Predicate Logic Semantics - Models

[@DJCNK97]

wow this is the best explanation on predicate logic on youtube.

[@LogicPhilosophy]

Thanks. Hope it helped!

[@philosophyversuslogic]

Someone has already said it, but I can positively confirm that - these cycle of videos are the best on the whole Internet. Absolutely!

[@luiz8098]

I was clueless with the material my professor provided me with, but now I see the light! Thanks!

[@LogicPhilosophy]

Glad I could help! Good luck!!!

[@schalkzijlstra878]

Thanks for going slow and not rushing.

[@LogicPhilosophy]

No problem 👍 Good luck in your logic journey!

[@connorkianpour1077]

Currently in grad school for philosophy, and have a final for logic coming up. I, like many others in my class, was already struggling with logic before the pandemic struck. Now that everything's been moved online and my professor has in no way adjusted his expectations for students with respect to command of the course material, I am struggling even more. These videos have been more helpful than I can possibly articulate. I feel like I am actually understanding predicate logic.

[@LogicPhilosophy]

Thanks for your really kind comments about my videos! Would be interested to know what topics your graduate course covers. I've thought about making a series of videos on either metatheory, modal logic, or various nonclassical logics. Good luck!

[@connorkianpour1077]

@@LogicPhilosophy Truth tables, logical translations, propositional logic, predicate logic and identity, and some modal logic. We do a bit of metatheory as well. The way you explain concepts is extremely helpful; please keep doing this!

[@rss2729]

😅 BL

[@rss2729]

Bbbb

[@hannahcora5939]

this is 10x better than my prof. pls keep making more videos about computability and logic

[@LogicPhilosophy]

I appreciate this! I'm hoping to do more in the spring of 2021. Some on modal logic, Russell's theory of definite descriptions, and maybe some stuff on theories of computation. But this is hopeful! Best wishes!

[@Peepeeloo-pee]

you know how to drive message home...Good job !

[@agnivobanerjee2864]

please do on algebraic or fuzzy logic too :)) great work!

[@VietnamSteven]

Thanks for this fantastic video!

[@s.o.peprah7114]

This is amazing and so good. Keep it up!

[@LogicPhilosophy]

Thanks!

[@EduardoMengesMattje]

Very good

[@LogicPhilosophy]

Thanks!

[@obrown4331]

Thank you so much you saved me just before my exam!!!

[@LogicPhilosophy]

+O Brown no problem. Good luck!

[@PETERKENTISH]

Very helpful! exam tomorrow :)

[@LogicPhilosophy]

+Peter Kentish thanks, and good luck!

[@PETERKENTISH]

Thanks, I dont suppose you could help me with a question I have? I would have to send a screenshot which i dont think i can do here

[@francescovaglienti2827]

This is incredibly clear and useful thank you so much.

[@LogicPhilosophy]

you are very welcome!

[@monoman4083]

nice and clear so far, thx..

[@LogicPhilosophy]

Appreciate it! Taking a class?

[@jonz9813]

nice tutorial! I have a question about the interpretation function. In the example that name a is interpreted to one, aka I(a) = 1, what is "a" and "1" in terms of the set of symbols from your first tutorial? Are they both names? Does this mean an interpretation function is a map closed under domain?

[@LogicPhilosophy]

Here "a" is a name in the language of predicate logic where "1" would simply be the integer 1 (I'm using it as a dummy object here so "1" could be whatever item you want it to be from the items you want to talk about. I could have just as easily picked people: Jon, Jill, Liz, et alia.). The basic idea is that the name "a" refers to the number 1 just as a proper name "David" refers to the person David. I know that sometimes people distinguish maps from functions (and I don't know enough to appreciate the difference).

