Re: Epistemology defeats itself with its own premisese
Posted: Thu Oct 24, 2013 1:07 pm
Ok, at least explains the poor French writing x)Kuznetzova wrote:No. I'm talking about Peter the Great
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Ok, at least explains the poor French writing x)Kuznetzova wrote:No. I'm talking about Peter the Great
Actually, Euler was Swiss, born in Basil, Switzerland.The Voice of Time wrote:If I also don't remember wrong, he made several great achievements throughout his life. He founded or at least started the process of building the first science university in Russia (which was a real great achievement, the German mathematician Euler for instance moved there and was hugely productive throughout his life, he's considered one of the greatest mathematicians in history, I've been reading about him in a work on a prime number theory), he built the first mighty Russian navy and he defeated the Swedish Empire in the battle of Poltava effectively marking the slow decline of the Swedish Empire back into mainland Sweden (and later also the loss of Finland). I think also it was the battle of Poltava which gave him the tittle "Great" although I'm quite unsure about that, great because the Swedish king was seen as unbeatable on the battlefield, Sweden at its prime was a huge powerhouse in Europe, fielding a peasant army well endowed in weaponry and skill and with his own genius had been taking victory after victory.Kuznetzova wrote:Woops. I was thinking of Peter the Great.
Sorry for the mixup.
I am afraid your last response did not seem to address my questions and by offering an explanation of why I am asking them only left me more confused about the point you are making. Can I summarise you as follows?Kuznetzova wrote: You are primarily drawn to philosophy because....
Hi Kuznetzova,Kuznetzova wrote:
- Assume there exists "minds" which are containers of "knowledge"
- Assume this knowledge is communicated in the form of English sentences.
- Assume English sentences are pure claims unadulterated by grammar or culture
- Assume there is a group of people who will make "propositions" in written format.
- Assume that "minds" exist transcendentally.
- Assume "sense perceptions" exist transcendentally.
- Assume "propositions" exist independently of their instantiations in language or by human mouths or human writing tools (pens, pencils, chalk).
- Assume the "mind" is a tabula rasa, upon which the transcendent sense perceptions act.
Never really understood this theorem but doesn't it just show that Maths and Logic are not the same thing? As as far as I understood it Russell logicized Number and Godel mathematised his logic and then used mathematical operations to produced what he said were true propositions in the logic that could not be proved from the logic but my question is then how did he define 'true' in this sense, if it wasn't logically true what truth was it?NielsBohr wrote:...
See Godel theorem about this problematic.
Do you mean 'elementary propositions'? If so then Wittgenstein agrees with you. But I thought Godel did something slightly different, as he used one formalism, Maths, to axiomatise Russell's logical axiomatisation of Number and produced 'propositions' that he said were true but could not be proved in the logic. What I'm confused about is how they are considered as being 'true'? As it can't be logical truth so what truth is it?NielsBohr wrote:Good question Arising_UK,
As I see Goedel's theorem, although a formalism can be well construct and coherent in itself, it cannot prevent some "elementary truths" of having no foundation in theirselves.
Hmmm...Logic itself constructs such meta-proofs so why 'another formalism'? Can you give me a simp example as I'm confused.We can try to find their constitution by using another formalism, more abstract, and not less abstract, a "meta-formalism" regarding the first.
Not sure what you mean by this? Psychology?By continuation, the more abstract formalism you can find is only about to be the mind itself. ...
Arising_uk wrote:Never really understood this theorem but doesn't it just show that Maths and Logic are not the same thing? As as far as I understood it Russell logicized Number and Godel mathematised his logic and then used mathematical operations to produced what he said were true propositions in the logic that could not be proved from the logic but my question is then how did he define 'true' in this sense, if it wasn't logically true what truth was it?NielsBohr wrote:...
See Godel theorem about this problematic.
russel did some logical thinking and found out that there is logically no class, without being a member of itself. paradox means illogical.Ginkgo wrote:Arising_uk wrote:Never really understood this theorem but doesn't it just show that Maths and Logic are not the same thing? As as far as I understood it Russell logicized Number and Godel mathematised his logic and then used mathematical operations to produced what he said were true propositions in the logic that could not be proved from the logic but my question is then how did he define 'true' in this sense, if it wasn't logically true what truth was it?NielsBohr wrote:...
See Godel theorem about this problematic.
I think Russell's criticism was specifically aimed at Frege's set theory, but as Niels points out Godel is relevant as well. Basically I think Russell was pointing out the problem of a collection, or class of things being a member, or not being a member of itself. Proof by contradiction could show an axiom to be false.
http://www.wikipedia.org/wiki/Barber_paradox
Yes, so one solution to this problem was to create additional axioms which excluded any class as being a member of itself.Mark Question wrote: russel did some logical thinking and found out that there is logically no class, without being a member of itself. paradox means illogical.
Logic is the metalanguage behind other languages. Logic is borders of our languages borders as borders of our world and truth.NielsBohr wrote:Arising_uk,
-No, I was really considering some truths. I do not know all the historic work of Goedel, but it seems to be extensible to any formalism. The reason is: it would lead to a circular reasoning. It has at most consistance, but it cannot "proof" itself under the proof considerations of the same language.
A reasoning self referring for the short:
a hypothesis H lead to an inference B, which lead to a conclusion C.
C may be a simpler way to express H (as a solution of a problem instruction).
So globally, as you re-get H, you have: H<-->H,
or if C is simpler C<-->C.
There is a big deal in understanding which kind is a demonstration, and I am surely not able to summarize all the ideas about it. I only had severe troubles in trying to understand the notion of demonstration.
In demonstrative geometry - I was 15 years old - I did not understand how we could consider a Hypothesis as True! because the literal meaning of a hypothesis is everything else than a truth...
Generally, a demonstration has the work to make obvious the understanding of an idea, to let it be admitted. But it is often not the case, as the demonstration can seem more complex than the idea, and lead to some corollary.
I remember also when reading a demonstration of some algebra in physics, I began to misunderstand the sense of an implication in a long demonstration (some of the arrows were bijective, what did not help a lot).
-I inferred about a more abstract formalism to try to explain some truths, because in formal logic, you do not have even the time notion.
The time may be understood as a principe of reality - so seeming for concrete - but is surely for me, a human invention.
It seem obvious for me, that the sense of a demonstration would have at least a composant of time.
But as the time is not in the ideas of logic, this means that he general process to understand is to get a higher level of abstraction.
Finally, psychology... why not. Even (meta-)mathematicians were about to go in quest of informations in psychology, to understand if the paradoxes emerging in some "elementary" sets theory, could also be persistant in other theories.
The purpose - according to Douglas Hofstadter - was to understand how eliminate some causes of the emergences of paradoxes, as self-referencies. And had this way to understand how most brains functioned, etc...
-My personal purpose:
In an extreme consideration, I think this is the faith which recognize the truths.