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.

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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 ...
Kristian Berry's user avatar
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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 ...
Kristian Berry's user avatar
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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 ...
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1 answer
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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)...
Cam J's user avatar
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2 answers
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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 ...
elemental123's user avatar
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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.
Sparrow Tree's user avatar
-1 votes
1 answer
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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.
Keith Lam's user avatar
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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.
srp352's user avatar
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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.
sannelavinia's user avatar
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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
Stanley's user avatar
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Fitch Proof help please

I think I got it, could you take a look, please.
Stanley's user avatar
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1 answer
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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.
srp352's user avatar
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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 ...
gallileo's user avatar
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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 ...
Falcon's user avatar
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How does one prove (A->B)vC from the premise ~A? [closed]

Is the premise really enough to prove this?
Fogsvans's user avatar
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1 answer
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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)...
ddd's user avatar
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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 ...
Maxwell Victoria's user avatar
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2 answers
510 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
Ye ocean's user avatar
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2 answers
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 ...
Maria G's user avatar
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2 answers
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fitch proof chapter 13 (ex. 13.29) [closed]

how to proof exercise 13.29 without using taut con
user47078's user avatar
-1 votes
2 answers
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 ...
Samaritna's user avatar
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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 ...
Jessie The Pink Man's user avatar
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1 answer
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Fitch Question, Please help! [closed]

Q ∧ S (Q ∧ ¬P) → ¬R Q → ¬P (S ∧ T) → (P ∨ R) The goal is:¬T
Mahiar's user avatar
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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 ...
eaglefern's user avatar
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1 answer
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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
jph2188's user avatar
-1 votes
2 answers
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.
Jessie The Pink Man's user avatar
-1 votes
1 answer
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
eaglefern's user avatar
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1 answer
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 ...
Luen's user avatar
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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.
Luen's user avatar
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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)∧...
Lainne's user avatar
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2 answers
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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.
uofa-student's user avatar
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1 answer
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 ...
Gavolak's user avatar
-1 votes
3 answers
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?
sunRise's user avatar
-2 votes
1 answer
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). ...
randomusergenerator's user avatar
-1 votes
1 answer
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 ...
NiceOnions's user avatar
-5 votes
2 answers
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
cluelesschloe's user avatar
0 votes
2 answers
1k 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
Jason Wu's user avatar
-1 votes
4 answers
580 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!
NiceOnions's user avatar
-1 votes
2 answers
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 ...
Kalerya Karina Kaftan's user avatar
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0 answers
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 ...
Grace's user avatar
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-1 votes
3 answers
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
CodingSlightly's user avatar
0 votes
1 answer
749 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
Grace's user avatar
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2 votes
1 answer
391 views

Contrapositive Fitch Proof

I can't seem to figure out how to get past this step. Any suggestions?
Grace's user avatar
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1 vote
2 answers
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)?
Katie Melosto's user avatar
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2 answers
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?
Rajamani Sarvesh's user avatar
0 votes
1 answer
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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.
Katie Melosto's user avatar
2 votes
1 answer
361 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,...
rzy's user avatar
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-3 votes
1 answer
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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)∧...
George P's user avatar
0 votes
2 answers
98 views

Fitch Question Please Help Me [closed]

I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : How do I reach this goal? Which rules do I use and with which support steps to each rule (proofs to prove ...
user avatar
1 vote
2 answers
126 views

Fitch Questions Please Help Me

I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : How do I reach this goal? Which rules do I use and with which support steps to each rule (proofs to prove ...
user avatar