The starting point of our thinking is based on the distinction between TRUE and FALSE. Discovering absolute truth has been a philosophical dream for centuries.
The most watertight system for distinguishing true from false is logic. In logic, you only have two options: a statement is 1 = true or 0 = false.
Among philosophers and mathematicians, there has been a wish to base mathematics or even reduce mathematics to logic. To be honest, I am not a mathematician,
but yet I wondered why they would like to do that. My guess was that logic only knows true and false, so at the end of any reasoning, the conclusion must be true or false, if it is valid.
Now, google on "Unsolved problems" in mathematics. You will learn that there are dozens of mathematical problems, for which they can't find a solution,
but if mathematics can be reduced to logic in the end you only would have a true or false for every problem. So, maybe that is the reason why Bertrand Russell (1872 -1970) and Alfred North Whitehead wrote "Principia Mathematica" (1910 -1913).
It was a masterpiece in an attempt to base mathematics on logical principles. Then I got the idea, that if I am not an expert in this field, let's ask ChatGPT.
What inflated my Ego, of course, was that my idea about the reason to relate logic and mathematics was correct. (No applause needed, thank you :-)
I won't bother you with all the reasons with which ChatGPT came up, but let me give you two, that are most telling:
Number one is Consistency. Logic ensures that mathematical arguments are internally consistent. This means that the conclusions drawn from mathematical reasoning follow logically from the premises, without any contradictions.
Number two is Proof: Central to mathematics is the concept of proof. A proof is a logical argument that demonstrates the truth of a mathematical statement beyond doubt.
By applying principles of logic, mathematicians construct proofs to establish the validity of conjectures and theorems.
In summary, mathematicians base mathematics on logic because it provides a framework for consistent, clear, and rigorous reasoning, essential for developing mathematical theories, proving theorems, and advancing the discipline as a whole.
Sounds good, but the big question is of course, did the project succeed? The answer is NO. Logical principles are definitely used in mathematical reasoning,
but then there was Kurt Gödel (1906 - 1978). He was a logician, mathematician, and philosopher, considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history.
Let me quote a passage from Wikipedia, that gave me shivers: -QUOTE- On December 5, 1947, Einstein and Morgenstern accompanied Gödel to his U.S. citizenship exam, where they acted as witnesses.
Gödel had confided in them that he had discovered an inconsistency in the U.S. Constitution that could allow the U.S. to become a dictatorship; this has since been dubbed Gödel's Loophole.
Einstein and Morgenstern were concerned that their friend's unpredictable behavior might jeopardize his application. The judge turned out to be Phillip Forman, who knew Einstein and had administered the oath at Einstein's own citizenship hearing.
Everything went smoothly until Forman happened to ask Gödel if he thought a dictatorship like the Nazi regime could happen in the U.S. Gödel then started to explain his discovery to Forman.
Forman understood what was going on, cut Gödel off, and moved the hearing on to other questions and a routine conclusion. -END QUOTE-
Fortunately, Mister T doesn't seem to read a lot, but if his sycophants in his entourage do, they may have given him this being a dictator (for one day) idea.....
Thank you for your attention.......
Main Sources:
MacMillan The Encyclopedia of Philosophy, 2nd edition
TABLE OF CONTENT -----------------------------------------------------------------
1 - 100 Philosophers 9 May 2009 Start of
2 - 25+ Women Philosophers 10 May 2009 this blog
3 - 25 Adventures in Thinking 10 May 2009
4 - Modern Theories of Ethics 29 Oct 2009
5 - The Ideal State 24 Febr 2010 / 234
6 - The Mystery of the Brain 3 Sept 2010 / 266
7 - The Utopia of the Free Market 16 Febr 2012 / 383
8. - The Aftermath of Neo-liberalism 5 Sept 2012 / 413
9. - The Art Not to Be an Egoist 6 Nov 2012 / 426
10 - Non-Western Philosophy 29 May 2013 / 477
11 - Why Science is Right 2 Sept 2014 / 534
12 - A Philosopher looks at Atheism 1 Jan 2015 / 557
13 - EVIL, a philosophical investigation 17 Apr 2015 / 580
14 - Existentialism and Free Will 2 Sept 2015 / 586
15 - Spinoza 2 Sept 2016 / 615
16 - The Meaning of Life 13 Febr 2017 / 637
17 - In Search of my Self 6 Sept 2017 / 670
18 - The 20th Century Revisited 3 Apr 2018 / 706
19 - The Pessimist 11 Jan 2020 / 819
20 - The Optimist 9 Febr 2020 / 824
21 - Awakening from a Neoliberal Dream 8 Oct 2020 / 872
22 - A World Full of Patterns 1 Apr 2021 / 912
23 - The Concept of Freedom 8 Jan 2022 / 965
24 - Materialism 7 Sept 2022 / 1011
25 - Historical Materialism 5 Oct 2023 / 1088
26 - The Bonobo and the Atheist 9 Jan 2024 / 1102
27 - Artificial Intelligence 9 Feb 2024 / 1108
The Discussion
[13:19] herman Bergson: The floor is yours :-)
[13:19] .: Beertje :. (beertje.beaumont): don't wake a sleepy dog..
