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Author Topic:   The use of logic in establishing truths
crashfrog
Member (Idle past 1466 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 73 of 171 (438994)
12-07-2007 12:26 AM
Reply to: Message 69 by LucyTheApe
12-06-2007 11:16 PM


Re: Down with Logic
Euclid was a brilliant Scientist.
Euclid was a mathematician, to be precise.
Number 1: Any two points can be joined by a straight line.
They can't. There is no such thing as a straight line: Space is subject to distortion.
2. False.
3. False.
4. True.
5. False(it can be disproved)
Whether or not Euclid's postulates are true about the world we actually inhabit is not actually relevant to geometry. They're defined as true, assumed to be true; that's what it means to be an "axiom." They're taken as true without actually having to be true. The conclusions that are drawn from them (say, that the sum of the angles of a triangle will equal 180 degrees) are only true insofar as you've already accepted the axioms.
If, as non-Euclidian geometers do, you reject the fifth postulate and substitute a different axiom, you can prove that the sum of the angles of a triangle will exceed 180 degrees.
Neither conclusion is any "more right" than the other. They're both right - depending on what axioms you start with. That's why axioms are of so little use to science.
Evolution requires it's own axiom.
Not so. Evolution is not based on axioms; like all good science, it's based on observation and experimentation.

This message is a reply to:
 Message 69 by LucyTheApe, posted 12-06-2007 11:16 PM LucyTheApe has replied

Replies to this message:
 Message 75 by Dawn Bertot, posted 12-07-2007 12:55 AM crashfrog has replied
 Message 78 by LucyTheApe, posted 12-07-2007 4:07 AM crashfrog has replied
 Message 79 by LucyTheApe, posted 12-07-2007 4:45 AM crashfrog has not replied

  
crashfrog
Member (Idle past 1466 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 102 of 171 (439093)
12-07-2007 10:56 AM
Reply to: Message 75 by Dawn Bertot
12-07-2007 12:55 AM


Re: Down with Logic
Something cannot be taken as true, if it can be shown, to be not true.
But that's what an axiom means. It means we accept it as true, for purposes of argument, without testing or confirming it.
If you test or confirm it, then it's not an axiom, it's a conclusion. Accepting Euclid's fifth axiom as true defines one kind of geometry. Accepting a contradictory postulate as fifth axiom instead defines a completely different kind of geometry that is every bit as valid as the first kind.
Euclid's fifth axiom is the perfect example of an axiom - it's accepted as true for no other reason but to define what conclusions you're going to be able to make. If you want to operate in a geometric system where the sum of the angles of a triangle equal 180 degrees, then you assume Euclid's fifth postulate as axiomatic. There's no other reason to. As Lucy has pointed out, Euclid's fifth isn't actually true in the universe we inhabit. It's certainly not true on Planet Earth (which has elliptic geometry, because we live on the surface of a sphere.)
The axioms that apply to these mathmatical processes may or may not be true depending on the accuracy of the mathmatical premises.
They are the premises. Axioms are the foundational premises of all mathematical reasoning. Every premise that isn't axiomatic can be proven through a series of transformations back to other premises, but eventually you get to a series of premises that can't be proven - that you just have to assume are true for purposes of argument.
Those are axioms. They're what we assume to be true, for no other reason than to get mathematics off the ground.
However, axioms that apply to the real world are testable and at times can be demonstrated completely accurate, with no fear of contradiction.
There are no axioms in the real world. There are only conclusions we have derived from evidence and testing, and those are always tentative and provisional. The "complete accuracy" you refer to is a feature of axiomatic reasoning like mathematics, but it doesn't exist in empirical science.

This message is a reply to:
 Message 75 by Dawn Bertot, posted 12-07-2007 12:55 AM Dawn Bertot has not replied

  
crashfrog
Member (Idle past 1466 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 103 of 171 (439094)
12-07-2007 10:58 AM
Reply to: Message 78 by LucyTheApe
12-07-2007 4:07 AM


Re: Down with Logic
Natural Scientists will
never
hijack science.
Too late. We hijacked it a millennium ago. "Science" refers to that body of knowledge gathered by the scientific method, which is inductive, empirical, and provisional.
Mathematics simply doesn't apply. It's deductive, axiomatic, and absolute. Mathematicians are not scientists; they're mathematicians. (Or, at worst, philosophers. I give most mathematicians more credit than that.)

