Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [fitch]

Frederic Brenton Fitch (1908 – 1987) was an American logician who taught at Yale. He invented the Fitch-style for natural deduction. He is also famous for the paradox of knowability. The tag may also refer to natural deduction proof environments in Fitch-style calculus for giving and checking proofs.

0
votes
1answer
55 views

Language Proof and logic Chapter 13 problem 31

I have been working on this problem for over an hour and I think I have simply missed something. I need some help. I don't see how this is supposed to work out Here are the premises: ∀x ∀y[Likes(x,...
0
votes
2answers
81 views

Language proof and logic Chapter 15 question 21 how?

I'm really not understanding the set up of how to go about solving this problem any help is welcome
0
votes
3answers
57 views

In Fitch, how does one prove ¬(B ∧ C) from two premises (A → ¬B) and (¬A → ¬C) [closed]

Help me out please!! I have been trying to solve it for hours
0
votes
2answers
104 views

Language proof and logic Chapter 15 question 16 help

I'm trying to go about solving this problem but I'm having problems even knowing how to approach it. Can someone help me to set it up? Here is the premise: ∀x∀y(x ⊆ y ↔️ ∀z(z ∈ x ⟶ z ∈ y) Here is ...
0
votes
2answers
68 views

language proof and logic chapter 13 question 49 Help

Premises: ∃xP(x) ∀x∀y((P(x)∧P(y)) → x = y) Prove: ∃x(P(x)∧∀y(P(y) → y = x)) I've started it but the end is starting to get super muddy and not work out and I don't know where I went wrong.
0
votes
1answer
46 views

language logic and proof chapter 12 question 49 and question 50

I've been working on this and I can't seem to figure out what exactly is going wrong can anyone help?
0
votes
2answers
86 views

In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?

I can't figure out how to prove that formally. Please, help!!
3
votes
4answers
1k views

How to prove ‘∃xP(x)’ from ‘¬∀x(P(x)→Q(x))’

What would a formal Fitch proof for this look like? I am given ¬∀x(P(x)→Q(x)), and need to derive ∃xP(x) from it. I started with this, but I don't know if I am doing the right thing, and where to go ...
1
vote
4answers
83 views

Symbolic Logic - Quantifier Proof (w/ Conditionals)

I'm not sure if lines 6 - 7 & 8 - 11 are being done correctly. I feel like it's necessary to prove 12 which proves the rest of the problem. I'm a bit stuck on lines 8 - 11. I initially tried to ...
1
vote
2answers
84 views

Fitch Proof by Contradiction help

Hi, I'm pretty new to writing formal proofs and I was wondering if I could get some help solving this question. I've set up the problem and I was thinking of perhaps proving it by contradiction that ...
2
votes
2answers
38 views

Fitch Biconditional Proof Help?

Hi, I'm starting to learn formal proofs using Fitch, but I'm having a bit of trouble figuring out my arguments. I've generally mapped out the subproofs I was considering to use, but I'm unsure how to ...
2
votes
4answers
194 views

How to prove : (( P → Q ) ∨ ( Q → R )) by natural deduction

Here's another of Tomassi's exercises I can't solve (Logic, page 106): : (( P → Q ) ∨ ( Q → R )) I have to use natural deduction and the only rules I know are: • assumptions, • modus ponendo ...
1
vote
1answer
25 views

Conditional IFF - Not sure what's wrong

"Not a valid application of the rule" I don't think 7 - 8 is something that really needs to be proven beyond a reit but I feel like you should be able to... I'm quite confused on proving Cube(a) ...
1
vote
2answers
100 views

Symbolic Conditional Help

Premise: (Tet(a) ^ Tet(b)) v (Cube(c) ^ Cube(d)) Cube(c) -> Dodec(e) Goal: ~Tet(a) -> Dodec(e) Anyone have a clue on where to start with this?
2
votes
2answers
77 views

How does one prove ‘(B→C)→¬A’ from ‘(A→B)∨C’ and ‘(A→¬C)’ in Fitch?

I am trying to work my way through this Fitch proof, and I am not sure what I am doing wrong, but I keep getting stuck no matter what I try. First attempt: Second attempt:
0
votes
2answers
81 views

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 ...
0
votes
2answers
147 views

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 ...
1
vote
0answers
32 views

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 ...
3
votes
3answers
239 views

2 simple Formal Fitch Proofs

I'm having difficulty proving these. They seem obvious, but I can't figure how to set up formal proofs for them. Could anyone give me clues on how to start them? ¬(P∧¬Q) from the premise P→Q; ¬Q→(R→P)...
1
vote
1answer
92 views

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
3
votes
4answers
779 views

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 ...
2
votes
3answers
134 views

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.
3
votes
1answer
569 views

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 ≠ ...
3
votes
4answers
218 views

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 ...
1
vote
4answers
143 views

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 ...
-1
votes
1answer
2k views

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 ...
3
votes
1answer
480 views

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 ∨...
2
votes
2answers
183 views

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∀...
5
votes
3answers
459 views

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, ...
4
votes
2answers
262 views

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) ...
3
votes
2answers
2k views

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 ...
1
vote
3answers
1k views

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 ...
4
votes
2answers
112 views

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?
5
votes
3answers
518 views

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 ...
1
vote
3answers
1k views

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.
1
vote
1answer
124 views

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 ...
1
vote
1answer
2k views

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 ...
3
votes
2answers
1k views

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 ...
4
votes
2answers
1k views

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 ...
3
votes
3answers
972 views

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 ...
2
votes
4answers
3k views

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 ...
4
votes
2answers
1k views

Disjunctive Syllogism in a Fitch Style System

I'm trying to prove an argument of the form: B ~(C & B) Therefore: ~C. I can expand out ~(C & B) into ~C OR ~B, and with the premise B, it is clear that ~C is the case. ...