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Questions tagged [fitch]

a natural deduction proof environment in Fitch-style calculus for giving and checking first-order proofs (per Wikipedia)

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Does rejecting the law of the excluded middle mean rejecting it for all propositions or only for those one cannot derive?

Wikipedia describes the law of the excluded middle as such: In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is ...
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Why does modal logic need to use ◻◻p?

In Frederic Fitch's Symbolic Logic he proves (11.8, page 66) that "◻p" coimplicates "◻◻p". In 11.10 (page 66), he writes, A system almost the same as the system Lewis calls S2 is obtainable by ...
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How did Fitch's opposition to the Russell-Whitehead theory of types turn out since the 1950's?

In a footnote to Appendix C of Frederic Fitch's Symbolic Logic (page 217), Fitch writes about his article, "Self-Reference in Philosophy": It is reprinted here in order to indicate more fully my ...
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2 simple Formal Fitch Proofs Help!

I'm having difficulty proving these. I've been stuck on them for nearly 4 hours. They seem obvious, but I can't figure how to set up FORMAL proofs for them. Could anyone give me at least clues how to ...
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Prove transitivity in Fitch

How to prove transitivity in Fitch. Is it Ok? | 1. a = b | 2. b = c | 3. c = c =Intro | 4. a = c =Elim: 3, 2 | 5. b = c =Elim: 4, 1
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Given p ⇒ q and m ⇒ p ∨ q, use the Fitch System to prove m ⇒ q

I have spent about 6 hours now trying to prove this using the Fitch system and I just keep going in circles! Attached is one of the 500 attempts :) I have a feeling it's done fairly simply and ...
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Prove ¬∃x ∀y (E(x, y) ↔ ¬E(y, y)) given no premises

The only way I could think of to do this problem is reductio, but since the two biconditional terms are not contradictory, I am pretty stuck.
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LPL ( language proof and logic) - FITCH - 14.12

what's wrong with the last line in my proof? i can't understand the error on line 21 i wrote the important line of the proof : 18 - ∀z (Cube(z) → (z = c ∨ z = f)) 19 - ∃y (Cube(c) ∧ Cube(y) ∧ c ≠ ...
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In fitch, S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R)

Construct a proof for the argument: S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R) I have gotten to the point in the illustration, but I am unable to figure out where to go from here. I get tricked up on ...
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Language Logic Proof Question: ¬∃x∀y[E(x,y) ↔ ¬E(y,y)]

I am wondering if I have completed this proof properly. I don't think I have it right. It's tricky! Conclusion: ¬∃x∀y[E(x,y) ↔ ¬E(y,y)] ¬¬∃x∀y[E(x,y) ↔ ¬E(y,y)] ∃x∀y[E(x,y) ↔ ¬E(y,y)] ¬E,1 ...
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fitch proof chapter 13 exercise 13.49 [closed]

Does anyone know how to solve 13.49 ∃x P(x) ∀x ∀y ((P(x) ∧ P(y)) → x = y) = ∃x (P(x) ∧ ∀y (P(y) → y = x)) and 13.50 ∃x (P(x) ∧ ∀y (P(y) → y = x)) = ∀x ∀y ((P(x) ∧ P(y)) → x = y) I have big ...
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prove: ∃x ∃y (Cube(x) ∧ Cube(y) ∧ x ≠ y ∧ ∀z (Cube(z) → (z = x ∨ z = y)))

I need a formal (Fitch) first order logic proof for: ∃x ∃y (P(x) ∧ P(y) ∧ x ≠ y ∧ ∀z (P(z) → (z = x ∨ z = y))) Given ∃x ∃y (P(x) ∧ P(y) ∧ x ≠ y) ∀x ∀y ∀z ((P(x) ∧ P(y) ∧ P(z)) → (x = y ∨ x = z ∨...
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I am stuck on how to prove the contradiction of R(b,a) can anybody help me?

