Does perfection exist in this universe?

[mtmynd1]

Does perfection exist in this universe?

Perhaps the logic of mathematics is perfection.

Is it mathematics or is it logic where perfection may be found?

Perfection is an endless goal that has no limits in a mathematical sense if one put Pi onto the plate.

Perfection defies logic to pin that ideal down to Universal agreement, for without that perfection does not exist.

Perhaps perfection can be most closely assimilated into the comfort of harmony, where all activity is working together without conflict. Look at the workings of an expertly construction hand-made watch... perfectly made to keep time perfectly..? The music of man, although not without disharmony, surely has attained a state of perfection with pieces of music, expertly played creating a perfect atmosphere that places the mind in a perfect, but short-lived, frame of mind.

Ahh... perfection is short-lived however attainable the mind may critique that which portrays said perfection. So mind is the conclusive say-so over what 'perfection' means..? If we allow that definition to stand (and we really shouldn't) then the Universe as we presently know is judged by what mind has "calculated" to be - so enormous, so grand and yet so mysterious with billions and billions of unknowns that have been expanding far, far longer that this hu'manity of ours that is but a imperfect being evolving ever so slowly and cautiously, (being the youngest life upon the rock), why the concern over perfection other than but yet, one more subject we enjoy talking about... as we do anything and everything else.

Does this put "talk" into the ill-understood word, 'perfection' ? Are we most perfect in putting what our senses perceive into words created from thoughts that continue to flow through mind on a seemingly endless stream that just might end up into the Oceanic Cosmos of Consciousness..? Ah, but another subject to talk about endlessly until we 'know'. Once knowing is known, does talk stop ? No. Knowing is based upon agreement with others and ourselves as to what has been concluded. We do not talk about "how much is 1 plus 1" because we all "know" the answer... and so it goes until we know what we need to know is fulfilled before we go from know to Being.

.... and so I know I don't know all there is to know, but I do know what I know is good enough to continue knowing for I am but a servant to Mind that often is not kind but will remind me to unwind from the mind who does not ever stop so it is I who must stop listening to mind and give it a rest. empty mind

mtmynd1

[Wyman]

Are you saying "perfection" is called Logic... or "the conception of perfection" is called Logic ?

No, I'm saying that Logic fits the definition that PhilX gave in answer to my question.

Which one of these, (if this are the choices), is the "one thing that Philosophy can call its own" ?

Neither, the recognition that Logic exists and the formalising of it is the one thing that Philosophy can call its own.

... and while I'm at this game of '50 questions', where do you place "reasoning" into this ?

Which type?

That's an interesting subject. Mathematics can be reduced - analysed into - logic plus set theory. The real numbers can be constructed - deduced and defined - from the axioms of set theory plus logic. Analytic geometry can be translated into (real) number theory. So can the calculus.

BUT - Arising - logic was only invented, in the modern sense, in an attempt to build/explain mathematics from fundamental principles - i.e to analyse math to its most fundamental level. So, when Frege and Russell and Whitehead set out to analyze mathematics into 'mathematical' logic - were they being 'philosophers' or 'mathematicians?'

And I would note the titles - 'Principia Mathematica' and 'Begriffsschrift: eine der arithmetischen nachgebildete Formelsprache des reinen Denkens.' I don't know Latin or German, but I am pretty sure they both deal with the foundations of mathematics.

[Arising_uk]

...
That's an interesting subject. Mathematics can be reduced - analysed into - logic plus set theory. ..

I didn't really understand it and Russell said Godel misunderstood but I thought Godel's Theorem showed that this was not the case?

The real numbers can be constructed - deduced and defined - from the axioms of set theory plus logic. Analytic geometry can be translated into (real) number theory. So can the calculus.

I'll take your word for it.

BUT - Arising - logic was only invented, in the modern sense, in an attempt to build/explain mathematics from fundamental principles - i.e to analyse math to its most fundamental level. So, when Frege and Russell and Whitehead set out to analyze mathematics into 'mathematical' logic - were they being 'philosophers' or 'mathematicians?'

I think Russell and Whitehead being philosophical logicians and Frege a philosophical mathematical logician. But Boole was about before and he wrote "An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities" and I agree with him about what Logic can concern, not saying it can't be used to be comcerned with Mathematics and add Aristotle to the mix. But I take your point whch is why I tend to stick with truth-functional logic, i.e. PL or Sentential as you and Frege call it.

And I would note the titles - 'Principia Mathematica' and 'Begriffsschrift: eine der arithmetischen nachgebildete Formelsprache des reinen Denkens.' I don't know Latin or German, but I am pretty sure they both deal with the foundations of mathematics.

Think they do as well but refer you to Boole's works as an excuse for what I say and Wittgenstein for his proposition that Logic has no number.

[Wyman]

I think Russell and Whitehead being philosophical logicians and Frege a philosophical mathematical logician.

Yeah, I was nitpicking. I guess it doesn't matter. I do like getting different perspectives on these things, though. I went and read some about Boole and have been thinking about the differences between PL and predicate logic because of our other discussion. I also happen to have a book on the shelf about Godel's incompleteness theorem.

I started rereading it and therefore may have to amend this later after I finish, but here's my take on it and on what you said about math being constructed from logic and set theory. Almost all of what you and I know as 'maths' can be constructed from logic and set theory - arithmetic, geometry, number theory, calculus. There may be same really esoteric 'high level' math that falls outside - probably some that were set up just for that reason.

I don't think the incompleteness theorem has much to do with it, though. It says that any formal system that is capable of simple arithmetic (like adding natural numbers, which are of course an infinite series, which is relevant to the proof) - including Principia Mathematica or 'PM' logic, which is what he was addressing in his proof - is necessarily incomplete. That means that there will be statements - theorems - in the language of the system which cannot be proven either true nor false - they are undecidable. This means that, before the proof twenty years ago of Fermat's conjecture, for instance, there was no guarantee that a proof for or against it would be forthcoming. This bothers mathematicians (e.g. Hilbert) because they like to think that any proposed theorem can, given enough time and knowledge, be proven or disproven. However, beyond that psychological irritation, the incompleteness theorem has little relevance to math - except the ones who study formal systems and logic.

So, I don't know that the theorem (I should say Part I, since there is another one, but I don't think it is of any relevance here) relates particularly to whether math - or most of it - can be constructed out of logic and set theory. I definitely could be wrong, but that is my understanding.