Introduction to Set Theory | Logic | Attic Philosophy

Sooner or later, you're going to need to know the basics of set theory. It can look really confusing, but actually it's not so bad! With just a few simple concepts, we can quickly get to grips with a fair bit of basic set theory as it's used in logic. In this video, I'll go over the basic concepts of set theory. In the follow-up, we'll look at the more philosophical side of things and ask, exactly what is a set?

00:00 - Intro
01:19 - What is a set?
04:11 - Membership
05:13 - Subset
08:37 - The Empty Set
10:34 - Set identity
11:30 - Operations on sets
15:06 - Power set
16:57 - Set comprehension

If there’s a topic you’d like to see covered, leave me a comment below.

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#logic #sets #philosophy

[BillboMC]

Lmao this channel is carrying me through first year. I love the videos!

[re-know]

Really, really enjoy this channel and your way of expounding knowledge. I’m a graduate student pursuing an MS in Risk Analysis in the US, but have always been extremely fond of mathematics and philosophy…and low and behold Set Theory is the bridge that connects them both! … Keep up the word class videos, lord knows we, the viewers, need and appreciate them!! 🤙🏻🤙🏻

[andrewwilson]

All great videos a difficult subject like Philosophy broken down into subdivisions easily explained

[voidzennullspace]

This is a phenomenal YouTube channel! I'm an aspiring mathematician, as well as an undergrad in both pure and applied mathematics, and so many people ask me where they can go to get a fundamental understanding of proofs and logic to improve their mathematical abilities. Namely, in areas like topology(an understanding of set theory is, of course, crucial in topology), real analysis, etc. Now I see why every pretty much mathematician claims that mathematics is just applied philosophy! I was wondering if you had any recommendations for books I could use to study and learn logic from a more philosophical perspective rather than just my typical mathematical perspective. Thanks for the great content!

[oniowolabiezekiel]

Can you give lectures on mathematical induction pls?... And explain how it can be used to prove some theorems in logic.

[harshavarsniv]

Very helpful video!👍 Could you cover relation and functions in terms of sets?

[karlfriedmann]

Great video :)....I just got curious thinking about membership: Is membersip (or y is an element of y) introduced as primitive or can it be defined in some way ?

[Bunnokazooie]

Dr. Jago, what makes mathematical logic different from plain old logic?

[ericd]

Hi Professor Jago, I was wondering if we could distinguish two empty sets by distinguishing their complements relative to their respective domains. That is, if the empty set isn't understood simply as a set with _no_ members, but as a set with no members _from a specified domain_, then couldn't each empty set have a distinct property and thus be distinguished from one another? So, suppose one domain is all the constituents of possible world W1, and another is all the constituents of possible world W2, and suppose no constituent of W1 is in W2, and vice versa. Then the empty set relative to W1 will be distinguished from the empty set relative to W2 by its distinct complement. So my first question is, is this sort of move permissible? And my second question is, to prevent this sort of move, must we conceptualize the empty set as empty relative to all possible objects or some totalizing domain (or something like that)?

[BillboMC]

Hi Attic! idk if you take questions in the comments but can you explain the answer to A ^ B |- A -> B

I tried assuming A then trying to get to B but ik that A is already true and so is B so assuming something I knew to be true felt weird.

[jeevsa]

I haven't studied much mathematics so will I have trouble taking logic.Im ready work hard.Somebody please reply.