Introduction to Predicate Logic

[@hevanhull2239]

1 video down, 17 more to go. Thank you for producing such a great quality educational series on RL (and PL).

[@LogicPhilosophy]

thanks. Good luck!

[@danielamartinez8939]

Thank you for this video! It is very clear, and the examples are very helpful.

[@LogicPhilosophy]

Super glad I could be of help!

[@lucarauchenberger628]

wow AMAZINGLY EXPLAINED!

[@LogicPhilosophy]

Many thanks!

[@Agustinoism]

Is set theory part of predicate logic or is it based on predicate logic

[@Mishkafofer]

Well done.

[@LogicPhilosophy]

thx!

[@oumdead9542]

Is this really a good example? Why couldn't we frame it has : S : Socrates, Mo : Mortals, Men If Men, then Mo If S then Men If S then Mo which is a valid argument in propositional logic

[@LogicPhilosophy]

Great question! I like the idea since there seems to be an explosion of different kinds of logics and sometimes people say "ok, what is the point of this addition!?!" A couple points. 1. In propositional logic, "S" needs to stand for a proposition (or wff, or sentence, or something that can be true or false). But, on your translation of "S", you treat it as a name "Socrates" (or sub-sentential / sub-propositional item). 2. It isn't totally clear what the sentences in your argument are saying. Take the conclusion "If Socrates, then mortal". This wouldn't be grammatical and the conditional would need to consist of two propositions P, Q connected by the arrow. Maybe you want to say something like "If Socrates exists, then Mortals exist", but this isn't the conclusion of the argument in question since the conclusion in the example says that "Socrates is mortal". Maybe I'm misunderstanding.

[@oumdead9542]

@@LogicPhilosophy Yeah I see what you mean. To I clarify, I can say: S:The entity x is Socrates Mo : The entity x is Mortal Men : The entity x is a man where "the entity x" is a generic reference to the subject of the discourse. I guess what I'm trying to say becomes much more convoluted expressed in this language compared to predicate logic, but it is still "valid", no? However, I can imagine that there are indeed examples of valid arguments that can't be expressed at all in propositional logic, I'd be curious to see an undisputable one.

[@archetypalmuse]

I was also confused by this. From what I learned, you could illustrate this as: ((M --> Mo) & (S --> M)) --> (S --> Mo). Now you might have to switch those things around to get your transitivity right but I just did the damn truth table and this is a tautology! I believe the mistake is translating the whole sentence into one letter, whereas each element of the sentences needs to be a letter. Kind of confusing.

[@AlainGenestier-tj8fn]

@@LogicPhilosophy I think this has nothing to do with existence. However, the translation of the argument stated in English to : S stands for "being Socrates" Ma stands for "being a man" Mo stands for "being mortal" S |- Ma Ma |- Mo hence S|- Mo isn't a perfect translation (it is quite artificial). Indeed, the problem can already be seen with S. What does it assert ? It can only have a meaning when assessed about an individual --i.e. in a disguised form, it is already a predicate : S(x), which is true if and only if x is Socrates. To assert that the (now deceased) person known as Socrates is mortal, you have to add S(Socrates), which means "Socrates is Socrates". In proposition logic, S can only be a formal symbol ; for every object x of the discourse you have to create a symbolic proposition X with intended meaning "being x" (but this intended meaning can not be expressed in the language of PL). Not a very appealing "solution"! The expressive power of predicate logic comes from the introduction of terms x, y,... which stand for variables, the grammatical possibility of substituting terms to variables, the grammatical possibility of forming predicates P(t,u, v,...). AND from the introduction of the two quantifiers \forall and \exists, which allow the formation of new predicates with a reduced number of variables. At first sight, the quantifier \forall seems dispensable (a proof of "\forall x, P(x)" is merely a proof of P(x) without an additional hypothesis on x) but the subtle point is that it allows the formation of the new predicate Q(y)=\forall x, P(x,y) from the predicate P(x,y).

[@MathCuriousity]

What if I replaced “all men” by just “men”? Would it work then?

[@monoman4083]

nice lesson thx..

[@LogicPhilosophy]

Thanks

[@sumanthprasad9135]

Is this course suitable for artificial intelligence (computer science) or only for philosophy?

[@LogicPhilosophy]

I'd say that if you are learning AI / computer science, then whatever language you are learning (e.g. Python) will already teach you the propositional calculus. I'd say that a dedicated course in AI / ML would be more beneficial if that is what you want to learn.

[@sumanthprasad9135]

@@LogicPhilosophy Thank you so much for replying.. This helped me ☺️

[@timothywise9731]

You say all men are mortal, then you Socrates is a man, then you it is false that Socrates is mortal. How is that false? Thats illogical by the definition of logic that I am familiar with. Did you make a mistake?

[@LogicPhilosophy]

thanks for the comment. I think I said it is impossible for the premises to be true and the conclusion to be false. That is, it cannot be the case that (1) all men are mortal is true, (2) Socrates is a man is true, and (3) Socrates is mortal is false.

[@ReginaldAplenty]

Nobody else here thinks Symbolic Logic is a total farce, and "crock of shit" as my grandmother would say?