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!!
logic proof fitch
edited Nov 26 at 20:42
Frank Hubeny
6,88951344
asked Nov 26 at 19:44
user36043
102
add a comment |
I can't figure out how to prove that formally. Please, help!!
logic proof fitch
edited Nov 26 at 20:42
Frank Hubeny
6,88951344
asked Nov 26 at 19:44
user36043
102
I made an edit which you may roll back or continue editing. Welcome to this SE! Look under the tags you used for other questions and answers on Fitch-style natural deduction.
– Frank Hubeny
Nov 26 at 20:43
add a comment |
I can't figure out how to prove that formally. Please, help!!
logic proof fitch
edited Nov 26 at 20:42
Frank Hubeny
6,88951344
asked Nov 26 at 19:44
user36043
102
I can't figure out how to prove that formally. Please, help!!
logic proof fitch
logic proof fitch
edited Nov 26 at 20:42
Frank Hubeny
6,88951344
asked Nov 26 at 19:44
user36043
102
edited Nov 26 at 20:42
Frank Hubeny
6,88951344
asked Nov 26 at 19:44
user36043
102
edited Nov 26 at 20:42
Frank Hubeny
6,88951344
edited Nov 26 at 20:42
Frank Hubeny
6,88951344
edited Nov 26 at 20:42
Frank Hubeny
6,88951344
6,88951344
asked Nov 26 at 19:44
user36043
102
asked Nov 26 at 19:44
user36043
102
asked Nov 26 at 19:44
user36043
102
102
I made an edit which you may roll back or continue editing. Welcome to this SE! Look under the tags you used for other questions and answers on Fitch-style natural deduction.
– Frank Hubeny
Nov 26 at 20:43
add a comment |
I made an edit which you may roll back or continue editing. Welcome to this SE! Look under the tags you used for other questions and answers on Fitch-style natural deduction.
– Frank Hubeny
Nov 26 at 20:43
I made an edit which you may roll back or continue editing. Welcome to this SE! Look under the tags you used for other questions and answers on Fitch-style natural deduction.
– Frank Hubeny
Nov 26 at 20:43
I made an edit which you may roll back or continue editing. Welcome to this SE! Look under the tags you used for other questions and answers on Fitch-style natural deduction.
– Frank Hubeny
Nov 26 at 20:43
add a comment |
2 Answers
2
active
oldest
votes
In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
One assumes not-P and uses a Reduction To Absurdity proof.
|_ (~P v Q) -> P Premise
| |_ ~P Assumption
| | : :
| | : :
| | : :
| ~~P Negation Introduction
| P Double Negation Elimination
answered Nov 26 at 22:34
Graham Kemp
85918
add a comment |
Here is a way to prove this using the rules in Klement's Fitch-style proof checker. The rules are described in forallx. Both are available in the links below and would make good supplementary material to whatever text you are using.
This proof uses the law of the excluded middle (LEM). To use this I take a simple statement and its negation and from both try to derive the same result. If I get the same result than I can invoke the law of the excluded middle. Here I chose "P" and "¬P", because one of these, "P", is the goal itself.
For "P" I need do nothing but add the subproof with assumption "P". For "¬P" I use disjunction introduction to get line 4 and then conditional elimination on line 5 (modus ponens) to get "P". I reached the goal, "P", in both cases and so I can discharge the two assumptions on line 2 and 3 and reach the end of the proof.
Reference
Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
answered Nov 26 at 20:25
Frank Hubeny
6,88951344
add a comment |
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "265"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphilosophy.stackexchange.com%2fquestions%2f57469%2fin-fitch-how-does-one-prove-p-from-the-premise-%25c2%25acp-%25e2%2588%25a8-q%25e2%2586%2592p%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
One assumes not-P and uses a Reduction To Absurdity proof.
|_ (~P v Q) -> P Premise
| |_ ~P Assumption
| | : :
| | : :
| | : :
| ~~P Negation Introduction
| P Double Negation Elimination
answered Nov 26 at 22:34
Graham Kemp
85918
add a comment |
In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
One assumes not-P and uses a Reduction To Absurdity proof.
|_ (~P v Q) -> P Premise
| |_ ~P Assumption
| | : :
| | : :
| | : :
| ~~P Negation Introduction
| P Double Negation Elimination
answered Nov 26 at 22:34
Graham Kemp
85918
add a comment |
In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
One assumes not-P and uses a Reduction To Absurdity proof.