This message is a reply to:
 Message 78 by LucyTheApe, posted 12-07-2007 4:07 AM LucyTheApe has replied

Replies to this message:
 Message 111 by LucyTheApe, posted 12-07-2007 12:36 PM crashfrog has replied

  
crashfrog
Member (Idle past 1466 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 113 of 171 (439168)
12-07-2007 2:59 PM
Reply to: Message 111 by LucyTheApe
12-07-2007 12:36 PM


Re: Down with Logic
Not while my blood is still warm!
Not what? I don't see anything in my post that you've refuted with the dictionary. Mathematics is mathematics, not science.
What was your point because this has been dragging on for so long your just giving everyone more reason to take the piss.
My point was Euclid's fifth postulate; it's an axiom that is accepted not because its true or false; you choose whether or accept it or not to determine what kind of geometry you'll be doing.
It's like all axioms in that regard. They form the basis of formal systems, but moreover, they're selected to form the basis of formal systems, for purposes of argument. They may or may not be true statements about the world we inhabit, but their acceptance as axiomatic has almost nothing to do with their truth. They're assumed to be true, without justification, except insofar as they're justified by how useful or interesting a formal system they establish.

This message is a reply to:
 Message 111 by LucyTheApe, posted 12-07-2007 12:36 PM LucyTheApe has not replied

  
crashfrog
Member (Idle past 1466 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 123 of 171 (439278)
12-08-2007 1:37 AM
Reply to: Message 122 by LucyTheApe
12-08-2007 1:32 AM


Re: Observation/Truth
Both fail miserably in being axiomatic.
Random mutation isn't an axiom, it's a conclusion from observation and experiment. Surely you realize that?

This message is a reply to:
 Message 122 by LucyTheApe, posted 12-08-2007 1:32 AM LucyTheApe has replied

Replies to this message:
 Message 125 by LucyTheApe, posted 12-08-2007 3:42 AM crashfrog has replied

  
crashfrog
Member (Idle past 1466 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 152 of 171 (439467)
12-08-2007 9:25 PM
Reply to: Message 125 by LucyTheApe
12-08-2007 3:42 AM


Re: Observation/Truth
Ooops- off-topic.
Edited by crashfrog, : No reason given.

This message is a reply to:
 Message 125 by LucyTheApe, posted 12-08-2007 3:42 AM LucyTheApe has not replied

  
crashfrog
Member (Idle past 1466 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 162 of 171 (439969)
12-11-2007 1:23 AM
Reply to: Message 161 by LucyTheApe
12-11-2007 1:05 AM


Half-assed quantum stuff by Crash
I'll tell you why I think you're wrong about the randomness stuff, and someone who actually knows physics can correct me where I'm drawing faulty conclusions.
If we know enough about the physics governing the decay of Radium then we can write an algorithm describing it.
According to Bell's Inequality, no, actually, you can't. Atomic decay is random - randomwoc in your terminology - and it can't accurately be described as a function of "local hidden variables."
That is, given a number of radium atoms, you can determine statistically how many of them will have decayed over a given time, but there's no mathematical model you can create - using "hidden local variables", in this case, the idea that atoms have little individual timers that "go off" when it's time for them to decay - that will accurately predict which atoms have decayed, because it isn't deterministic in that way. In other words Bell's Inequality proves that various apparently random quantum behavior is actually random; it's not just pseudorandom output of an unknown, deterministic function.
Nonetheless, all this is essentially irrelevant to evolution. Darwin's model is that individuals are born with variances in physical characteristics, regardless of what adaptations are advantageous; then, over the course of their lifetimes, individuals with characteristics that are better-suited to the environment experience greater reproductive success than those individuals who are not as well-suited.
This is opposed to Lamark's model, where individuals are born largely the same among a cohort group, and then individuals acquire characteristics throughout their lifetimes which they then pass on to their offspring; as well as opposed to special creation, which contends that organisms were created by God exactly as they now are, and have not changed throughout their species lifetime.
It's an objective fact that Darwin's model is substantially better supported than either of the other two. And with the rise of molecular analysis techniques we've come to learn why individuals vary amongst themselves and from their parents: random mutations of their genetics.
Edited by crashfrog, : No reason given.

This message is a reply to:
 Message 161 by LucyTheApe, posted 12-11-2007 1:05 AM LucyTheApe has replied

Replies to this message:
 Message 163 by LucyTheApe, posted 12-11-2007 5:41 AM crashfrog has not replied

  
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