry as far as accumulation of fact goes.
She responds with the claim that experimentation leads to fact and so chemistry isn't so fact-free as one might think.
This means, at least to me, that she's an empiricist. A fact is what can be reasonably assumed with some degree of evidentiary burden of proof for backup.
Not just a mathematical absolute proven by equations and formulae.
And my assumption is backed up by the ensuing argument about maths.
Your statement of fact is one of a philosopher, by the way.
No necessary absolute truth.
Just state a claim, and then proceed from that claim on unquestionable ground, and you end up with fact.
Which, if you think about it, is basically the exact same thing as an experiment.
You start with an idea, neither fact nor fiction, and then proceed through unquestionable ground via experimentation to a conclusion about the fact/fiction relationship of the idea to the world.
me: I don't think your parallel holds.
Gregory: No?
me: No.
At least, her "unquestionable" conclusions are very weak - along the lines of "No experiment to date has shown that gravitational attraction is not proportional to the masses involved."
Gregory: Mm. Well, let me keep reading, then.
I'm offering comment as I go through and pausing to do so.
me: Thank you.
I may well misstep - please point out such problems.
Gregory: Right. Well, on the basis of the first conversation I think that you and she are looking at fact in slightly different ways based on what it is that you end up doing.
One of the reasons why I say this is because I view fact as something else from either of you, and I suspect it's because my discipline of choice is history.
Your definition of fact is what she labels 'assumptions.' We can take that as understood, since there would not be the argument about facts otherwise.
me: Curiously enough, what she calls facts are what I'd label assumptions.
Gregory: Yep.
That's about the size of it.
And I think my point here is going to be that what you two are looking at are the same thing. By virtue of the nature of maths and science both it is necessary that what you call fact be an assumption of some sort.
Now whether it can or can't be fact and assumption at the same time, I don't think I can say.
But that your facts be at least in some part assumption... that I think I can say.
me: I don't think so - maths says nothing that isn't a contingent tautology.
Gregory: Mm.
And that's where you and she part company in the debate.
See, a 'contigent tautology' can quite easily be seen as in some part assumption.
me: How so?
Gregory: You said "With maths I define the things I'm
dealing with, and my conclusions are necessarily true by virtue of
being tautologous."
The key point there is that you definine what you're going to start with and go from there.,
Yes, the conclusion holds formation with that which comes before it.
me: Hmm, I should take that back and set up a better logical model.
Gregory: But that doesn't mean that your initial definitions are guaranteed to produce a fact in line with the natural model.
me: In fact, I do.
Mathematics is the subject of considering the contingent conclusions arising in certain arbitrary axiom systems.
Gregory: Hmm. Perhaps. Though I still think that the boundry between scientific experimentation and logical progression of thought is a very small and blurry thing.
Here's a question for you:
From your point of view, where does an experiment diverge from an abstract construct of logic?
Is there any reason why I can't say that logic is just an experiment conducted entirely in someone's head or on paper?
me: Hmm, I've seen two formalisations of scientific thought. One is probabilistic, the other is completely assumption-based.
There isn't - gedankenexperimente exist. I think the distinction is in the conclusions of the experiments and their motivation. Maths has no concern with reality.
Gregory: You are so right. Maths does have no concern with reality. But I digress, tongue firmly in cheek. Back to the discussion.
Gregory: I think that if you look at it, the point where maths truly becomes a realm apart from reality is a fairly high-end area. And at that point, science becomes fairly diverged from observable reality as well, since it's getting into such things as quantum physics, radical state-based chemistry, and microbiology and the genome.
So if you think that science is a bit messy, I encourage you to look a little farther.
me: Hmm, I disagree. Maths never claims to be founded in reality, and science always tries to be tied to observations - string theory is just waiting for engineering to catch up, the biological sciences are firmly reality-based.
Gregory: Hmm. Only to a certain point of view.
How real is the genome?
Scientists say it is.
They point to how it is expressed.
me: Oh? Deny me.
Even Euclidian geometry doesn't hold in any real space.
Gregory: But the point is that it's a concept which is really only proveable by science, and fairly abstract science at that.
me: It's not proved.
