Re: Epistemology 201: The Science of Science

From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 02/07/05 

Date: Mon, 07 Feb 2005 15:28:52 GMT

On Sun, 06 Feb 2005 13:51:41 +1300, Jason
<jasonstevensNOSPAM@free.net.nz> in comp.ai.philosophy wrote:

>>>Not at all. I would say that mathematics includes set theory, which is
>>>an extension of logic. When proofs in set theory are performed, they
>>>are not at odds with its formal system. I'm arguing that all valid
>>>mathematical proofs are in accordance with one formal system or another,
>>
>>
>> Okay. But is there a formal system to formal systems? And if not where
>> is the formality of the system defined? Obviously it isn't arbitrary
>> or you would simply call it the system and not the formal system. So
>> there must be principles of formality in formal systems.
>
>Good point to raise. A formal system is defined as two grammars. One
>describing the language, what a 'well formed formula' (wff) is, and the
>other describing rules of inference, what sentence forms follows from
>what. So one describes state and the other describes state-change.
>
>So note that the rules of inference tend to describe the /form/
>inferences take. So it is this form, not the particular content, that
>is important. I figure this is what is meant by 'formal'.
>
>So in general, a formal system is a static language that has rules for
>moving from one sentence to another. And that these rules are precise
>enough so that the language does not need to have a meaning, that it can
>be done by syntax alone.
>
>With this said, formal systems can be studied. Because formal systems
>are not particularly restrictive, they could quite easily be couched in
>a meta-language and/or meta-rules. There is a lot of scope for
>creativity and intuition of course. The formalisms just lay down some
>constraints.

The foremost of which I expect would be the absence of self
contradiction.

Regards - Lester

Relevant Pages

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