# 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.

101 questions
Filter by
Sorted by
Tagged with
1 vote
22 views

### Are quantum epistemology and intuitionistic constructivism compatible?

A somewhat recent article coming out of the University of Toronto and the Institute for Theoretical Physics in Zurich claims "no": Constructivist epistemology posits that all truths are ...
• 13.5k
57 views

### Could Dummettians use indefinite extendibility to get around Fitch's paradox?

Could Dummettians use indefinite extendibility to get around Fitch's paradox? I was reading over my answer to "Metaphysical indeterminacy and necessity" here on the PhilosophySE, and I ...
• 13.5k
75 views

### Fitch derivations for equivalence relation properties

Primarily, this a request to check Fitch-style derivations in the file, https://drive.google.com/file/d/1du-EIZG3CSdrcfDbldlzwgRftDzeVc8K/view?usp=drivesdk This is not trivial. The reflexiveness ...
50 views

### Fitch Proof Help, Conclude ~B from ~(A > B) [closed]

I'm in the process of learning fitch proofs and I've come across one I'm having trouble setting up. Premise: ~(A > B) Goal: (A & ~B) In other words, it looks something like this: 1 | ~(A > B)...
127 views

### I've been working on this for way too long :/

I've made a lot of progress on the proof below, but I am stuck on the last steps where I need to add existential quantifiers back in: ¬∃x ∃y Smaller(x,y) For context, I'm a logic novice, but I'm ...
1 vote
50 views

### Assume: (C∧D)∨(¬C∧D); Prove: C↔D

Is it possible to prove this formally in fitch? I found that when C is false and D is true the conclusion is false while the premise is true.
98 views

### Trying to do proof for ~(A->B) |- A^~B by Fitch Style proof. with Condition do not use de Morgan's law [closed]

Need help to Proof ~(A->B) :- A ^ ~B I was following William Rose proof from 1 to 33. but I am stuck on this.
106 views

### Fitch proofs help?

I'm new to logic and can see how to write these out informally, but need some help seeing how they should be translated into formal proofs in Fitch.
89 views

### Why is the use of the ND rule ∃E not correct in this proof?

Is there anyone who could explain to me why these errors occur? It seems to me the rule was used properly.
58 views

### Question about proving a set that is quantificationally inconsistent in PD+ (Finished the proof but want it to be checked)

Does ∃x(Nx & ~Nx) contradiction itself? Is there an error in my proof? Thank you
99 views

I think I got it, could you take a look, please.
110 views

### Help with Fitch formal proof?

I'm having trouble solving this formal proof in Fitch. I've put together most of it, but I think I need to use disjunction elim(?) at some point and am having trouble doing that.
118 views

### How do I prove ∀x(A(x) -> B(x)) from ~∃x(A(x) ^ ~B(x)) using a fitch proof? [closed]

What would the formal fitch proof for this be? This question came up in my practice problems and I'm really stuck on how to proceed. I'm assuming that you start with an assumption, but I can't figure ...
46 views

### Is the included derivation feasible? If so, would my proof be correct?

The simple derivation seems correct and intuitive, and yet I feel as if something is off. I would greatly appreciate it if someone could double-check the provided formal proof. Thank you in advance ...
• 63
108 views

### How does one prove (A->B)vC from the premise ~A? [closed]

Is the premise really enough to prove this?
86 views

### How to prove the following arguments [closed]

I'm trying to do a bunch of proofs to get better at them but it seems like I need some help with negation. Can anyone who has time prove the following arguments? I would really appreciate it! ¬(P ∧ ¬Q)...
• 9
42 views

### Validity of the Definiton of the Conditional [closed]

Can a proof for Premise (P→Q) ... Goal (¬P∨Q) be derived using only the following rules? Conjunction Introduction Conjunction Elimination Left Conjunction Elimination Right Disjunction Introduction ...
515 views

### Question about fitch 6.19 proving A or C from premises A or B and -B or C

How to prove A or C from premises A or B and -B or C. Am using fitch and have been stuck on this for an hour
491 views

### How to prove A<—>not A

So basically there are no premises, but the file I have received to start this problem has a contradiction symbol as step one. I’m not sure if this was a mistake or purposeful, and if it was ...
504 views

### fitch proof chapter 13 (ex. 13.29) [closed]

how to proof exercise 13.29 without using taut con
356 views

### Logic – Deduction in Tarski's World (Fitch/LPL 13.22) [closed]

I am trying to use existential elimination to derive Brillig(a) & Tove(a). how would I do this? I have tried to do separate sub proofs to prove both Brillig(a) & Tove(a) but that doesn't work ...
134 views

### Complex Fitch exercise to prove ∀x.r(x) [closed]

Assume a language with the object constant a and the function constant s. Given r(a), ∀x.(p(x) ⇒ r(s(x))), ∀x.(q(x) ⇒ r(s(x))), and ∀x.(r(x) ⇒ p(x) ∨ q(x)), use the Fitch system with Linear Induction ...
46 views

Q ∧ S (Q ∧ ¬P) → ¬R Q → ¬P (S ∧ T) → (P ∨ R) The goal is:¬T
255 views

### fitch proof. P v Q, Q→ ¬ R, ¬ P, ¬ R → ¬ S GOAL: ¬ S

Need help exercise using the FITCH program format. I'm stuck on where to start. The following 4 steps must be used to prove the goal. P v Q Q→ ¬ R ¬ P ¬ R → ¬ S GOAL: ¬ S Now I know: ¬ P and P v Q ...
119 views