Gregory: Math may not claim to be founded in reality, and may not hold in any real space, but it's just as.... unique to those who pursue it.
me: And I know, as scientists know, that the human genome is probably 0.1% +/- 0.1% wrong.
Gregory: No, it's not properly 'proved.' as you say.
me: I suspect that "unique" isn't a good word - what point were you looking to raise?
Gregory: To get to high-end maths one must be a mathmatician. The abstractions and quite frankly arcane rules governing the setup and execution of high-end maths are really only useable by those who already know what they're doing. An average lay-person can be shown the formulae, the graphs, and the whole shebang but isn't going to follow much beyond recognizing the few numbers actually present and understanding that the whole thing is math.
That same statement may be made about science.
And so, although you see a difference in grounding in reality or not, I think that it's a fairly minor point at the level where it makes a difference.
me: Mathematics is all arcane.
Not quite - I can at least understand the conclusions of something like this monster - [Note: edited out mispaste]
http://www.ncbi.nlm.nih.gov/entrez/quer
There.
Gregory: Really?
Let me try something, then.
Yep, it applies to reality just fine.
2 pens plus 2 pens does in fact still equal 4 pens.
There comes a point in math where reality and math go down the two different paths in the woods, but up to that point math is applicable.
me: I'm going to go out on a limb here and say that the claim that maths applies to reality is science, not maths.
Gregory: Interesting. And quite possibly correct.
But can you dispute that math began as a series of observations with some abstract thought to connect one observed reality with another?
me: Furthermore, this applicability is largely incidental - if you don't listen to the impure lot of applied mathematicians around.
I cannot, but I need not worry about the beginnings of a subject.
Gregory: And what do I need with a paper on tuberculosis mortality as connected with aids?
See, I think you do need to worry about its beginnings.
If only so that I can show you that science began there as well.
And is about as far away from reality in its theoretical gyrations as math is.
It's just that nobody's bothered to remind math that we'll catch up to it one day.
me: Which theoretical gyrations of science are you talking about?
Gregory: Have you looked at quantum physics lately? It's scientists trying to figure out how to make the word "perhaps" scientifically acceptable. They've painted themselves into a theoretical corner where they either have to accept that reality is mutable or back out and try all over again.
And they still don't know what to call light.
People are working on all kinds of base definitions of light and going different places with it.
me: I'm pretty sure your information is a couple of decades out of date. Feel free to show me to be wrong - cite away.
Gregory: It may well be several decades out of date. I never got far enough into quantum physics to find the edge.
But no matter what, the scientists are still out there ahead of reality, trying to figure out what the working system they've created actually implies.
And the great part is it doesn't really matter.
It will have meaning later, but so will the high end maths.
me: Actually, there you are wrong - science tells us the limits of techology, and thus matters.
Gregory: Oh, and math doesn't?
Where, by the way, does computer science fall?
me: Anyway, this is a very interesting digression, but where are we going?
Computer science is pure maths, but you aren't going to find a Turing machine in the known universe.
Gregory: Nope. But anyway, my point is and has been that science and math both view fact as something absolute, but by necessity there is some fuzz in their definition somewhere.
me: I don't think that science does view fact as something absolute. Where do you get that they do?
Gregory: You can't try to prove something without thinking it's an absolute, at least in a specific situation.
me: That's easily answered - science doesn't try.
Gregory: Hmm.
Let's try it a different way. Are there assumptions made in math?
me: What do you mean?
Gregory: Do you, in the course of performing math, make any assumptions?
me: Not really. Assumptions can be used in a) proofs by contradiction and b) contingent approximations.
The former are just assumptionless uses of Excluded Middle, and the latter are constructions of slightly different mathematical systems which are then proven to be reasonably compatible with a main one.
Gregory: Okay. So when you sit down to a proof you start from the beginning. And I mean the very beginning. And work from the beginning of all maths to where you can actually perform the proof, having first proven everything you need to prove the proof?
Gregory: Because otherwise you've made assumptions.
me: Yes.
http://us.metamath.org/mpegif/2p2e4.htm
Here's a proof.
Gregory: Okay, that's good.
me: It's simplified a great deal by theorem citation, but that does not introduce assumptions.
Gregory: No, I agree entirely.
me: Um, so where were we?