[13:19] Max Chatnoir: Yikes, Herman!
[13:19] herman Bergson: You say it Beertje.....
[13:19] Particle Physicist Bejiita (bejiita.imako): (shudders)
[13:19] Particle Physicist Bejiita (bejiita.imako): Well MrT might indeed become that very dictator
[13:19] Max Chatnoir: Umm, Herman, would you consider NOT publishing this one?
[13:20] Particle Physicist Bejiita (bejiita.imako): idk its a mess but
[13:20] Particle Physicist Bejiita (bejiita.imako): hmhm
[13:20] Daruma Boa: Well, there really are a lot of things that go on behind our backs - or our knowledge. Like, for example, the spiritual breakfast club of the presidents in America
[13:20] herman Bergson: I don't think I am the only one who knows about Gödel's Loophole, Max
[13:21] Max Chatnoir: No, I don't suppose you are, Herman.
[13:21] herman Bergson: It is outthere since 1947
[13:21] Particle Physicist Bejiita (bejiita.imako): ok
[13:21] Max Chatnoir: Heavy sigh....
[13:21] herman Bergson: But we never saw a criminal becoming president in the US
[13:22] Daruma Boa: Until Trump came....
[13:22] .: Beertje :. (beertje.beaumont): i think now we do
[13:22] Particle Physicist Bejiita (bejiita.imako): indeed thats fashinating
[13:22] herman Bergson: right..
[13:22] herman Bergson: But what is more important is this relation between mathematics and logic
[13:23] Particle Physicist Bejiita (bejiita.imako): already before he became president first time and i for the first time ever saw the dude and heard his blabbering i said to myself "that one belongs in a padded cell in an asylum NOT in white house"
[13:23] herman Bergson: Just imagine....
[13:23] herman Bergson: our brain produces both....
[13:23] Particle Physicist Bejiita (bejiita.imako): still it went all way to that and now...
[13:23] Particle Physicist Bejiita (bejiita.imako): sheesh!
[13:23] Max Chatnoir: https://www.newyorker.com/news/daily-comment/kurt-godels-loophole-and-donald-trumps-defiance
[13:23] herman Bergson: and this brain also produces mathematical problems that can not be solved by the same brain
[13:24] herman Bergson: Oh my, Max!!!!
[13:24] herman Bergson: It is out there!@!!!!
[13:24] Daruma Boa: ;-)
[13:25] herman Bergson: Told you...I am not the only one....
[13:25] Max Chatnoir: Not quite. It says he never defined it. Is that true?
[13:25] herman Bergson: I don't know, Max...I'll do research on it
[13:26] Particle Physicist Bejiita (bejiita.imako): he maybe never defined it as that, others might have coined the actual term
[13:26] herman Bergson: But back to logic an mathematics.....
[13:26] Daruma Boa: I think that all events in life can be calculated.
[13:26] herman Bergson: Our brain produces theories and runs into unsolvable rpobles within these theories
[13:27] herman Bergson: THAT is my point, Daruma.....
[13:27] Daruma Boa: ;-)
[13:27] Neuro Wonder: wonder if there is a logical or mathematical proof showing the relationship between logic and mathematics
[13:27] herman Bergson: We are not able to calculate everything, it seems
[13:27] Daruma Boa: We are only a part of the system. Called "nature"
[13:28] herman Bergson: Gödel showed that there is not Neuro
[13:28] Daruma Boa: Perhaps this is what is called "The True Will". Wich cannot be calculated.
[13:28] herman Bergson: Yes Daruma, but nature is not a logical or mathematical machine....that is what we invented and projected on nature
[13:28] Max Chatnoir: I think that the logic gets into trouble when it becomes self referential. Like The statement on the other side of this paper is true.