|_ (~P v Q) -> P Premise
| |_ ~P Assumption
| | : :
| | : :
| | : :
| ~~P Negation Introduction
| P Double Negation Elimination
answered Nov 26 at 22:34
Graham Kemp
85918
In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
One assumes not-P and uses a Reduction To Absurdity proof.
|_ (~P v Q) -> P Premise
| |_ ~P Assumption
| | : :
| | : :
| | : :
| ~~P Negation Introduction
| P Double Negation Elimination
answered Nov 26 at 22:34
Graham Kemp
85918
answered Nov 26 at 22:34
Graham Kemp
85918
answered Nov 26 at 22:34
Graham Kemp
85918
answered Nov 26 at 22:34
Graham Kemp
85918
85918
add a comment |
add a comment |
Here is a way to prove this using the rules in Klement's Fitch-style proof checker. The rules are described in forallx. Both are available in the links below and would make good supplementary material to whatever text you are using.
This proof uses the law of the excluded middle (LEM). To use this I take a simple statement and its negation and from both try to derive the same result. If I get the same result than I can invoke the law of the excluded middle. Here I chose "P" and "¬P", because one of these, "P", is the goal itself.
For "P" I need do nothing but add the subproof with assumption "P". For "¬P" I use disjunction introduction to get line 4 and then conditional elimination on line 5 (modus ponens) to get "P". I reached the goal, "P", in both cases and so I can discharge the two assumptions on line 2 and 3 and reach the end of the proof.
Reference
Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
answered Nov 26 at 20:25
Frank Hubeny
6,88951344
add a comment |
Here is a way to prove this using the rules in Klement's Fitch-style proof checker. The rules are described in forallx. Both are available in the links below and would make good supplementary material to whatever text you are using.
This proof uses the law of the excluded middle (LEM). To use this I take a simple statement and its negation and from both try to derive the same result. If I get the same result than I can invoke the law of the excluded middle. Here I chose "P" and "¬P", because one of these, "P", is the goal itself.
For "P" I need do nothing but add the subproof with assumption "P". For "¬P" I use disjunction introduction to get line 4 and then conditional elimination on line 5 (modus ponens) to get "P". I reached the goal, "P", in both cases and so I can discharge the two assumptions on line 2 and 3 and reach the end of the proof.
Reference
Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
answered Nov 26 at 20:25
Frank Hubeny
6,88951344
add a comment |
Here is a way to prove this using the rules in Klement's Fitch-style proof checker. The rules are described in forallx. Both are available in the links below and would make good supplementary material to whatever text you are using.
This proof uses the law of the excluded middle (LEM). To use this I take a simple statement and its negation and from both try to derive the same result. If I get the same result than I can invoke the law of the excluded middle. Here I chose "P" and "¬P", because one of these, "P", is the goal itself.
For "P" I need do nothing but add the subproof with assumption "P". For "¬P" I use disjunction introduction to get line 4 and then conditional elimination on line 5 (modus ponens) to get "P". I reached the goal, "P", in both cases and so I can discharge the two assumptions on line 2 and 3 and reach the end of the proof.
Reference
Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
answered Nov 26 at 20:25
Frank Hubeny
6,88951344
Here is a way to prove this using the rules in Klement's Fitch-style proof checker. The rules are described in forallx. Both are available in the links below and would make good supplementary material to whatever text you are using.
This proof uses the law of the excluded middle (LEM). To use this I take a simple statement and its negation and from both try to derive the same result. If I get the same result than I can invoke the law of the excluded middle. Here I chose "P" and "¬P", because one of these, "P", is the goal itself.
For "P" I need do nothing but add the subproof with assumption "P". For "¬P" I use disjunction introduction to get line 4 and then conditional elimination on line 5 (modus ponens) to get "P". I reached the goal, "P", in both cases and so I can discharge the two assumptions on line 2 and 3 and reach the end of the proof.
Reference
Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
answered Nov 26 at 20:25
Frank Hubeny
6,88951344
answered Nov 26 at 20:25
Frank Hubeny
6,88951344
answered Nov 26 at 20:25
Frank Hubeny
6,88951344
answered Nov 26 at 20:25
Frank Hubeny
6,88951344
6,88951344
add a comment |
add a comment |
Thanks for contributing an answer to Philosophy Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphilosophy.stackexchange.com%2fquestions%2f57469%2fin-fitch-how-does-one-prove-p-from-the-premise-%25c2%25acp-%25e2%2588%25a8-q%25e2%2586%2592p%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
I made an edit which you may roll back or continue editing. Welcome to this SE! Look under the tags you used for other questions and answers on Fitch-style natural deduction.
– Frank Hubeny
Nov 26 at 20:43