Gregory: I'm still beating my head against my desk trying to find a way to get you to see that although you see a large difference between math and science and their respective definitions of 'fact', that there really isn't as much as you'd suspect.
And that it's that very thing which made you and her see each other's definitions as being more assumption and less fact.
me: I'm going to suggest that there is actually that difference as I see.
Gregory: Okay, you see a scientific 'fact' as being an assumption because... why?
me: Science does not and cannot establish definitive positives about reality (What it establishes in its models are undisputably fact, they're just all wrong.) The two main models of science get around this by allowing science to establish things, but running with them as assumptions.
Indisputably, sorry.
Gregory: ...
Interesting.
Gregory: My one problem with all that is this statement: "Science does not and cannot establish definitive positives about reality "
Whether it can or it can't, Math cannot either. You admitted so yourself.
So how does that further your argument that there is a difference between definitions of fact and assumption?
me: I dispute that - while mathematics may not be tied in applicability to reality, it is directly derived from logic, which is innate to reality, and thus is itself true in reality, insofar as it says nothing.
Gregory: Okay, and how is science not innate to reality? Your statement about a direct derivation from logic being an innate tie to reality and by extension true, is a bit suspicious.
me: Science uses models, but those models aren't science.
I said science doesn't give facts.
Gregory: ... Okay, I rather suspect we'll be agreeing to disagree here. Your argument seems circular and quite frankly simply a rejection of what you don't want to hear. Science is only assumptions because it's not tied to reality by pure and ennobling logic and so it can't give facts. Math is a science, Vol. It may have cleaned up its image, but it came from the same place.
me: What do you mean, I'm simply rejecting what I don't want to hear? What have I said that is unsound or irrelevant?
It may well have come from the same place. That doesn't matter. I'm not dismissing science - I'm very interested in it and its philosophy
Gregory: The point of this debate is that (at least from my perspective) both math and the other branches of science do not have any exclusive claim to 'fact.' Assumptions are a part of deriving facts and are necessary to making heads or tails of what is otherwise just a sea of observable data. As far as I can tell, from your perspective math is a sacred endeavor which has a unique claim to truth, justice, and Mom's apple pie (or at least Truth) and assorted sciences are just messy businesses of guessing.
There may be some hyperbole there, but I think you get the drift.
And so my perspective says that what a 'fact' is has no bearing on whether or not it came from a logically supportable series of presumptions based on a definition given by the presumer.
That's all very nice and makes for a good refutation to those who say that your facts aren't so, but a fact does not have to be supported. It just can be.
me: Not exactly - I said nothing about uniqueness on the part of mathematics, for one thing. I claim that mathematics establishes fact. The conclusions are not fact - it's the deductions which are.
Not even supported by observation?
Gregory: What do you mean, not even supported by observation. What is or isn't?
me: You said "... but a fact does not have to be supported. It just can be."
I am definitely not making the [nonsensical claim in my opinion] that everything has a reason.
Gregory: Okay. I didn't say you were, either.
me: Can you respond to my "Not even supported by observation?", then?
Gregory: I'm still not sure what you mean by "Not even supported by observation?"
me: Okay. What is a fact that is not supported by deduction or observation?
Gregory: Hmm. Well, quite probably an unsupported fact. If challenged, it is a weak fact that must be supported, but unless challenged there's no reason to call it anything else.
me: Hmm. I think that is a nonsensical position to hold. How are you defining your facts, and is this definition commonly acceptable?
Gregory: Hmm. Where is the line between fact and assumption, then? I've put it all the way to one side, now where do you move it to?
me: I construct a trichotomy - facts (supported, irrefutable), assumptions (your unchallenged "weak facts") and refuted claims.
Assumptions, to clarify, stand until refuted, not until challenged for support.
Gregory: I divide it further: Fact (irrefutable), fact (supported but disputable), assumptions (reasonable), assumptions (unreasonable, and nonsense.
me: Aha. So in your classification my dividing line goes between your two classes of fact. Can you show yours to be more commonly accepted re: understanding of facts?
Gregory: A claim may be made that is true but not the entire truth. This is not a partial or incorrect fact because the fact itself is true, but there is more to the situation than that one fact displays. Your construction works in general, much like newtonian physics in that it still works fine until you need something more precise.
