Peter Soderqvist
Critical Thinker
- Joined
- Nov 29, 2001
- Messages
- 305
Re: Re: 1 + 1 = 2
Soderqvist1: abstract units are undefined terms, which have no content! Bricks, mud, cats are labels for concrete objects in our empirical world! Inconsistent system is not system P! I alleging that Principia Mathematica and related systems are essentially incomplete, but truth according to the premises Kurt Godel proposed in Königsberg 1931, and that truth doesn't change with time! Do you alleging otherwise?
new drkitten said:Yes. For example, if I have a lump of mud and stick another lump of mud to it, I don't have two lumps of mud; I have a single, larger, lump of mud. (If you don't like mud, I can do the same thing with a lump of peanut butter.)
If I have a cold room and I add a space heater to it, I get a warm room. If I add another space heater to it, I don't get two warm rooms -- or even necessarily a warmer room.
If I have one happy cat on my lap, and someone adds another happy cat on my lap, I probably now have zero[ happy cats.
And if I have a cup of water and I add a cup of alcohol to it, the resulting solution isn't two cups of liquid.
Of course, if I have a brick and add another brick to it, that does indeed make two bricks.
But why should our hypothetical "abtract units" be defined to -- or indeed, self-evidently have the properties of bricks, instead of lumps of mud or happy cats?
Yes, that proposition is sometimes incorrect. For example, I can develop an inconsistent system where the Godel sentence for that system is not even expressible within the system, and therefore not provable.
Soderqvist1: abstract units are undefined terms, which have no content! Bricks, mud, cats are labels for concrete objects in our empirical world! Inconsistent system is not system P! I alleging that Principia Mathematica and related systems are essentially incomplete, but truth according to the premises Kurt Godel proposed in Königsberg 1931, and that truth doesn't change with time! Do you alleging otherwise?