Recent content by Mathelogician

You don't have to use perfect circles in Venn diagrams. Try more complex figures! Also you don't have to show the intersections with shadows only! You can try figures containing objects.

It seems it's the case that circles are filled up with numbers (look at numbers as objects like tomatoes!) and the image is asking you find solve the desired equations. Just you should decide at first the sets A, B and C in the image! unless you would not be able to solve it:). For example, for...

You mean that a formula of the form ( Ex A(x) -> A(c) ) for some constant c, is also a formula of existential form? I thought a formula of existential form is of form Ex (Ax). May you explain more?

Look at the picture; i need to know why the red part holds? I mean in T*, we have added proper constants to all 'existential formed' sentences of T. So what would remain from such formulas that the red part mentions and that we use the lemma 3.1.8 to overcome the problem? - - - Updated - - -...

As you said, I tried to solve it explicitly and exactly. The book doesn't explain about definition derivations in predicate calculi; It just adds two rules to the propositional rules of natural deduction. But if i guess right about the atomic formulas that they are the BASIC step of the...

Thanks... I'll try it and talk about my thoughts.

Hi all, I need Explanation on the attached image from Van Dalen's Logic and Structure; specially on how the red part follows from the lines before it! Regards.

I think my problem with the concepts of closed and open hypotheses is more philosophical than mathematical. You may remember that we have had a discussion on that before! but now i think i am still unconvinced about that! So i prefer to first talk about those concepts (Closed and Open...

Re: A question on 'universal quantifier Intriduction' rule in Natural deduction of Predicate logic I mean: how do we ensure this?!

Re: A question on 'universal quantifier Intriduction' rule in Natural deduction of Predicate logic I mean how these two assertions are the same? 1-The variable x does not occur free in elements of H. 2- those hypotheses which contain x as a free variable, get canceled before using the...

Re: A question on 'universal quantifier Intriduction' rule in Natural deduction of Predicate logic Perfect! Just a 2questions: 1- Is the tactic (which here for example comes from the axioms of the structure) to reach phi, included in the inference tree? Or we just use the tactic outside of the...

In Natural deduction in Predicate logic we have a rule which says [assume the set of hypotheses to be H) if H implies phi(x) then H implies [for all x phi(x)] such that x doesn't belong to FV(psi) for all psi in H [indeed such that x occurs free in no one of formulas in H] In other words, if...

Of course they are axiom schemes; but I'm afraid my question is something else! Thanks.

Hi all; Look at the attached part from Van Dalen's Logic and structure. What is he doing exactly? In axiomatizing 'Identity' as he does, what is gained rather than what we had before (i.e., looking at 'Identity' as a binary predicate)?! Even in the axioms, he is again using a symbol in the...

Perfect! As always...