And my whole point here has been that this is one such situation.
That science has facts which are supported but disputable, a fact with a bit of assumption thrown in.
And math does as well.
me: Maths does? Prove it.
Newtonian mechanics may work fine, but it is wrong in the presence of anything at all. It never applies - not when there's something to apply it to, anyway.
Gregory: Eh. I don't know that I can.
I am no expert on maths.
me: Anyway, I think the issue is one of your more inclusive definition of "fact" - can you show it to be preferable?
Gregory: To a historian this is not just preferable but necessary.
And as far as science goes...I think it should still holed.
hold, rather.
me: Necessary? Science talks about observations (facts, irrefutable) and theories (assumptions, reasonable).
Gregory: Medical science works on the basis of facts which are supported but disputable, this is why we have multiple treatment options.
me: Actually, no. It works on the basis of facts which are supported and indisputable - and the (again, supported and indisputable) probabilistic information resulting.
me: http://scienceblogs.com/interactions/20
This is an example. If you give me a month or so I'll have a handful of books to cite when I get back to my university.
Gregory: Okay.
Well, I need to be dressing and heading on to class anyway.
me: That was an interesting conversation.
Gregory: Yes, it was.
me: I think I maintained consistency throughout.
Gregory: Mm.
me: Well, later! Mind if I post this conversation up, by the way?
Gregory: Not at all.
me: Okay!
I'm ignorant, and would appreciate correction - though often it might be easier and more helpful to cite something which corrects me (I've found a few myself that I'll look up when I get back, but more don't hurt.).
me: Hello.
Gregory: Hello, Vol.
me: How are you?
Do you know much about philosophy of mathematics or science? I don't.
Gregory: I'm fairly well. Life has been keeping me incredibly busy by throwing opportunities into my path that I have been 'carpe'-ing as best as I can.
And about the philosophy of mathematics and science... that sounds a lot like late 18th and early 19th century science.
When scientists were called 'natural philosophers'
and science was seen as some way of trying to discern a set of natural laws through reason.
me: I had a rather frustrating conversation, and on further thought I'd like a critique of my own statements, at least a few of which were probably suspect.
Gregory: Okay.
I don't have to be out of here for about 2 hours, and so long as I get a bit more reading done at some point in there I can do other stuff too.
That's the advantage to getting up early, really.
me: Okay, thanks!
Gregory: Hmm. Interesting claim there, midway through.
Your debatee says that he prefers facts over assumptions and therefore wouldn't like philosophy.
I think his definition of 'fact' is rather different than yours.
me: Her - please, tell me more.
Gregory: Ah. Excuse me. Her definition.
Well, you say that maths would be better than chemistry as far as accumulation of fact goes.
She responds with the claim that experimentation leads to fact and so chemistry isn't so fact-free as one might think.
This means, at least to me, that she's an empiricist. A fact is what can be reasonably assumed with some degree of evidentiary burden of proof for backup.
Not just a mathematical absolute proven by equations and formulae.
And my assumption is backed up by the ensuing argument about maths.
Your statement of fact is one of a philosopher, by the way.
No necessary absolute truth.
Just state a claim, and then proceed from that claim on unquestionable ground, and you end up with fact.
Which, if you think about it, is basically the exact same thing as an experiment.
You start with an idea, neither fact nor fiction, and then proceed through unquestionable ground via experimentation to a conclusion about the fact/fiction relationship of the idea to the world.
me: I don't think your parallel holds.
Gregory: No?
me: No.
At least, her "unquestionable" conclusions are very weak - along the lines of "No experiment to date has shown that gravitational attraction is not proportional to the masses involved."
Gregory: Mm. Well, let me keep reading, then.
I'm offering comment as I go through and pausing to do so.
me: Thank you.
I may well misstep - please point out such problems.
Gregory: Right. Well, on the basis of the first conversation I think that you and she are looking at fact in slightly different ways based on what it is that you end up doing.
One of the reasons why I say this is because I view fact as something else from either of you, and I suspect it's because my discipline of choice is history.
