and that is indeed my fault. I'm jumping around too much and I should be more considerate of the other person.As you can see, I don't know what are you tryng to say
Witt is not arguing that there is no wrong way of interpreting these mathematics, they didn't then (and we still don't) understand how exactly we are able to do mathematics. Wittgenstein is pointing out that in such a situation, while there are certainly wrong interpretations, because we lack the ability to fully understand what math is there arises the conundrum that two equally valid interpretations can arise in that neither can prove themselves or prove the other wrong. That does not mean they are useless, they are helpful in that they help us know what ends are dead and what ends are open. Good questions can only lead to better ones, not answers.Tell me, in a few and simple words, what he's saying, pls.
That's why HE made the reference to what HE would say to someone who used words incorrectly "Don't talk bosh" i.e. don't talk bullshit. This seems to draw upon the kantian tradition concerning the unknown, that such concepts while not providing the same epistemological validity as say a chemistry lab experiment or tasting a hot meal, we can none the less learn from the "shadows they cast upon the void."
That would be a recent change, not a modern one. As you pointed out "Von Neumann" was very much interested in Axioms (don't know about Barnett) but that was because the guy was interested in fame and glory. From an early age he was interested in putting forth irrefutable axioms that would ground mathematics in axiomatic set theory in his doctoral thesis in 1925. Sadly his hopes for fame, glory, bitches and blow were dashed upon the rocks in 1930 by Kurt Godel's incompleteness theorem ended that. This seems to be something that happens repeatedly, von Neumann keeps missing the mark, as he did with game theory and John Nash <-- more on that further down. We've changed our viewpoint on mathematic axioms, which is why postulate now stands with axioms, but this is not something that existed from the start. To superimpose an anachronism on ancient mathematics and to not recognize the modern split with the Greek perspective is just silly.*Sigh... Give me an example of an axiom and and example of a postulate
In modern maths, there's no difference between those terms.
In ancient Greece, there was a slight difference of scope, pretty subtle.
No, he's working from Frege, who sent him to Russell with a personal recommendation (who was also working/continuing on Frege's work who was retiring). Russell's work (and Whitehead's) was developed into logical atomism. Wittgenstein's atomism was the split. Russell was trying to reduce everything into axiomatic parts, to get at the root of math and language. Witt argued that such atomism was impossible as you have music, were you cannot reduce a song to it's individual notes as the individual notes say nothing, or say a poem, where the meaning exists within the poem as a whole. There are complex aspects of communication that can be reduced to their component parts without destroying the meaning. The same is true of math. This is a rough picture of what he's talking about.And to say that obviety he needed years of lectures? What a Gaylord
These lectures come after he broke with this perspective, during the 1940s.
The split with Euclidian Geometry didn't fully set in until Newton was shaken from his pedestal. It takes time for the realization that axioms are useful bullshit, as I said, to set in. That doesn't change the fact that they are no more than useful bullshit ie axioms.WTF are you babbling about dude?
and my original assertion is that COMMUNICATION is not MATHEMATICS. Do you get me now sweetheart?original assertion was: "Kim Peek never wrote a maths text. In fact, he couldn't explain the moral lesson of any child's book"
You're claiming that the perfect number "2" or even "1" exists? Do tell!Not external/internal, that dicotomy is absurd. Reality has a mathematical structure, as demonstrated by the fact that huge chunks of it can be mathematically described with positive results.
How would a deaf person's with specific defective sensory organs deride the brain's ability to interpret sensory input?So deaf people are worse matemathicians? Or are you saying that we have intuitive and innate grasp of multidimensional geometry, exotic manifolds and the cardinality of infinite sets?
LoL they knew about that before your "centuries of elaboration from axioms"No dude, we (except again, some geniuses) have intuitive grasp of thing like 2,+, 1/2, maybe square roots and negative numbers and the like. The most basic mathematical concepts. The 99,99999999999999% remaining it's not intuitive and comes from centuries of elaboration from axioms
That's what I'm talking about. We don't know how some of this shit works Maggot, what's more the human brain is simply remarkable. Even the functions we would call "basic" surpass our best technology. I don't believe in superior/inferior.There, there...all is gonna be okay...who's the prettiest? who's the prettiest? Talby is!!!
John Nash, one of those geniuses we are talking about, once marched into a fellow professor's office and drew two potato like blob on a chalk board and pointing at one stated, in horror, "This is heaven" then pointed at the other "this is hell." He also claimed he received secret messages "from outer space." When asked take "messages from outer space seriously?" Nash simply said that they had come to him the same way as his brilliant mathematical theorems. A genius isn't intrinsic, someone is only a genius in relation to something.Please, explain in a few and simple words what in that sentence is deserving of a facepalm.
Not quite. Here's a thought experiment from Wittgenstein that is invaluable for this discussion.His point is that axioms, which are self-evident or universally recognized truths, are unnecessary in mathematics. That's about all I could gather from his text walls.
I will have to paraphrase:
Imagine your with several other people and each person has a box, inside of which is something that everyone intends to refer to with the word "beetle". Further, suppose that no one can look inside another's box, and each claims to know what a "beetle" is only by examining their own box. Wittgenstein suggests that, in such a situation, the word "beetle" could not be the name of a thing, because supposing that each person has something completely different in their boxes (or nothing at all) does not change the meaning of the word; the beetle as a private object "drops out of consideration as irrelevant". Thus, Wittgenstein argues, if we can talk about something, then it is not private, in the sense considered. And, contrapositively, if we consider something to be indeed private, it follows that we cannot talk about it.
So how is it possible that anyone can talk about "beetle", or anything else for that matter considering that no one can "see" for themselves what "beetle" looks like for someone else?