### Trouble with fitch and the use of existential elimination rule [closed]

I am wondering why fitch is not allowing me to use existential elimination for this final step
142 views

### Given the premises ∀x.(p(x) ⇒ q(x)) and ∀x.(q(x) ⇒ r(x)), use the Fitch system to prove the conclusion ∀x.(p(x) ⇒ r(x))

I'm not able to move forward from step 4. I've tried Implication Introduction applied to 3 and 4 but nothing happens, any help is much appreciated.
180 views

### Solving a proof with Fitch

I'm working on an assignment and I'm stuck on this proof. I feel like I'm on the right track but I can't find the way to prove the goal. B ^ D (B^¬A) → ¬C B → ¬A (D^E)→ (A v C) GOAL: ¬E
224 views

### Use the Fitch system to prove the tautology (p ∨ ¬p). Stalled for days (NOT duplicated)

First of all, please don't close this question cause I don't get the explanation given in: Use the Fitch system to prove the tautology (p ∨ ¬p) I have been trying to solve this exercise for days ...
• 1
54 views

### Use the Fitch system to prove the tautology (p ∨ ¬p). Stalled for days [duplicate]

I'm having trouble solving this one. I've been stuck in step 9 for days now. Any help is very much appreciated.
• 1
120 views

### fitch arrow proof

using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C7 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
177 views

### How to prove (A v ¬ B), (¬ A v C), (¬ C → B) therefore (¬ D v C)

My idea is to use disjunction elimination on (¬ A v C)to obtain C, and then use disjunction introduction to obtain (¬ D v C), but I'm having a hard time obtaining C.
590 views

### Complete a formal proof of ~(~A&~B) from A in as few lines as possible

Prove ~(~A&~B) from A in as few lines as possible. ~ = negation & = conjunction v = disjunction | = line in a subproof Here's what I have: A - Premise |~A - Assume |~B ...
107 views

### How to prove H → M ￢H → ￢M prove H↔M?

I'm using the program Fitch and I need to make a formal proof for this: H → M ￢H → ￢M Prove: H↔M Any ideas on how to do so?
605 views

### Language, Proof and Logic Exercise 14.13 (Fitch)

Having trouble proving this. I know how to prove the first conjunct of the conclusion, but not the second one. Picture shown is the attempt proof of the second conjunct (rules haven't been added yet). ...
888 views

### Language, Proof, and Logic 14.11 Fitch Proof

Been stuck on this question for awhile now and I just don't know how to get Cube(x) so that I can use ^ intro with Cube(x) and ∀y (Cube(y) → y = a) and then use ∃ intro to get the conclusion. This is ...
175 views

### how to prove ‘¬∃xP(x)→(P(a)→Q(a))’ from no premises? fitch

I am totally lost on how to do this... can anyone help? What does it mean? I tried to understand what it means before proof but am totally clueless
2k views

### Fitch Proof Exercise 6.20

I am working on a proof and am stuck on a step. I am not sure why I cannot assume the negation of B. Is it not allowed or am I missing something? Thank you]1
• 39
581 views

### Language Proof & Logic 8.31 Fitch Proof

Been working on this one question for the past hours and I can't ever seem to get the last step working. Any help would be appreciated!
298 views

### How can I prove the law of excluded third (p ∨ ¬p)) using Fitch?

Good day. I do not quite understand how I can get ~~p after the 11th line. According to the proof of the law itself (and all reasonable logic) I should get it, and then simplify the expression - but ...
61 views

### How would I go about proving P>Q from the premise (notP v Q)? [duplicate]

A similar question had already been asked, but the solution involves steps I am unfamiliar with. in class, we have only been exposed to intro and elim rules, as well as contradiction rules. Here is ...
• 39
1k views

### Fitch Proof - Logic LPL 6.31

I am trying to complete the following proof in Fitch but am completely clueless on how to approach it. Any help would be appreciated! Thanks
756 views

### De Morgan's Law Formal Proof [duplicate]

Does anyone know how to do this without the use of addition rules? We have not covered that in class, and all the info I can find online suggests that as a solution. Thanks]1
• 39
392 views

### Contrapositive Fitch Proof

I can't seem to figure out how to get past this step. Any suggestions?
• 21
1 vote
313 views

### How to use use the Fitch System to prove (¬p ⇒ q) ⇒ ((¬p ⇒ ¬q) ⇒ p)?

I'm getting a bit stuck in a tailspin on this one. I'm quite new to logic. I'm not sure how or when we use negation to get P. How then does that connect to (¬p ⇒ q) ⇒ ((¬p ⇒ ¬q)?
167 views

### Given premise ~(P↔Q) how can one derive (~P↔Q) using Fitch?

Given premise ~(P↔Q) derive (~P↔Q) using Fitch-style natural deduction. I thought of simplifying the premise but I am still not able to find an answer. Can someone please help me?
132 views

### How do you prove (p => q => r) => (p => q) => p => r using the Fitch system?

I'm quite new to logic. Thank you for taking the time to review this post. I tried the following and got to the conclusion I wanted but I was never able to prove the statement.
362 views

### Fitch Proof - Arrow's logic of preferences

I've been stumped on this one question in particular for several days now and I'm hoping to get some help on where I'm going wrong. Given the following premises: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,...
• 29
295 views

### Fitch Arrow Proofs [closed]

Using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C10 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
• 11