Your definition of fact is what she labels 'assumptions.' We can take that as understood, since there would not be the argument about facts otherwise.
me: Curiously enough, what she calls facts are what I'd label assumptions.
Gregory: Yep.
That's about the size of it.
And I think my point here is going to be that what you two are looking at are the same thing. By virtue of the nature of maths and science both it is necessary that what you call fact be an assumption of some sort.
Now whether it can or can't be fact and assumption at the same time, I don't think I can say.
But that your facts be at least in some part assumption... that I think I can say.
me: I don't think so - maths says nothing that isn't a contingent tautology.
Gregory: Mm.
And that's where you and she part company in the debate.
See, a 'contigent tautology' can quite easily be seen as in some part assumption.
me: How so?
Gregory: You said "With maths I define the things I'm
dealing with, and my conclusions are necessarily true by virtue of
being tautologous."
The key point there is that you definine what you're going to start with and go from there.,
Yes, the conclusion holds formation with that which comes before it.
me: Hmm, I should take that back and set up a better logical model.
Gregory: But that doesn't mean that your initial definitions are guaranteed to produce a fact in line with the natural model.
me: In fact, I do.
Mathematics is the subject of considering the contingent conclusions arising in certain arbitrary axiom systems.
Gregory: Hmm. Perhaps. Though I still think that the boundry between scientific experimentation and logical progression of thought is a very small and blurry thing.
Here's a question for you:
From your point of view, where does an experiment diverge from an abstract construct of logic?
Is there any reason why I can't say that logic is just an experiment conducted entirely in someone's head or on paper?
me: Hmm, I've seen two formalisations of scientific thought. One is probabilistic, the other is completely assumption-based.
There isn't - gedankenexperimente exist. I think the distinction is in the conclusions of the experiments and their motivation. Maths has no concern with reality.
Gregory: You are so right. Maths does have no concern with reality. But I digress, tongue firmly in cheek. Back to the discussion.
Gregory: I think that if you look at it, the point where maths truly becomes a realm apart from reality is a fairly high-end area. And at that point, science becomes fairly diverged from observable reality as well, since it's getting into such things as quantum physics, radical state-based chemistry, and microbiology and the genome.
So if you think that science is a bit messy, I encourage you to look a little farther.
me: Hmm, I disagree. Maths never claims to be founded in reality, and science always tries to be tied to observations - string theory is just waiting for engineering to catch up, the biological sciences are firmly reality-based.
Gregory: Hmm. Only to a certain point of view.
How real is the genome?
Scientists say it is.
They point to how it is expressed.
me: Oh? Deny me.
Even Euclidian geometry doesn't hold in any real space.
Gregory: But the point is that it's a concept which is really only proveable by science, and fairly abstract science at that.
me: It's not proved.
Gregory: Math may not claim to be founded in reality, and may not hold in any real space, but it's just as.... unique to those who pursue it.
me: And I know, as scientists know, that the human genome is probably 0.1% +/- 0.1% wrong.
Gregory: No, it's not properly 'proved.' as you say.
me: I suspect that "unique" isn't a good word - what point were you looking to raise?
Gregory: To get to high-end maths one must be a mathmatician. The abstractions and quite frankly arcane rules governing the setup and execution of high-end maths are really only useable by those who already know what they're doing. An average lay-person can be shown the formulae, the graphs, and the whole shebang but isn't going to follow much beyond recognizing the few numbers actually present and understanding that the whole thing is math.
That same statement may be made about science.
And so, although you see a difference in grounding in reality or not, I think that it's a fairly minor point at the level where it makes a difference.
me: Mathematics is all arcane.
Not quite - I can at least understand the conclusions of something like this monster - [Note: edited out mispaste]
http://www.ncbi.nlm.nih.gov/entrez/quer
There.
Gregory: Really?
Let me try something, then.
Yep, it applies to reality just fine.
2 pens plus 2 pens does in fact still equal 4 pens.
There comes a point in math where reality and math go down the two different paths in the woods, but up to that point math is applicable.
me: I'm going to go out on a limb here and say that the claim that maths applies to reality is science, not maths.
Gregory: Interesting. And quite possibly correct.
But can you dispute that math began as a series of observations with some abstract thought to connect one observed reality with another?
me: Furthermore, this applicability is largely incidental - if you don't listen to the impure lot of applied mathematicians around.
