Predicate Logic, Proofs (Universal Introduction)

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This video covers the use of Universal Introduction (also known as Universal Generalization) for predicate logic proofs. I explain how the rule is used and its restrictions.

Timestamps
00:00 Introduction
2:00 Restrictions
8:35 Examples
11:58 Review

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Thank you so much, this was so helpful. Specifically, thank you for the examples!

kcmayoco

thanks, you're the only one who made a decent video on this. idk why my teacher covered this in like 5 seconds and expects us to do so many proofs using these rules

violinsheetmusicblog

It's not that the name could be any name - it's because whether a lowercase letter can be interpreted is a variable proper or a name is totally determined by the context

We don't have a set of lowercase letters that are fixed name symbols and a set of lowercase letters that are variable symbols - we have a set of uninterpreted symbols that are lowercase letters, and depending on the context those lowercase letters may either be variables or constants/names

A constant/name is just a symbol which you're not using at any other point for a variable and you're not using it at any other point for a distinct object!

The interpretation of lowercase letters as variables/constants is context specific!

Flynn-hlug

Thank you for your lectures! Must say that I never support the arbitrariness, and will never do. This idea of arbitrariness as well as universal introduction/existential instantiation both are taken me as wrong, and non-logical. (They are indeed non logical.) But what I've got against the idea of generalizing the arbitrary variables? Here is it. Usually, we use the arbitrary examples in a way like this:
1) if a triangle's sum of angles equals 180, then each (all) triangles have sum of its angles equal 180
But what about this example:
2) If Fido loves bones, then each dogs (that are like Fido) love bones
Usually they don't allow us to generalize the constants, but is it so? Fido can be assumed as some kind of a model for any Fido-like models. I see absolutely no difference between arbitrary constants and variables. They must be identical according to their own meaning. The next two examples:
3) if a house is for to live there, then all the houses are for to live there
4) if a hat is to wear it on a head, then all the hats is to wear them on heads.
We can pluralize the examples finding more and more wrong ones. I am disagree with the idea of arbitrariness, and cannot accept it. That's why Predicate logic is assumed for me as less perfect, than propositional logic. Maybe Predicate logic must be limited by UE and EG only. This type of logic can be solved algorithmically if we accept that any possible truth tablets for them will have the same patterns for different cases. Predicate logic as far as I know was invented for mathematician's purposes, but even if it works good for them, it doesn't mean it reflects our thinking. I am sure it doesn't do it.

philosophyversuslogic

Pls we need your videos completeness theorem and related theorems. I will be anticipating your reply. Thanks 🙏🏻

oniowolabiezekiel

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