Suppose you have already published the first volume of your opus magnum and are almost ready with the second volume.
Then you receive a letter in which the writer explains that there is a problem in the system you just have developed: a paradox!
That is what happened to Gottlob Frege in 1902. He had developed a completely new symbolism and had attempted to derive, by use of his symbolism, all of the laws of arithmetic from axioms he asserted as logical.
He thought he had succeeded in his project and then came this letter from some wisely, named Bertand Russell from the UK. It must have been a real shock.
Before receiving the famous letter from Bertrand Russell informing him of the inconsistency in his system, Frege thought that he had shown that arithmetic is reducible to the analytic truths of logic
A paradox is an argument that derives or appears to derive an absurd conclusion by rigorous deduction from obviously true premises.
Let's take the popular description of what Russell showed Frege. The barber of Seviella is the only barber in town who shaves all men who don't shave themselves.
And who shaves the barber? If he shaves himself the thesis is not true, for then the barber shaves a man, who shaves himself too.
If he keeps his beard, then the barber doesn't shave all men who don't shave themselves. Again the thesis is untrue.
His wife!!!! His wife shaves him! That doesn't help for then the barber does not shave all men who don't shave themselves either.
This is what Russell found out when he strictly applied the rules, which Frege had formulated. Well, no this barber story, but something which sounds more mathematical.
How Russell professionally would have said it about the paradox concerning the set S of all sets x such that x is not a member of x. He would ask: is S a member of itself? A moment’s reflection shows that S is a member of itself if and only if S is not a member of itself - a contradiction.
Due to a renewed interest in logic and the decline of Aristotelian logic around 1900 paradoxes became a well known companion in the logical discourse.
The most devastating paradox is this simple sentence: "This statement is not true."
A variation Russell describes: take a piece of paper and write on it:
"What is written on the backside of the paper is not true". Then turn the paper and write there the same statement. Then start pondering about the truth of the statements.
For 2300 years now philosophers are puzzled by this paradox. Yes, that long, for it were again the Greek, who loved to think about paradoxes.
These are what we cal logical and semantical paradoxes, but you have all kinds of (seemingly) paradoxes in all kinds and flavors. Wikipedia offers you a wide range.
Not only in logic and semantics you run into paradoxes. Also ethics confronts you with serious problems.
Suppose it is a fundamental principle of yours that you never will steal. Your fellowmen are not that ethical. They steal really everything, also all the food.
When you stick to your moral rule, you will starve to death. On the other hand to survive you have to steal food too.
And those who have attended a long range of lectures here certainly remember how we time and again ran into the paradox of thought about thought.
Our attempts to measure the ruler in my hand with the rule in my hand. It has something to do with Tarski's Undefinability Theorem.
It is about what he calls semantically closed or not closed languages. Informally, the theorem states that arithmetical truth cannot be defined in arithmetic.
When you take the statement "This statement is not true." then, to keep it simple, this "true " should be semantically a word of a higher level, which makes it possible to refer to that statement, so to speak a word from another language.
Like in "Es regnet hier" is German.
So Tarski, like we did several times, concluded that you can not express everything regarding truth values in a natural language like English.
This suggested to him that English itself may not be semantically closed, or, if English is closed, then it is self-contradictory.
This shocking result indicates to some that our thought about our thoughts is incoherent.
And here we see the true value of paradoxes in philosophical thinking. It is a lot of fun to puzzle and try to figure out a solution,
but in essence they show us the incompleteness of the functioning of our mind, our thinking and reasoning.
[13:26] herman Bergson: so much on paradoxes
[13:26] herman Bergson: this was the last lecture in the series on Adventures in Thinking...
[13:27] herman Bergson: if you have any questions or remarks, feel free..you have the floor
[13:27] Kurk Mumfuzz: are you suggesting that paradoxes make ethical relativism an acceptable form of thought... that, for example, it is ok in SOME cases to steal to survive, say...? and if so, where are the limits...?
[13:27] herman Bergson: A good question....
[13:27] Paula Dix: hi all :)
[13:27] Frederick Hansome: Is it that the human mind has difficulty in wrapping itself around something that is "true" and "not true" at the same time, or is it just a problem with the language?
[13:27] Abraxas Nagy: Hey Paula
[13:28] Lovey Dayafter: Hi:-)
[13:28] herman Bergson: One thing seems apparent and that is that we cant create a consistent 'ethical calculus" so to speak
[13:28] herman Bergson: I think that this does not imply an argument for ethical relativism
[13:29] Kurk Mumfuzz: butitis used that way...
[13:29] Kurk Mumfuzz: witness american politics...
[13:29] Kurk Mumfuzz: hehe..
[13:29] herman Bergson: I see....
