about maths: strictly speaking, off topic, but justified.
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From: rabid_fan on 17 Mar 2010 11:59 On Wed, 17 Mar 2010 15:40:57 +0000, rabid_fan wrote: >> > Yes, it is. Mathematics is a formal system, which contains symbols, a > grammar, a set of axioms, and inference rules. Logic is the process by > which the whole thing proceeds from axioms and inferences to statements, > based on the grammar, and theorems. "Verbs" are to be construed as the > assertions made regrading any of the objects, as they are in ordinary > language. > > But actually, the statement that "mathematics is a language" is being > used a bit more loosely, I would think, in this discussion. > Mathematics, like language, is used to convey meaning about the world, > and mathematical objects, like the objects of language, are used as a > basis for thought and conjecture. Oops! I didn't finish. Although we may using the statement "mathematics is a language" in sort of a loose manner, mathematics certainly does contain all of the elements of a formal language or formal system.
From: J. Clarke on 17 Mar 2010 13:54 On 3/17/2010 11:59 AM, rabid_fan wrote: > On Wed, 17 Mar 2010 15:40:57 +0000, rabid_fan wrote: > >>> >> Yes, it is. Mathematics is a formal system, which contains symbols, a >> grammar, a set of axioms, and inference rules. Logic is the process by >> which the whole thing proceeds from axioms and inferences to statements, >> based on the grammar, and theorems. "Verbs" are to be construed as the >> assertions made regrading any of the objects, as they are in ordinary >> language. >> >> But actually, the statement that "mathematics is a language" is being >> used a bit more loosely, I would think, in this discussion. >> Mathematics, like language, is used to convey meaning about the world, >> and mathematical objects, like the objects of language, are used as a >> basis for thought and conjecture. > > Oops! I didn't finish. > > Although we may using the statement "mathematics is a language" > in sort of a loose manner, mathematics certainly does contain all > of the elements of a formal language or formal system. And that makes it "logic" how exactly?
From: rabid_fan on 17 Mar 2010 15:51 On Wed, 17 Mar 2010 13:54:39 -0400, J. Clarke wrote: > > And that makes it "logic" how exactly? > Because mathematics does not exist when one is on LSD.
From: J. Clarke on 17 Mar 2010 20:36 On 3/17/2010 3:51 PM, rabid_fan wrote: > On Wed, 17 Mar 2010 13:54:39 -0400, J. Clarke wrote: > >> >> And that makes it "logic" how exactly? >> > > Because mathematics does not exist when one is on LSD. So?
From: rabid_fan on 17 Mar 2010 21:20
On Wed, 17 Mar 2010 20:36:38 -0400, J. Clarke wrote: > > So? > For a New York City dweller, the only way to know New York City is to know what is not New York City. The only way to know logic is to know what is not logic (i.e. to know illogic). Therefore, drop some acid (LSD). Happy trails, and please file a report when you return. |