Professor Thorsby explains how to use the rules of inference in predicate logic using the the Universal Generalization, Universal Instantiation, Existential Generalization, and Existential Instatiation rules.
From 100 level - 300 level, wednesday 13th of March 2024 will be the day I will be writing my last symbolic logic exam in Philosophy department, university of Lagos, Nigeria. All thanks to you Prof. Mark Thorbsy for making symbolic logic easy for me all through the years✨🙇🏾♂️😮💨
It's so helpful to just hear/see another way of explaining the rules and how to approach the proofs. And it's especially helpful for me since we are using this same book. Thank you!
Great video. But how can we recognize the scope of qualifiers. Like Q12, ∃x Ax → ∀x(Bx → Cx), why doesn't ∃ cover the first arrow? In short, why is ∃x( Ax )→ ∀x(Bx → Cx) correct instead of ∃x( Ax → ∀x(Bx → Cx) )?
28:10 instead of calling the constant implied by Ex Fx a 'mechanical device' it might be better to call it an auxiliary constant, since the existential instantiation gives the (previously not used) constant an auxiliary or perfunctory (stand-in) role. The referent of this auxiliary constant is a real thing, though we may not be able to pinpoint what or who exactly it is. Whatever it is, it exists and we call it 'a'. But i wonder how the axioms of predicate logic actually allow for this, since in a given model the constants refer to specific fixed objects. The constant 'a' refers to some specific individual or object, it is not available as a 'constant placeholder' so to speak. I guess you could make a 'without loss of generality' meta-logical argument - ignore what 'a' previously referred to and use it now to label the referent of Ex Fx.
You really didn't have to instantiate twice for #9. Rather, it can look like this: 1. (x)(Ax>Bx) 2. ~Bm / (3x)~Ax 3. Am>Bm (1 UI) 4. ~Am (2,3 MT) 5. (3x)~Ax (4 EG)