[13:30] Ludwig John: to avoid paradoxes in ethics therefore it is the best to have not so strict principles
[13:30] herman Bergson: If you would accept that view than all rulings of courts are just plain relativism too
[13:30] Kurk Mumfuzz: but that is inherent in the administration of "justice", is it not...?
[13:31] herman Bergson: No I wouldnt agree with that...
[13:31] herman Bergson: In the first place you have a definition of being human
[13:31] herman Bergson: from there you start to build your epistemological and ethical identity, I would say
[13:32] herman Bergson: For instance..the definition asks for a meaning of life
[13:32] herman Bergson: a meaning of being a social individual
[13:33] herman Bergson: so ...before you come to the question what is right and what is wrong you have to answer al lot of other questions first
[13:33] Kurk Mumfuzz: there is the cynic in me that suggests that law does not define what is right and what is wrong but, rather, what we (or a privileged few) can get away with...
[13:33] herman Bergson smiles
[13:34] herman Bergson: I don think that that is the starting point of the law giver....but maybe that of those who have to obey the law
[13:34] Kurk Mumfuzz: and therein are found many paradoxes...
[13:34] Ludwig John: life itself is paradox: I have to kill other beings in order to survive ?
[13:35] Lovey Dayafter: doesn't each individual decide what is right and wrong?
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[13:35] Lovey Dayafter: decide
[13:35] herman Bergson: If it were only the individual you can join Kurk in his relativism
[13:35] Paula Dix: lol kurk, a friend here says the same, laws are made so riches can stay rich
[13:36] Lovey Dayafter: i don't want someone deciding for me
[13:36] herman Bergson: well....you got some point there...
[13:36] Kurk Mumfuzz: anybody paying attention the creation of law in the US will affirm that, paula... „ã°
[13:36] Kurk Mumfuzz: unless they were part of it... *laughs*
[13:36] Lovey Dayafter: where r u from Kurk?
[13:36] Paula Dix: lol
[13:36] herman Bergson: Let me give you a Dutch example in this context.....
[13:37] Paula Dix: i guess anywhere its the same...
[13:37] Kurk Mumfuzz: san francisco... the left coast of the US... „ã°
[13:37] herman Bergson: They have reformed tax laws here such that as a citizen you hardly had posts you can use for tax reduction...
[13:37] Lovey Dayafter: don't use the US as example
[13:37] herman Bergson: They never did such a reform for the Multinationals....
[13:38] Paula Dix: lol herman this is looking like brazil!
[13:38] herman Bergson: Result..the citizens pay taxes...the Dutch multinationals keep 16 billion dollars a year in their pockets by legal tricks
[13:38] herman Bergson: It is a known fact
[13:38] Frederick Hansome: left coast? Only if you are considering it from a certain perspective
[13:39] herman Bergson: and not a paradox at all...
[13:39] Kurk Mumfuzz: ??
[13:39] herman Bergson: But I want to get back to the subject.....the epistemological meaning of paradoxes for philosophical thinking
[13:39] Kurk Mumfuzz: yes..
[13:40] herman Bergson: that is what I find most interesting actually
[13:40] Paula Dix: it means our thinking is flawed?? in essence we cant really be "right"?
[13:40] herman Bergson: well...within given contexts we can think perfectly and correct without flaws
[13:41] Paula Dix: but not in a whole
[13:41] herman Bergson: otherwise we werent able to land a man on the moon for instance
[13:41] Paula Dix: lol yes
[13:41] herman Bergson: Yes..Paula...the overall system doesnt seem to be waterproof..
[13:41] Paula Dix: i mean, it means the whole of universe isnt really a whole, some "pieces" are missing from the "puzzle"?
[13:42] herman Bergson: I dont know....
[13:42] herman Bergson: but I come to another observation....
[13:42] herman Bergson: the more symbolic the language is we use, the more accurate we can be...
[13:42] herman Bergson: I mean ..
[13:42] oola Neruda: poetry
[13:42] oola Neruda: art
[13:43] Paula Dix: ah, interesting!! I knew there was a reason for me to choose art :)
[13:43] herman Bergson: everything that is describable mathematically against what only cna be expressed in language
[13:45] herman Bergson: matybe a matter to look into
[13:46] herman Bergson: At least natural language is less efficient than mathematics
[13:46] Paula Dix: i wonder if this "problem" is human only or general...
[13:46] herman Bergson: general in what sense. Paula?
[13:46] herman Bergson: That your dog has the same problem?
[13:46] Paula Dix: like if any intelligent aliens would find them too :)
[13:46] Paula Dix: lol
[13:47] Kurk Mumfuzz: some languages seem to be very figurative (english for example has many words to express the same things, some with nuance and some with none) and other languages, particularly asian languages based on "pictures" tend to be more literal... is one laguage in an advantage over another...?