I cannot, but I need not worry about the beginnings of a subject.
Gregory: And what do I need with a paper on tuberculosis mortality as connected with aids?
See, I think you do need to worry about its beginnings.
If only so that I can show you that science began there as well.
And is about as far away from reality in its theoretical gyrations as math is.
It's just that nobody's bothered to remind math that we'll catch up to it one day.
me: Which theoretical gyrations of science are you talking about?
Gregory: Have you looked at quantum physics lately? It's scientists trying to figure out how to make the word "perhaps" scientifically acceptable. They've painted themselves into a theoretical corner where they either have to accept that reality is mutable or back out and try all over again.
And they still don't know what to call light.
People are working on all kinds of base definitions of light and going different places with it.
me: I'm pretty sure your information is a couple of decades out of date. Feel free to show me to be wrong - cite away.
Gregory: It may well be several decades out of date. I never got far enough into quantum physics to find the edge.
But no matter what, the scientists are still out there ahead of reality, trying to figure out what the working system they've created actually implies.
And the great part is it doesn't really matter.
It will have meaning later, but so will the high end maths.
me: Actually, there you are wrong - science tells us the limits of techology, and thus matters.
Gregory: Oh, and math doesn't?
Where, by the way, does computer science fall?
me: Anyway, this is a very interesting digression, but where are we going?
Computer science is pure maths, but you aren't going to find a Turing machine in the known universe.
Gregory: Nope. But anyway, my point is and has been that science and math both view fact as something absolute, but by necessity there is some fuzz in their definition somewhere.
me: I don't think that science does view fact as something absolute. Where do you get that they do?
Gregory: You can't try to prove something without thinking it's an absolute, at least in a specific situation.
me: That's easily answered - science doesn't try.
Gregory: Hmm.
Let's try it a different way. Are there assumptions made in math?
me: What do you mean?
Gregory: Do you, in the course of performing math, make any assumptions?
me: Not really. Assumptions can be used in a) proofs by contradiction and b) contingent approximations.
The former are just assumptionless uses of Excluded Middle, and the latter are constructions of slightly different mathematical systems which are then proven to be reasonably compatible with a main one.
Gregory: Okay. So when you sit down to a proof you start from the beginning. And I mean the very beginning. And work from the beginning of all maths to where you can actually perform the proof, having first proven everything you need to prove the proof?
Gregory: Because otherwise you've made assumptions.
me: Yes.
http://us.metamath.org/mpegif/2p2e4.htm
Here's a proof.
Gregory: Okay, that's good.
me: It's simplified a great deal by theorem citation, but that does not introduce assumptions.
Gregory: No, I agree entirely.
me: Um, so where were we?
Gregory: I'm still beating my head against my desk trying to find a way to get you to see that although you see a large difference between math and science and their respective definitions of 'fact', that there really isn't as much as you'd suspect.
And that it's that very thing which made you and her see each other's definitions as being more assumption and less fact.
me: I'm going to suggest that there is actually that difference as I see.
Gregory: Okay, you see a scientific 'fact' as being an assumption because... why?
me: Science does not and cannot establish definitive positives about reality (What it establishes in its models are undisputably fact, they're just all wrong.) The two main models of science get around this by allowing science to establish things, but running with them as assumptions.
Indisputably, sorry.
Gregory: ...
Interesting.
Gregory: My one problem with all that is this statement: "Science does not and cannot establish definitive positives about reality "
Whether it can or it can't, Math cannot either. You admitted so yourself.
So how does that further your argument that there is a difference between definitions of fact and assumption?
me: I dispute that - while mathematics may not be tied in applicability to reality, it is directly derived from logic, which is innate to reality, and thus is itself true in reality, insofar as it says nothing.
Gregory: Okay, and how is science not innate to reality? Your statement about a direct derivation from logic being an innate tie to reality and by extension true, is a bit suspicious.
me: Science uses models, but those models aren't science.
I said science doesn't give facts.