[13:28] Particle Physicist Bejiita (bejiita.imako): ah
[13:29] herman Bergson: cool one Max, yes...that is the fun thing
[13:29] Neuro Wonder: should we strive to calculate even when something seems incalculable? the calculations are there whether we do them or not
[13:30] herman Bergson: The primary question here is is everything quantifiable, Neuro
[13:30] Max Chatnoir: computers can help when it's very complex
[13:30] Particle Physicist Bejiita (bejiita.imako): yes
[13:30] herman Bergson: Yes, Max, but they can't solve the unsolvable problems in mathematics
[13:31] Neuro Wonder: yet
[13:31] herman Bergson: that is what puzzles me at the moment
[13:31] Max Chatnoir: Right, because they are missing a relationship somewhere.
[13:31] herman Bergson: even that won't work Neuro
[13:31] herman Bergson: because computer still are based on logic....1 and 0
[13:32] Particle Physicist Bejiita (bejiita.imako): a computer can only do calculatable things however as everything is based on math, the very word computer means calculator and before the dawn of the machine being a computer was a task designated tp a person
[13:32] Max Chatnoir: Yes, probability is not always 100%
[13:32] Particle Physicist Bejiita (bejiita.imako): human computers = someone doing calculation
[13:32] Neuro Wonder: quantum computers do not have to do computations serially
[13:32] herman Bergson: Yes, they always come up with quantum mechanics....:-)
[13:33] Daruma Boa: *GIGGLES* :)~~~~
[13:33] herman Bergson: as if that is the final answer...
[13:33] herman Bergson: I don't know....not an expert on that
[13:33] Neuro Wonder: i wouldn't shut the door on it is all i'm saying
[13:33] herman Bergson: No no, Neuro...
[13:33] Daruma Boa: Yes I think its always important to keep every door open.
[13:34] herman Bergson: science goes on....philosophers keep on asking questions....that is the human condition
[13:34] Particle Physicist Bejiita (bejiita.imako): an analogy i heard before was a normal computer is a lawn mower mowing 1000s of straws per second but taking hours to mow the entire lawn still. A quantum computer is like every straw of grass has its own scissors that need say half an hour to cut that single straw but since every straw have its own pair of scissors the entire lawn gets cot in half an hour
[13:34] Particle Physicist Bejiita (bejiita.imako): cut
[13:34] herman Bergson: bejiita...stick to the debating rules here...
[13:34] herman Bergson: are on my pulpit...
[13:35] Particle Physicist Bejiita (bejiita.imako): well thats the entire analogy i heard
[13:35] Particle Physicist Bejiita (bejiita.imako): computer vs quantum computer
[13:35] Particle Physicist Bejiita (bejiita.imako): how they work
[13:35] Particle Physicist Bejiita (bejiita.imako): quantum computer solve all problems simultaneously
[13:35] Particle Physicist Bejiita (bejiita.imako): instead of serially
[13:36] Particle Physicist Bejiita (bejiita.imako): thats the power of them
[13:36] herman Bergson: Whatever they do, they still have to work with 1 and 0
[13:36] herman Bergson: That is all we have got....or probability
[13:36] Particle Physicist Bejiita (bejiita.imako): but they can be both 1 and 0 at same time here
[13:36] Particle Physicist Bejiita (bejiita.imako): thats how i understand it
[13:37] Particle Physicist Bejiita (bejiita.imako): very weird things happening
[13:37] Particle Physicist Bejiita (bejiita.imako): quantum effects
[13:37] herman Bergson: But yet our brain can't Bejiita....
[13:37] Particle Physicist Bejiita (bejiita.imako): almost like magic even it itsnt
[13:37] Particle Physicist Bejiita (bejiita.imako): true
[13:37] herman Bergson: It is true or false....or maybe Fake News :-)))
[13:38] Particle Physicist Bejiita (bejiita.imako): the 3rd state!
[13:38] Particle Physicist Bejiita (bejiita.imako): ㋡
[13:38] Particle Physicist Bejiita (bejiita.imako): hehe
[13:38] herman Bergson: which is some grey area of information to many
[13:39] herman Bergson: So....next lectures we'll see what this all means for computers and artificial intelligence
[13:40] Max Chatnoir: Interesting!
[13:40] Particle Physicist Bejiita (bejiita.imako): ah yes
[13:40] herman Bergson: Unless you still have that question or remark....
[13:40] herman Bergson: if not.....Class dismissed
[13:40] herman Bergson: and thank you all again for participating
[13:41] .: Beertje :. (beertje.beaumont): Thank you Herman
[13:41] Max Chatnoir: Thank you, Herman!
