Are These Logic Problems Valid or Invalid? A Scientific Analysis

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Discussion Overview

The discussion revolves around the validity of two logic problems presented by a participant. The focus is on evaluating logical statements using different deduction systems, exploring their implications and interpretations within the context of formal logic.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents two logic problems and requests assistance in determining their validity.
  • Another participant asserts that the first statement is valid based on axioms and universal specification, while the second is deemed invalid, citing an analogy with apples.
  • A subsequent participant questions the use of different symbols and confirms their understanding of the first statement as valid based on their interpretation of deduction systems.
  • Another participant mentions using a different deduction system (intro-elim) and expresses unfamiliarity with the original system used by the first participant.
  • One participant suggests that despite the different systems, the results regarding the validity of the statements may still align, proposing that the first is valid and the second invalid.
  • Another participant expresses a positive reaction to the discussion and shares their experience with learning about deduction systems through different resources.

    • Areas of Agreement / Disagreement

    Participants express differing views on the validity of the logic problems, with some asserting validity for the first statement and invalidity for the second, while others acknowledge the use of different deduction systems leading to potential variations in interpretation. No consensus is reached on the overall validity of the statements.

    Contextual Notes

    Participants reference different deduction systems, which may affect their interpretations and conclusions regarding the validity of the logic problems. There is also mention of varying familiarity with these systems, which could influence the discussion.

    Who May Find This Useful

    Individuals interested in formal logic, deduction systems, and the evaluation of logical statements may find this discussion relevant.

Kr1s
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Hi people, I'm trying to solve a logic problem but I'm having some issues with a couple of them. I appreciate if you can help me with it.

1.- (∀x) (∃y) (x=y)
2.- (∃x) P(x)→(∀y)P(y)

Demostrate if valid or invalid each one.

Thank you!
 
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(1)
a=a (axiom)
(Ey) a=y (E+)
(Ax) (Ey) x=y (A+)

(2)
definitely invalid. If an apple is rotten, it does not mean all apples are rotten.
 
First at all, thank you for your answer. Now, I have a few questions because looks like I use another symbols .

(1)
a=a (axiom) This means the Universal Specification Ax, where x is a, right?
(Ey) a=y (E+) And this is the product of the US.
(Ax) (Ey) x=y (A+) This is the result adding the Universal Generalization.

Hence, this one is valid.

Tell me if that's right please, thank you very much!
 
Oh I think you are using a different deduction system. I am using the intro-elim system, which is a little different, and is more popular with philosophers. I am not too familiar with your system, so can't you , sorry.
 
Well when I saw your solution I inmediatly thought that you were using an equivalent to quantifier logic. Results are the same though, so It may be the same answer. First one valid and second one invalid. What do you think?
 
Intuitively yes :)
I have seen your system before. I think some of these logic for dummy guide teaches this system. I did not really understand it. So I went to read the Schaum series, which teaches the intro-elim system - which i understand. Now I am writing a computer windows program to help me do it on computers
 
Oh, ok. That's pretty awesome, the computer windows program. I wish you succes with it. Thank you for trying to help me. ;-)
 

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