Gregory: ... Okay, I rather suspect we'll be agreeing to disagree here. Your argument seems circular and quite frankly simply a rejection of what you don't want to hear. Science is only assumptions because it's not tied to reality by pure and ennobling logic and so it can't give facts. Math is a science, Vol. It may have cleaned up its image, but it came from the same place.
me: What do you mean, I'm simply rejecting what I don't want to hear? What have I said that is unsound or irrelevant?
It may well have come from the same place. That doesn't matter. I'm not dismissing science - I'm very interested in it and its philosophy
Gregory: The point of this debate is that (at least from my perspective) both math and the other branches of science do not have any exclusive claim to 'fact.' Assumptions are a part of deriving facts and are necessary to making heads or tails of what is otherwise just a sea of observable data. As far as I can tell, from your perspective math is a sacred endeavor which has a unique claim to truth, justice, and Mom's apple pie (or at least Truth) and assorted sciences are just messy businesses of guessing.
There may be some hyperbole there, but I think you get the drift.
And so my perspective says that what a 'fact' is has no bearing on whether or not it came from a logically supportable series of presumptions based on a definition given by the presumer.
That's all very nice and makes for a good refutation to those who say that your facts aren't so, but a fact does not have to be supported. It just can be.
me: Not exactly - I said nothing about uniqueness on the part of mathematics, for one thing. I claim that mathematics establishes fact. The conclusions are not fact - it's the deductions which are.
Not even supported by observation?
Gregory: What do you mean, not even supported by observation. What is or isn't?
me: You said "... but a fact does not have to be supported. It just can be."
I am definitely not making the [nonsensical claim in my opinion] that everything has a reason.
Gregory: Okay. I didn't say you were, either.
me: Can you respond to my "Not even supported by observation?", then?
Gregory: I'm still not sure what you mean by "Not even supported by observation?"
me: Okay. What is a fact that is not supported by deduction or observation?
Gregory: Hmm. Well, quite probably an unsupported fact. If challenged, it is a weak fact that must be supported, but unless challenged there's no reason to call it anything else.
me: Hmm. I think that is a nonsensical position to hold. How are you defining your facts, and is this definition commonly acceptable?
Gregory: Hmm. Where is the line between fact and assumption, then? I've put it all the way to one side, now where do you move it to?
me: I construct a trichotomy - facts (supported, irrefutable), assumptions (your unchallenged "weak facts") and refuted claims.
Assumptions, to clarify, stand until refuted, not until challenged for support.
Gregory: I divide it further: Fact (irrefutable), fact (supported but disputable), assumptions (reasonable), assumptions (unreasonable, and nonsense.
me: Aha. So in your classification my dividing line goes between your two classes of fact. Can you show yours to be more commonly accepted re: understanding of facts?
Gregory: A claim may be made that is true but not the entire truth. This is not a partial or incorrect fact because the fact itself is true, but there is more to the situation than that one fact displays. Your construction works in general, much like newtonian physics in that it still works fine until you need something more precise.
And my whole point here has been that this is one such situation.
That science has facts which are supported but disputable, a fact with a bit of assumption thrown in.
And math does as well.
me: Maths does? Prove it.
Newtonian mechanics may work fine, but it is wrong in the presence of anything at all. It never applies - not when there's something to apply it to, anyway.
Gregory: Eh. I don't know that I can.
I am no expert on maths.
me: Anyway, I think the issue is one of your more inclusive definition of "fact" - can you show it to be preferable?
Gregory: To a historian this is not just preferable but necessary.
And as far as science goes...I think it should still holed.
hold, rather.
me: Necessary? Science talks about observations (facts, irrefutable) and theories (assumptions, reasonable).
Gregory: Medical science works on the basis of facts which are supported but disputable, this is why we have multiple treatment options.
me: Actually, no. It works on the basis of facts which are supported and indisputable - and the (again, supported and indisputable) probabilistic information resulting.
me: http://scienceblogs.com/interactions/20
This is an example. If you give me a month or so I'll have a handful of books to cite when I get back to my university.
Gregory: Okay.
Well, I need to be dressing and heading on to class anyway.
me: That was an interesting conversation.
Gregory: Yes, it was.
me: I think I maintained consistency throughout.
Gregory: Mm.
me: Well, later! Mind if I post this conversation up, by the way?
Gregory: Not at all.
me: Okay!