Here are some well-known properties of dyadic (2-place) relations: ∀xR(x, x) (Reflexivity) ∀x¬R(x, x) (Irreflexivity) ∀x∀y(R(x, y) → R(y, x)) (Symmetry) ∀x∀y(R(x, y) → ¬R(y, x)) (Asymmetry) ∀x∀y∀...
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In Fitch, how does one prove “(P → Q)” from the premise “(¬P ∨ Q)”?

It's all in the question really. I am working on a proof in Fitch for a class, but I am very much stuck. I am proving the tautology that "(P → Q) ↔ (¬P ∨ Q)", and I have already finished half of it, ...
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Formal proof : predicate logic

This is what I need to prove formally: 1.∃x Cube(x) ∧ Small(d) . . . . Goal :∃x (Cube(x) ∧ Small(d)) I have already tried different ways, but I still can't prove the goal. 1. ∃x Cube(x) ∧ Small(d) ...
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Fitch Proof - LPL Exercise 8.17

I am currently finding the third part of this exercise (Conditional 3) difficult to prove. I was sure that my proof was correct, but the Fitch program is saying otherwise. I am finding it ...
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Fitch Proof - Logic LPL 13.11

I am currently doing questions for my course from LPL Chapter 13.11. I have posted the screenshot of what I am trying to do. I am quite stuck and I can not think of a way to get to ~Tet(a). Any hint ...
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Suppose A is a set of premises of an argument and B the conclusion of that argument. Prove that if A U {¬B} ⊢ ⊥, then A ⊢ B

Suppose A is a set of premises of an argument and B the conclusion of that argument. Prove that if A U {¬B} ⊢ ⊥, then A ⊢ B. (Use Fitch) I have no idea where to start, can someone help?
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How can I prove a contradiction follows from P <-> Q and P -> ~Q?

I am so close to solving this problem: (Language Logic and Proof 8.36). http://imgur.com/a/nzYCU All I need to do to complete the proof is show that P <-> Q and P -> ~Q is a contradiction (the ...
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Fitch Formal Logic Help 6.26

6.26 Premise: A v (B ^C) Premise: ~B v ~C v D Goal: A v D Prove it formally without using DeMorgan's Law.
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How would I deduce a≠c from a≠b and b≠c in Fitch?

How would I deduce a≠c from the premises a≠b and b≠c in Fitch? This is what I've done so far. b=b (=Intro) b≠a (Ana Con) b≠c (Reit) And then for some reason I get stuck here? I know this sounds ...
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Logic – Deduction in Tarski's World (Fitch/LPL 13.36)

I am working on proving the following question: | ∀x [Dodec(x) → LeftOf(x, a)] | ∀x [Tet(x) → RightOf(x, a)] |––– | ∀x [SameCol(x, a) → Cube(x)] The question has the following rules: […] give a ...
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LPL 10.26 - Fitch - How to use ∀ Intro and ∃ Elim?

I am using LPL (Language, Proof, and Logic, commonly known as LPL) and the bundled Fitch program. I am trying to solve problem 10.26: 10.26: ∀x Tet(b) ↔ ∃w Tet(b) Looks simple enough, as the ...
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Fitch style disjunction elimination

I am having difficulty in formally proving a simple argument. Consider P(x) v Q(x) not P(x) ---------- Q(x) It is easy to see that the argument is indeed valid, but I cannot seem to prove it ...
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Prove A ∨ D from A ∨ (B ∧ C) and (¬ B ∨ ¬ C) ∨ D ( LPL Q6.26) without using --> or material implication

This is a repeated question: Language Logic and Proof Q. 6.26 Using the natural deduction rules, give a formal proof of A ∨ D from the premises A ∨ (B ∧ C) (¬ B ∨ ¬ C) ∨ D ...
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Conditional disjunction equivalence proof using FItch

Prove P v Q ⇔ ¬Q → P So far I have the obvious things... 1. P v Q _ | 2. ¬Q | _ | 3. | 4. | 5. | 6. | 7. | 8. P 9. ¬Q → P → Intro 2-8 I think the problem here is that I do not ...