Avi Love wrote:It seems to me that logic proves or disproves all arguments, but the proof of logic is logic.
Avi Love wrote:I was not familiar with Goedel's theroem, but it's a fascinating point.
It would seem that a fully consistent logic should actually be impossible.
I'm going to make a few assertions that may not be seen as fully agreeable but which are necessary to support the statement above. The first concerns the bundle view of the self. We are a collection of parts which produce some extremely sophisticated processes. There is no core self of some kind which is separate from all of the parts.
If this can be taken to be the case (which I think it can), our perception is a facet of the way our parts work. Each of our sets of parts are fairly similar but also uniquely different. I do not perceive the same as you, but we perceive similarly enough that you have some understanding of what I'm saying. Logic would seem to be the attempt to formalize a certain type of communication in order to allow better communication between those of us who think that way, but that has a few unintended consequences.
My bundle of parts cannot directly perceive your bundle of parts or really anything else for that matter. Any information received must be translated into a form that my bundle understands. So when you say something to me, I hear my bundle's interpretation of it, not yours. This can hopefully be clarified to a larger extent through further questioning and explanation, but it cannot be ultimately resolved. Logic proposes an ultimate resolution.
However the use of logic will cause a loss of information that was included in the original user's thought process as well as the elimination of the perspectives of all individuals who do not think in a manner conducive to the rules of logic.
If I am thinking something diverse and complicated, but have to whittle it down to be logical, I have inevitably lost certain information that was included in my initial set of perceptions. This is perhaps, to some degree, unavoidable in any communication with another individual, but it seems necessary to note that logic perpetuates this.
Additionally, if a certain individual expresses their perceptions through dance, they are removed from the community of logical discussion. That means that anything which might be radically different in their perspective from those in the logical community, which could be an accurate perception of a kind only to be found in the mind of a dancer, is entirely lost to logic. Logic, in putting itself above all other languages, loses the ability to learn from them.
So what I'm proposing here is not even remotely that we should abandon logic. It's incredibly useful. Dance, and other mediums, all have their own standards of formal communication as well. I think, though, that it's important to acknowledge that every rule of logic is not the handed down wisdom of the universe but simply something that those who use that particular rule agree represents truth. This conclusion seems to be in line with what many of you are saying.
By Robert P. Crease
STONY BROOK, N.Y. – Pythagoras's theorem changed the life of the British philosopher Thomas Hobbes (1588-1679). Until he was 40, Hobbes was a talented scholar exhibiting modest originality. Versed in the humanities, he was dissatisfied with his erudition and had little exposure to the exciting breakthroughs achieved by Galileo, Johannes Kepler, and other scientists who were revolutionizing the scholarly world.
One day, in a library, Hobbes saw a display copy of Euclid's "Elements" opened to Book I, Proposition 47 - Pythagoras's theorem. He was astounded, exclaiming, "This is impossible!" He read on, intrigued. The demonstration referred him to other propositions, and he was soon convinced that the startling theorem was true.
Hobbes was transformed. He began drawing figures and writing calculations on bedsheets and even on his thigh. His approach to scholarship changed. He began to chastise philosophers of the day for their lack of rigor and for being unduly impressed by their forebears. He compared other philosophers unfavorably with mathematicians, who proceeded slowly but surely from "low and humble principles" that everyone understood.
neuro wrote:Avi Love wrote:It seems to me that logic proves or disproves all arguments, but the proof of logic is logic.
This reminds me of Goedel's theorem.
If you look for an "exact" (fully consistent) logics, then you won't be able to have an unlimited logics (applicable to everything).
If you look for an every-encompassing logics, you won't manage to make it fully consistent.
Usually, one uses logics - because IT WORKS, as it has been said above - within the domain for which it was developed.
The fact it cannot exit such domain, and proof its own validity from the outside like a person who flew by pulling on her bootstraps, does not take anything out of logics.
For example, you may turn to "fuzzy logics" to deal with physical, social or epistemic problems that are ineffectively dealt with by classical logics: you shall have a more powerful tool for those domains, but a less powerful tool for discerning a true/false dichotomy.
Lomax wrote:I agree with the principle that logics should be chosen simply on the basis of whether they work (which, by the way, leaves us with the problem of showing that a logic works without relying on logic to do so).
Yorkshire wrote:AVI & ATHENA
Apologies for over-posting.
Abstract is neither good or bad.
All science, with the exception of physics (mostly), is abstract.
Any study or creation that takes the observer into account is not abstract.
Art, fiction, etc. are not abstract.
My statistical graph cannot show anything, but I can show you my statistical graph.
To make this graph I had to weigh thousands of stream pebbles to create a mean, median, and mode for their masses.
I show you my graph, and you say, "So the average pebble in this stream has a mass of 1.478g."
You logically infer from my "observations" from which I constructed a graph that you could search more than one-hundred lifetimes and never find a pebble of that mass.
Is this inference, reasoning, logic? I am trying to learn from you folks. I am not sure of your terminology.
Avi Love wrote:So it seems that both Whut and Yorkshire are saying that logic is a category which cannot be self-refential. However logic is not just a category. It is a process.
Why does it follow?
It cannot be simply based on observation. Neither person in that dialogue has to actually have seen a whale. That is inherently the point of logic.
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