Freethought & Rationalism ArchiveThe archives are read only. |
05-14-2003, 09:03 PM | #221 | ||
Junior Member
Join Date: Apr 2003
Location: Florida, USA
Posts: 69
|
Quote:
Where did you come up with the flower analogy? You had to realize how weak and unrelated that was as you were typing it. If beauty is truth, then yes, the flower contrived its own beauty, through its ability to attract pollinators better than they less beautiful flowers, in the population of these flowers you mention. How on earth would hypotheses back up my statements? Well, you gave us a bit of insight by stating that God cannot be judged objectively. I'll chew on that tonight. Quote:
Going to bed, pick this up tomorrow, if the thread survives. Tenspace |
||
05-14-2003, 09:12 PM | #222 | |
Veteran Member
Join Date: Apr 2003
Posts: 2,199
|
Quote:
|
|
05-14-2003, 09:13 PM | #223 | |
Senior Member
Join Date: Feb 2003
Location: San Diego, California
Posts: 719
|
Quote:
|
|
05-14-2003, 09:17 PM | #224 | |
Senior Member
Join Date: Feb 2003
Location: San Diego, California
Posts: 719
|
Quote:
For example, I could say "let x = 5." Asking one to prove an axiom would be like asking me to prove that x = 5. It's simply a nonsense request. |
|
05-14-2003, 09:25 PM | #225 | |
Moderator - Science Discussions
Join Date: Feb 2001
Location: Providence, RI, USA
Posts: 9,908
|
Quote:
4*2: **** **** 2*4: ** ** ** ** |
|
05-14-2003, 09:37 PM | #226 |
Senior Member
Join Date: Feb 2003
Location: San Diego, California
Posts: 719
|
As far as I know I'm not advocating a purely axiomatic approach to arithmetic. I'm simply saying that the axioms present in arithmetic are defined as the truth and the arithmetic universe is constructed from them. The only requirement is that these axioms do not lead to inconsistencies. I'm not saying you can define any axioms you want, for if they conflict then your universe will be quite poorly designed (perhaps it would be fair to call it unstable?). I'm just saying that questioning the validity of axioms that survive the model of which you speak is meaningless within the universe for which they are axiomatic. Or am I still misunderstanding what you're trying to say?
|
05-14-2003, 10:12 PM | #227 |
Moderator - Science Discussions
Join Date: Feb 2001
Location: Providence, RI, USA
Posts: 9,908
|
I'm saying that we can see the axioms of arithmetic are consistent because we have a mental model of what the various symbols "mean", and that when we say "1+1=2 is true" we are referring to this mental model, not just saying "the statement '1+1=2' is provable using the axioms of peano arithmetic". Likewise, we can see the Godel statement G for peano arithmetic is a true statement about our mental model of arithmetic, even if it's not provably true or false within the axiomatic system itself.
"1+1=2" is true by definition within a particular axiomatic system which we use to represent part of our mental model of arithmetic. But in the context of the mental model itself, "1+1=2" is not true by definition, any more than the Godel statement G for peano arithmetic is true by definition. But we know both statements must be true if the symbols correspond to the elements of our mental model (for example, the symbol "+" corresponds to our mental idea of addition). |
05-14-2003, 10:41 PM | #228 | |
Veteran Member
Join Date: Feb 2002
Location: Tokyo
Posts: 1,126
|
Quote:
So no change there, then. |
|
05-15-2003, 08:13 AM | #229 | |||||
Veteran Member
Join Date: Apr 2003
Posts: 2,199
|
Quote:
Quote:
Quote:
Quote:
Quote:
|
|||||
05-15-2003, 08:25 AM | #230 | ||
Veteran Member
Join Date: Apr 2003
Posts: 2,199
|
Quote:
Quote:
|
||
Thread Tools | Search this Thread |
|