How to translate Quantifiers in Symbolic Logic | Attic Philosophy

In this tutorial video, we look at how to translate the quantifiers in First-Order Logic, EVERY and SOME. We'll translate some example English sentences, of increasing complexity, into quantified logic. Along the way, we'll look at some of the issues that arise.
00:00 - Intro
01:37 - Anna goes
01:51 - Someone goes
02:16 - Everyone who goes is happy
03:12 - Someone likes everyone who goes
03:49 - No one who goes is unhappy
04:36 - Everyone who goes likes someone
05:11 - Everyone who goes likes someone who goes
05:56 - Quantifier order
06:59 - Active and passive
08:49 - Everyone likes someone
This is the second in a series of videos on First-Order Logic. Previously:
How to use Quantifiers • How to use Quantifiers...
Coming soon:
Relations in First-Order Logic
Semantics for First-Order Logic
Quantifier Equivalence
Normal Forms in First-Order Logic
If there’s a topic you’d like to see covered, leave me a comment below!
Links:
My academic philosophy page: markjago.net
My book What Truth Is: bit.ly/JagoTruth
Most of my publications are available freely here: philpapers.org/s/Mark%20Jago
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#logic #quantifiers #firstorderlogic

[@MaruRaida]

How does this only have 56 views??? It must be the youtube algorithm because I just know so many people need this! Thankyou for the vid, your videos are so easy to understand and to the point

[@AtticPhilosophy]

I don't know! Hopefully more people will find it over time.

[@scepticalsaint]

It is great!

[@chachachi-hh1ks]

How to understand different order of quantifiers better: I heard that it can be helpful to imagine expression with several different quantifiers like a game. We go from the left to the right, universal quantifier gives a move to your opponent (and its variable is controlled by them), existentional quantifier gives a move to you(and its variable is controlled by you). Your opponent tries to find such value for controlled variable that to make its scope false at the least once. Expression is true if you will always win. Like in E(x)ALL(y)(Loves(y,x))you move first and then your opponent. You win if you find such x, that no matter what y your opponent will try to use, it will be loved by y. In case of ALL(y)E(x)(Loves(y,x)) the opponent moves first. You win if each time the opponent chooses y you can find such x, that given specific y it will love x. Each time this x can be different, specific only for given y.

[@AtticPhilosophy]

Yes, that's a valid interpretation of strings of quantifiers. Also of box and diamond in modal logic. It can even be fun - you draw out a model and then take turns to move around it, seeing who wins. Practically speaking, however, we rarely get long strings of quantifiers in natural language or in logic classes (usually just 2 or 3), so there's a lot of milage in learning the basic patterns, eg:
AxEy(Rxy)
AyEx(Rxy)
ExAy(Rxy)
EyAx(Rxy)

[@user-sc9ix2by2v]

Thanx for amazing vid

[@AtticPhilosophy]

Glad you liked it!

[@ahmed_mahrouky]

thanks alot , this is very helpful. can ypo recommend a book to solve some solved exercises about symbolic logic

[@AtticPhilosophy]

Greg Restall’s intro book, Logic, is good. I think he has solutions to exercises on his website

[@joes46985]

Not sure AOC is liked by everyone, specially given the current state the US is in lol, but anyways, great video!

[@AtticPhilosophy]

Thanks - and yes, point taken! I like her.

[@matepenava5888]

I believe it is quite impossible to find an individual liked by everybody, but this has nothing to do with logic😅

[@Contribute_TakeCare_Learn_Play]

Damn I'm stupid

[@AtticPhilosophy]

Well, logic makes everyone feel stupid at some point!