What is an Axiom? (Philosophical Definition)

This video covers the philosophical definition of an axiom of a logical system. It explains the difference between an axiom and a postulate, a theorem, and a definition, including examples.

Sponsors: João Costa Neto, Dakota Jones, Thorin Isaiah Malmgren, Prince Otchere, Mike Samuel, Daniel Helland, Mohammad Azmi Banibaker, Dennis Sexton, kdkdk, Yu Saburi, Mauricino Andrade, Diéssica, Will Roberts, Greg Gauthier, Christian Bay, Joao Sa, Richard Seaton, Edward Jacobson, isenshi, and √2. Thanks for your support!

Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more! (#Axiom #Logic)

[danielray]

I would say "some parts of mathematics" is an understatement. they are everywhere on mathematics, not especially on geometry, but especially in set theory

[JIYOSHI]

An axiom is cool sounding word and its my favorite word.

[GodsOwnPrototype]

This is why I frequently refer to axioms with materialist atheists as 'articles of faith' & speak of traditional articles of faith as 'religious system axioms'.

[curtd]

NOTES
Spectrum of Rules of constant relations from which we perform deduction, induction, abduction, and guessing (trial and error).
1. Axioms must be declared: Ideal. Arbitrary. Presumed(declared) True. Used in formal Logic, Mathematics.
2. Premises may be assumed, and may be true, false, or unknowable. Pragmatic. Used in argument.
3. Laws (Theories) must be identified: Real. Laws are true with stated limits. Constrained. Used in Sciences.

The most common problem I deal with correcting is the conflation of the three.

[chrissidiras]

Could you make a video on non-Aristotelian logics?

[munstrumridcully]

I think the best axiom is "whatever system can help us to best navigate experience is preferred"? Pragmatism, I guess?

[GabriTell]

Good video!

As a Math Degree student, I couldn't give a better definition of "Axiom". All in Maths is constructed either by axioms or by definitions, and in many cases you use "axioms" in order to define something.

For example, if you want to give necessary condition for anything to be called "Set", you give a set of rules that must that must be verified (in this case, the ZFC axioms). It's not like an universal set of rules, but an universal set of rules that must be fulfilled if you belong to the class of "Sets".

Similarly, the peano axioms give a necessary condition for anything to be a "natural number".

[DennisPulido]

Also another question - since axioms are presumed, doesn't it make axioms subjective inventions rather than universal objective truths?

[joonalehtinen]

Why can't this be an axiom: "something can exist" only the existence of that idea proves that it's correct. It doesn't need anything outside of it to be true

[Anonylek]

Thank you so much this made things vary clear

[kemar]

This video explain axiom really well. But i want to ask something. Isn't the fact that we believe our minds are able to reason or find truth is an axiom by itself? We believe that our mind have the capability to find truth by the get go right? We assume that is true withouth any proof.

And even if we try to find proof that support our assumption that our mind can find truth. It's going to end up in a contradiction. Because to find proof that our mind able to reason, firstly we have to assume the very thing we are trying to prove.

So based on this, i conclude there is actually some axiom that we have to take.because without, we couldnt know or believe anything.

[Naijiri.]

How do we define _proof_, without a system of axioms?

[vinceofyork]

I personally find Tetralemma logic found in the east to be more viable and less rigid than the binary logic found in the west. It also helps in understanding quantum physics which wouldn’t make any sense using the rigid forms of binary logic.

[louisng]

Axioms in mathematics is not particularly special to geometry. Most of mathematics work off axioms. Notable examples include the Peano axiom, the field axioms, and the Zermelo–Fraenkel axioms.

[nathanboy]

If Axioms are statements that are presumed true without proof. Then how can they be the basis for proving a theorem to be true?

[rubenc]

Hmmm I believe that there are things that are self-authenticating.

[cromi]

Hey, I love your videos, I am learning so much from them. However I keep on stumbling on your claim that you are a sceptic. Something feels off about it. You said that as a sceptic, the axiomatic nature of logic is problematic. However, it seems to me, that scepticism itself rests on one or more axioms. The main axiom of a sceptic is that one should doubt claims, which one has not proven. This itself seems axiomatic to me. More then that, as it is an axiom, it is a self-contradictory one, because it claims that axioms themselves are not valid.

[michaelpisciarino]

Action + Backround rationality that promotes said action

[reginaldcruz]

Random qwesh but what font is this video in? I just gotta know

[missworldtamil]

I have to write a free essay after the holidays. The theme is, “Life is not an axiom. ” I know basically what an axiom is, but the subject itself doesn’t make any sense at all. Can someone help me there??? Because I can’t ask the teacher, because it’s holidays.