JeffTheLearner's challenge
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- Start date
Water,
It feels to me that time is a neccessary tenet for anyting to have ever existed, even gods. It is not so much a perception as it is an abolute neccessity without which nothing makes sense.
Even if you were to say that to a god everything appears to occur at the same instant - even then isn't that single instant an example of time? One simply cannot refer to anything occurring if time is not involved.
Perhaps, but can you propose a scenario where something can occur without the passage of time? If there is a change of state of anything from one instant to the next then time will have passed, otherwise the very meaning of an "event" is nonsense, nothing could occur.
It feels to me that time is a neccessary tenet for anyting to have ever existed, even gods. It is not so much a perception as it is an abolute neccessity without which nothing makes sense.
Even if you were to say that to a god everything appears to occur at the same instant - even then isn't that single instant an example of time? One simply cannot refer to anything occurring if time is not involved.
Water,
Proof that 1+1=2
The proof starts from the Peano Postulates, which define the natural
numbers N. N is the smallest set satisfying these postulates:
P1. 1 is in N.
P2. If x is in N, then its "successor" x' is in N.
P3. There is no x such that x' = 1.
P4. If x isn't 1, then there is a y in N such that y' = x.
P5. If S is a subset of N, 1 is in S, and the implication
(x in S => x' in S) holds, then S = N.
Then you have to define addition recursively:
Def: Let a and b be in N. If b = 1, then define a + b = a'
(using P1 and P2). If b isn't 1, then let c' = b, with c in N
(using P4), and define a + b = (a + c)'.
Then you have to define 2:
Def: 2 = 1'
2 is in N by P1, P2, and the definition of 2.
Theorem: 1 + 1 = 2
Proof: Use the first part of the definition of + with a = b = 1.
Then 1 + 1 = 1' = 2 Q.E.D.
Note: There is an alternate formulation of the Peano Postulates which
replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the
definition of addition to this:
Def: Let a and b be in N. If b = 0, then define a + b = a.
If b isn't 0, then let c' = b, with c in N, and define
a + b = (a + c)'.
You also have to define 1 = 0', and 2 = 1'. Then the proof of the
Theorem above is a little different:
Proof: Use the second part of the definition of + first:
1 + 1 = (1 + 0)'
Now use the first part of the definition of + on the sum in
parentheses: 1 + 1 = (1)' = 1' = 2 Q.E.D.
Hope you follow that OK.
Cris
Proof that 1+1=2
The proof starts from the Peano Postulates, which define the natural
numbers N. N is the smallest set satisfying these postulates:
P1. 1 is in N.
P2. If x is in N, then its "successor" x' is in N.
P3. There is no x such that x' = 1.
P4. If x isn't 1, then there is a y in N such that y' = x.
P5. If S is a subset of N, 1 is in S, and the implication
(x in S => x' in S) holds, then S = N.
Then you have to define addition recursively:
Def: Let a and b be in N. If b = 1, then define a + b = a'
(using P1 and P2). If b isn't 1, then let c' = b, with c in N
(using P4), and define a + b = (a + c)'.
Then you have to define 2:
Def: 2 = 1'
2 is in N by P1, P2, and the definition of 2.
Theorem: 1 + 1 = 2
Proof: Use the first part of the definition of + with a = b = 1.
Then 1 + 1 = 1' = 2 Q.E.D.
Note: There is an alternate formulation of the Peano Postulates which
replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the
definition of addition to this:
Def: Let a and b be in N. If b = 0, then define a + b = a.
If b isn't 0, then let c' = b, with c in N, and define
a + b = (a + c)'.
You also have to define 1 = 0', and 2 = 1'. Then the proof of the
Theorem above is a little different:
Proof: Use the second part of the definition of + first:
1 + 1 = (1 + 0)'
Now use the first part of the definition of + on the sum in
parentheses: 1 + 1 = (1)' = 1' = 2 Q.E.D.
Hope you follow that OK.
Cris
Let us go to advanced math :
1 + 1 = 1
1 piece of clay + 1 piece of clay = 2 pieces of clay
I fuse the 2 pieces of clay together in my hand to = 1 piece of clay
1 + 1 = 1
1 + 1 = 3
1 woman + 1 man = 2 humans
they get a baby, which means they are now = 3 humans
1 + 1= 3
Sorry , just teasing ...............please don´t be offended ....
1 + 1 = 1
1 piece of clay + 1 piece of clay = 2 pieces of clay
I fuse the 2 pieces of clay together in my hand to = 1 piece of clay
1 + 1 = 1
1 + 1 = 3
1 woman + 1 man = 2 humans
they get a baby, which means they are now = 3 humans
1 + 1= 3
Sorry , just teasing ...............please don´t be offended ....
Cris said:
I don't know, but I don't just assume that human perception is all there is.
Not to make an ad ignorantiam, but since humans keep on finding new things, new theories, I am skeptical of positing the present understanding of causality and time to be ultimate.
It is a perception still -- you perceive time as an absolute necessity without which nothing makes sense.
And the criteria for making sense is your present understanding -- which may drastically change when new insights come (if you allow for them).
If we consider ourselves bound by time, in time, then I think we are not competent to make predictions about how an entity that is not bound by time would regard time.
If you firmly believe so, then so it is!
Water,
Well, no I don't, but I can't perceive a meaningful alternative. While we can glibly talk of something existing outside of time, just what does that mean? The nature of everything we understand and can define rests on time being present. While I can imagine how gods might exist I cannot perceive of a condition where time would not exist. It defies definition of any type as far as I can see. So I would genuinely like to see someone show otherwise.