This Lecture Will Surprise You: When Logic is Illogical - Professor Tony Mann

Mathematics offers certainty. That there are infinitely many prime numbers or that four colours suffice to colour any map so that adjacent regions are differently coloured are statements which have been rigorously proved so that there can be no doubt about their truth.

Mathematics, uniquely amongst human activities, is grounded on absolute truth, or so it has seemed to generations of mathematicians. But what happens when there appears to be contradictions in the logic on which mathematics is based?


This lecture will explore paradoxes which cast doubt on logic itself. I guarantee that you will be surprised!

[tsc]

I'm dreaming I'm a man listening to an incredibly witty lecture that illustrates the problems associated with reason as it's practiced by humans. When I wake up and am a butterfly once again I'll see the truth of it all. Thank you for the lecture.

[FlockOfHawks]

It took a few minutes to get used to this man's way of talking, and then i rewound . This lecture is brilliant !

[Rog]

He must be a poet, as all his sentences are rhythmic.
A Paradox is a creation of language.

[miroslaw]

at 5 minutes and 9 seconds is mine illustration of doctor, istockphoto probably sold it to Microsoft clip-art? fun to see it as a Pair o' Docs :) all the best !

[RickDelmonico]

If all of the information stored in the universe is stored as relationships
then, meaning becomes an essential component and truth is relational.
If it doesn't apply it isn't true. When the philosopher makes a
statement that can be both true and false, he should realize that the
statement has no application. He is not being clever, nor is he being
wise. A pointless pursuit is always pointless. Thus we should
simplify for clarity and application. Simpler is almost always closer
to truth. Additional note; we are talking about a hologram with a
fractal probability distribution so, even logic (fuzzy) has a fractal
quality to it. Explanations can be in the form of nested hierarchies.
In the end, all we have are the relationship of measured things and
incomplete descriptions.

[kennethflorek]

I don't see that paradoxes cast doubt on logic itself. In a paradox we see that not every starting point produces results free of contradiction. What I see in most of these paradoxes is that the scope of application of the assumption gets enlarged past what you may have originally envisioned, to pertain to itself. With good luck we arrive at circular reasoning, which is worthless. With bad luck we arrive at a contradiction, which is worse than worthless. Your understanding is not improved any more by knowing "This statement is true" is consistent than it is in knowing "This statement is false" is inconsistent. The self-aggrandizing presumption of omnipotence it takes to seriously believe you could prove the consistancy of mathematics itself is mind-boggling.

[fandore]

thank you Tony Mann, i have been trying to say this for years now.

[alexandragroombridge]

Semantics obscures the lack of logic in many of these examples. For example, with Plato and Socrates on the bridge; if the statement 'You will throw me in the river', then he must first be thrown into the river before the statement proves to be true. Only then should he logically be allowed to cross. How many philosophers does it take to change a light bulb? well it all depends on what you mean by change, I suppose.

[SamuelJohnUs]

Don't many of these aparent paradoxes vanish with careful application of the law of non-contradiction? Namely: "in the same sense at the same time"?

[chazbuck]

Questioning the presuppositions, the terms and whether they are indeed truthful and accurate especially if they are translations from other languages. IE. Hebrew, Greek, and Latin.

[gvardon]

I found the lecture interesting and logical.  This is a paradox of sorts because Professor Mann implied that his would show that logic is illogical.   

[haydentrozzi]

This is just general knowledge for anyone who understands solipsism. After 47 minutes we have gained no knowledge if anything particularly important from this. The whole world could just be your internalized lie for escaping the actuality. It's just a perception.

[Dyslexic-Artist-Theory-on-Time]

This lecture will explore paradoxes which cast doubt on logic itself. I guarantee that you will be surprised! 

[xoppa]

32:35 why does he say there is a number less than n^140 that can't be put in a tweet of 140 characters, if he just finished saying that there are n^140 possible different integers that you can put in a 140 character tweet. maybe there is a number greater than n^140?

[davidwilkie]

(Not wanting to get into logical difficulties, but...) The paradoxical postulates all seem to be suspended in a knowledge vacuum where the facts of the situation should decide outcomes, meaning that it's all talk. And the equivalent mathematical postulates deal with undefined values without a relationship, and that is like division by zero. So if the sets do not have a basis in a common standard, comparison is invalid. (?) (..my own choice for removing paradox, but I don't know if someone has already tried this or not; and I'm not worried about it)

[marksmith]

The false dichotomy that is only two possibilities- truth or lie but in reality there is a whole shade between the two extremes and similarly many other paradoxes evaporate once sophisticated logic is added.

[lyrimetacurl]

Before I say anything, I'd just like to say a few words.

Next 👏 comment 👏

The interview and Cretan lies do have a back door:-

In the first one, the interviewee was telling the truth (at that moment) that he *would* lie.

In the Cretan one, he was lying that Cretan *always* lie - because sometimes they tell the truth.

However, "this sentence is false" has no back door. Unless you conclude: "it is true that it is false" and stop there without thinking more about it...

Next 👏 comment 👏

Not all words are either "Heterologous" or not - for example, the word "Paradoxical" is neither paradoxical nor not paradoxical.

[marksmith]

A set of all sets is not a set- it is a superset.

[founderofisis]

I don't understand how logic can be illogical and yet valid and not a reductio ad absurdum thus inferring some disproof.

[tonyrosam]

pi is an irrational number.

true or false? 
:) good luck!