Predicate Logic Semantics - Models

In this video, I give a brief overview of the notion of a model in predicate logic. This video sets the stage for a discussion of predicate logic valuations.

_____________________________________________________

[DJCNK]

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

[philosophyversuslogic]

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

[luiz]

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

[schalkzijlstra]

Thanks for going slow and not rushing.

[jonz]

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?

[connorkianpour]

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.

[hannahcora]

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

[Peepeeloo-pee]

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

[s.o.peprah]

This is amazing and so good. Keep it up!

[obrown]

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

[keivwangz]

you just saved my life lol. amazing videos!!

[francescovaglienti]

This is incredibly clear and useful thank you so much.

[agnivobanerjee]

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

[daffmaul]

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

[theodore]

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

[diegoaraujo]

("_" 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

[Whositlover]

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

[ManInTheTimeMachine]

giving me mad anxiety bro, but thanks