[13:47] Lovey Dayafter: if we knew what aliens thought
[13:47] herman Bergson: Yes..that is what I wondering about myself too now and then
[13:47] oola Neruda: excellent point Kurk
[13:47] Paula Dix: oh, our dog here is amazing, she saw the cat running and being able to pass thru the bars on the window so one day she tried running and jumping... got a nice cut on her nose :)))
[13:47] herman Bergson: I would say all languages have the same semantical problems
[13:48] oola Neruda: i am not so sure they do
[13:48] Myriam Brianna: no, I would say they have different semantical problems :)
[13:48] oola Neruda: agreed
[13:48] herman Bergson: Well the question was....is this kind of problems inherent to intelligence in general..
[13:49] herman Bergson: Here you run into the paradox of thinking again I am afraid
[13:49] oola Neruda: i think our view of the world is very much a part of our language... and vice versa
[13:49] oola Neruda: and as Kurk said... there is a concreteness to the asian languages... that the romance languages do not share
[13:49] Paula Dix: yes, how we think before we can talk??
[13:49] herman Bergson: Yes….and we can not think about thinking from outside thinking
[13:50] Kurk Mumfuzz: the impact of language on culture is significant... and that has a lot to do with the way we thin... i think...
[13:50] oola Neruda: nods
[13:50] herman Bergson: Or should we say...the impact of culture on language is significant?
[13:51] Kurk Mumfuzz: maybe...
[13:51] Paula Dix: lol a case of feedback?
[13:51] herman Bergson: maybe the chicken- egg paradox?
[13:51] oola Neruda: they probably affect each other
[13:51] Kurk Mumfuzz: hehe...
[13:51] herman Bergson: does language create our world or does our world create language?
[13:52] Lovey Dayafter: what do you think?
[13:52] Paula Dix: lol biologists says the egg came first, the chicken is just an egg carrier :)
[13:52] Lovey Dayafter: the egg had to come first
[13:52] herman Bergson: Anaximander 600 BC already thought about that..
[13:52] herman Bergson: he asked..where did the egg come from?
[13:53] Lovey Dayafter: does it matter?
[13:53] Paula Dix: my bet would go to paradoxes being universal...
[13:53] Kurk Mumfuzz: we need language to make our world meaningful... but what we find in our world often prompts the creation and expansion of language...
[13:53] oola Neruda: this will sound strange... but consider the way maps came into being... is it not a bit like how language came into being
[13:53] Myriam Brianna grumbles - I wish you all a good time. Gotta go *waves*
[13:53] oola Neruda: out of necessity
[13:54] Paula Dix: bye Myriam!
[13:54] herman Bergson: Bye Myriam...
[13:54] Ludwig John: we have our language to describe and explain the world
[13:54] Paula Dix: its language is built in in the brain
[13:55] Paula Dix: all humans have it
[13:55] herman Bergson: And in the context of todays's lecture we see that language is an incomplete system
[13:55] Paula Dix: and most probably many other species also
[[13:56] Paula Dix: exact, its imprecise... but it wonders me that math is also like that!
[13:56] herman Bergson: So…always work to do for a philosopher
[13:56] Paula Dix: lol
[13:56] Kurk Mumfuzz: hehe...
[13:56] Lovey Dayafter: you will always have a job to do
[13:56] herman Bergson: So I would saugest to conclude that we have to stay sharp and philosophical
[13:57] herman Bergson: as paradoxes show is that there are some flaws in our system
[13:57] herman Bergson: But we can live with them perfectly
[13:58] herman Bergson: For we stall havent solved the Lair paradox after 2300 years and we are still here
[13:58] Lovey Dayafter: what is the next discussion about?
[13:58] herman Bergson: This weekend I will do the final count on the voting...
[13:59] herman Bergson: at the moment most votes go to the Modern theories of Ethics
[13:59] Kurk Mumfuzz: (sorry, folks, gotta go... thanks for an interesting hour... )
[13:59] Paula Dix: yes, its really amazing that we can go to the moon even with paradoxes showing the system has flaws!
[14:00] Paula Dix: bye Kurk
[14:00] Ludwig John: bye I have to go too - good night
[14:00] herman Bergson: Well Paula, in former lectures we already had concluded that there is no absolute truth and yet some things are true
[14:00] Paula Dix: bye ludwig
[14:00] Frederick Hansome: Thanks, herman
[14:00] Violette McMinnar: good night all
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[14:00] herman Bergson: Bye Ludwig
[14:01] herman Bergson: Thank you all.....class dismissed for today