'When Are Relations Neither True Nor False?
in [Math]
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From: Aatu Koskensilta on 6 Mar 2010 05:39 MoeBlee <jazzmobe(a)hotmail.com> writes: > I've not counted whatever that definition may be, since he's already > been told a million times what a formal proof is. According to Nam, any piece of reasoning the conclusion of which is formally provable in some formal system is a formal proof. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 6 Mar 2010 05:43 Marshall <marshall.spight(a)gmail.com> writes: > For me, Nam has mostly moved into the same category as AP. Come now, even if you don't find Nam's posts worth reading comparing him to Archimedes Plutonium is surely excessively harsh. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Nam Nguyen on 6 Mar 2010 09:12 Aatu Koskensilta wrote: > Nam Nguyen <namducnguyen(a)shaw.ca> writes: > >> I think you meant the passage I had earlier said: >> >>>> if there's a formal system where what he asserted is a theorem, then >>>> his proof is a formal proof. If not then his proof isn't. It's >>>> that's straight forward which doesn't require explanation on thing >>>> such as "ordinary mathematical proof", as you said. >> Why is that definition of a _formal proof_ "bizarre and pointless"? > > This has already been explained. It is bizarre and pointless because > according to it pretty much any and every piece of reasoning, however > vague or informal, however cogent or inane, is a formal proof. You've just repeated your position, *not* explained it! How can my definition allow "every piece of reasoning" to become formal proof when I already said my definition is just Shoenfield's definition of formal system proof? It appears very difficult to make sense of your argument when you _ignoring_ the other side's new explanations, arguments, definition, or what have we. [And in this post this isn't the only time your _ignoring_ could be noticed!] In fact it's the other way around: your "formal proof" definition's not being the same with Shoenfield's definition of "formal system" proof would virtually enable "abuse" the word "formal" - a reserved word in FOL syntactical property of formulas and proofs, as clearly stipulated in Shoenfield definitions. > >> But for crying out loud, why on Earth would one want flip the >> semantics of "formalized" into "in-formalized"? > > What on earth are you talking about? You really didn't understand a few simple English sentences? Or is your asking me here due to your _ignoring_ what I did explain? This is the context of my definition of "formal proof": >> This is what he said: >> >> "We need the third part of a formal system which will enable us to _conclude_ >> _theorems from the axioms_. This is provided by the rules of inference..." >> >> [The highlight are mine]. >> >> My definition of _formal proof_ is basically just a repeat of Shoenfield's >> definition of _formal system proof_. Are you saying Shoenfield's definition >> here is "bizarre and pointless"? So, I was talking about your sense of the word "formal" isn't in the same sense when we typically talk about FOL "_formal_ system": hence it's an "informal" sense. Iow, to you, "formal" means "ordinary mathematics" kind of reasoning. To me "formal" means conforming to strict definition as stipulated by Shoenfield's definition of "formal system" proofs. So to me your your notion of "formal" is informal. Do you now understand what I was talking about?
From: Nam Nguyen on 6 Mar 2010 09:13 Aatu Koskensilta wrote: > MoeBlee <jazzmobe(a)hotmail.com> writes: > >> I've not counted whatever that definition may be, since he's already >> been told a million times what a formal proof is. > > According to Nam, any piece of reasoning the conclusion of which is > formally provable in some formal system is a formal proof. > Where did I even allude to that?
From: Nam Nguyen on 6 Mar 2010 09:37
Aatu Koskensilta wrote: > Marshall <marshall.spight(a)gmail.com> writes: > >> For me, Nam has mostly moved into the same category as AP. > > Come now, even if you don't find Nam's posts worth reading comparing him > to Archimedes Plutonium is surely excessively harsh. > Thanks. But it's ok Aatu. I've been"blasted" by both the "orthodox" and the "crank" for years; nothing is new. It's hard to be in a 3rd party isn't it? In the past one "crank" alluded that I wasn't "liberal"/"open-minded" enough in my critique of the current regime of reasoning, and recently AP "lumped" me together with the "standard theorists". It's hard to defend the good, relativistic, and "humanistic" mathematical reasoning. The other 2 sides (the "crank" and the "orthodox") seem to fight against it: they seem to sense there's going to be a "regime" change in in reasoning in which their "spheres of influence" are going to be in an upheaval <so-to-speak-of-course> The irony though is it's between the MR (Mathematical Relativity) "rebel" and the "orthodox" who are _disciplined_ that the bitter-end conflict would occur. So bitter that "scorched-earth", "no-prisoner-taken" policies have been applied, something one wouldn't see when they fought against the "crank", jointly or separately! </so-to-speak-of-course> |