[@jonz9813]

Logic & Philosophy thank you very much! Love your tutorials. Super helpful

[@GustavoOliveira-gp6nr]

It makes more sense if you imagine "a" as a physical symbol to represent an abstract idea and "1" is the idea. Actually while writing this very text, i am using the indoarabic character "1" to represent an idea, which is the idea of the integer number greater than zero and less than two. Imagine you are solving an equation and you come up with a solution "a=b". That means that "a" and "b" are symbols that stand for the same mathematical object, which is unique. That is what he meant in the video when he said two symbols can stand for the same mathematical object.

[@gingerbeardworkouts2955]

Great explanations ! Thanks

[@LogicPhilosophy]

Appreciate it!

[@daffmaul9813]

First video I have seen from you and I think its damn good

[@LogicPhilosophy]

Awesome! Appreciate the feedback.

[@theodore8178]

I like the empty domain. Anything I want to say about the elements is true. And proofs are much faster.

[@LogicPhilosophy]

Yes. Isn't that strange? It's true if you are saying "All men are mortal" when there are no men, but you run into issues if you say something like "there exists a man" since the truth of that wff would imply the exists a man.

[@theodore8178]

@@LogicPhilosophy right

[@keivwangz]

you just saved my life lol. amazing videos!!

[@LogicPhilosophy]

+Austin Genovaczeck your welcome

[@dvendator]

this is great!!! Thankyou

[@LogicPhilosophy]

You are welcome. Best wishes!

[@scovila]

Thanks!!

[@LogicPhilosophy]

Ur welcome

[@viktorbonev5654]

RESPECT!

[@LogicPhilosophy]

Respect right back to you!

[@diegoaraujo4141]

("_" means subscript, quantifiers are specified in brackets) Hi David, I am having trouble with an unsure conclusion that i share with Gamut's Logic, Language and Meaning. Chapter 3, exercise 9: Prove that ( [for all]x(fi) → [t/x](fi) ) is universally valid (using valuations under a model M and an assignment function g). The demonstration that the book gives (pp. 249) goes like this. "Suppose V_M,g([for all]x(fi)) = 1. It is to be proven that V_M,g([t/x](fi)) = I. That V_M,g([for all]x(fi)) = I means that for all d [in] D, V_M,g((fi)) = 1. In particu- lar, [[t]]_M,g is such an element of D. From this it follows that V_M,g([t/x](fi)) = 1 (strictly, this should be proven with induction on the length of (fi))." My concern is: from where does it comes the assumption that every name or variable "t" member of L is defined for the interpretation function I? Couldn't just exist a term t such that I(t) = undefined? In such a case, I(t) [not member of] D, where it follows that there is a counter-example to the universal validity of the initial formula. Nevertheless, great videos and promulgation of logic to youtube :D

[@LogicPhilosophy]

So your question concerns an earlier part of Gamut's book where they define the Interpretation and variable-assignment functions. While there is no guarantee that everything in the domain has a term that picks it out, your pointing out how can they assume that every name picks out an element in the domain. It is pretty standard for logic textbooks to make this assumption and when they do, it is nothing more than an idealization (or just pure stipulation). I imagine there is a debate over it but where you would look to see if anyone has argued for this is the literature on Free Logic or anything on empty names or non-referring names. So, yes, it could be the case that there are terms (e.g. names) that are undefined for certain models. As an example, suppose our domain contains only living physical objects found here on planet Earth in 2018, the name "Pegasus" would thus be non-referring or undefined for the interpretation function. In short (but I'd have to check on this), I would imagine that a logic that doesn't make this assumption (aka free logic) would not regard the formula in question as being universally true. That is, even if we assume that (Ax)(fi)=T, it isn't the case that [t/x](fi)=T for all terms (t).

[@ManInTheTimeMachine]

giving me mad anxiety bro, but thanks

[@LogicPhilosophy]

Hope it ain't me that is giving you that stress. Good luck!

[@Whositlover]

why to logic professors have such hard times teaching it...

[@LogicPhilosophy]

Not sure about the question but sometimes the discussion of models isn't terribly clear in introductory logic textbooks. There are some exceptions though! Hope the video helped. Good luck!