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?
symbolic-logic fitch
asked Nov 13 '18 at 23:58
J. MartinezJ. Martinez
254
add a comment |
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?
symbolic-logic fitch
asked Nov 13 '18 at 23:58
J. MartinezJ. Martinez
254
add a comment |
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?
symbolic-logic fitch
asked Nov 13 '18 at 23:58
J. MartinezJ. Martinez
254
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?
symbolic-logic fitch
symbolic-logic fitch
asked Nov 13 '18 at 23:58
J. MartinezJ. Martinez
254
asked Nov 13 '18 at 23:58
J. MartinezJ. Martinez
254
edited Nov 14 '18 at 9:02
J. Martinez
asked Nov 13 '18 at 23:58
J. MartinezJ. Martinez
254
asked Nov 13 '18 at 23:58
J. MartinezJ. Martinez
254
asked Nov 13 '18 at 23:58
J. MartinezJ. Martinez
254
254
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
I agree with Graham Kemp's "skeleton for the proof".
Rather than provide a skeleton, I will provide a completed proof but using a different proof checker. To make this work in the proof checker I renamed the statements.
You may not be able to use all of the inference rules as they are used here. I used conjunction elimination (∧E), contradiction introduction (⊥I), explosion (X), conditional introduction (→I), and disjunction elimination (∨E).
Klement's proof checker and information about the rules I used can be found in forall x referenced below.
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 14 '18 at 1:12
Frank HubenyFrank Hubeny
7,55151446
Thanks, I managed to understand what was going on and able to apply it!
– J. Martinez
Nov 14 '18 at 8:53
add a comment |
Clearly you want a Conditional Proof to prove that conditional. Assume ~Tet(a) aiming to derive Dodec(e).
Now look at the to premises and the assumption and ask: how may I derive Dodec(e) from that disjunction, conditional, and negation?
| (Tet(a) ^ Tet(b)) v (Cube(c) ^ Cube(d)) Premise
|_ Cube(c) -> Dodec(e) Premise
| |_ ~Tet(a) Assume
| | :
| | Dodec(e)
| ~Tet(a) -> Dodec(e) Conditional Introduction
answered Nov 14 '18 at 0:57
Graham KempGraham Kemp
85918
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%2f57078%2fsymbolic-conditional-help%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
I agree with Graham Kemp's "skeleton for the proof".
Rather than provide a skeleton, I will provide a completed proof but using a different proof checker. To make this work in the proof checker I renamed the statements.
You may not be able to use all of the inference rules as they are used here. I used conjunction elimination (∧E), contradiction introduction (⊥I), explosion (X), conditional introduction (→I), and disjunction elimination (∨E).
Klement's proof checker and information about the rules I used can be found in forall x referenced below.
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 14 '18 at 1:12
Frank HubenyFrank Hubeny
7,55151446
Thanks, I managed to understand what was going on and able to apply it!
– J. Martinez
Nov 14 '18 at 8:53
add a comment |
I agree with Graham Kemp's "skeleton for the proof".
Rather than provide a skeleton, I will provide a completed proof but using a different proof checker. To make this work in the proof checker I renamed the statements.
You may not be able to use all of the inference rules as they are used here. I used conjunction elimination (∧E), contradiction introduction (⊥I), explosion (X), conditional introduction (→I), and disjunction elimination (∨E).
Klement's proof checker and information about the rules I used can be found in forall x referenced below.
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 14 '18 at 1:12
Frank HubenyFrank Hubeny
7,55151446
Thanks, I managed to understand what was going on and able to apply it!
– J. Martinez
Nov 14 '18 at 8:53
add a comment |
I agree with Graham Kemp's "skeleton for the proof".
Rather than provide a skeleton, I will provide a completed proof but using a different proof checker. To make this work in the proof checker I renamed the statements.
You may not be able to use all of the inference rules as they are used here. I used conjunction elimination (∧E), contradiction introduction (⊥I), explosion (X), conditional introduction (→I), and disjunction elimination (∨E).
Klement's proof checker and information about the rules I used can be found in forall x referenced below.
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 14 '18 at 1:12
Frank HubenyFrank Hubeny
7,55151446
I agree with Graham Kemp's "skeleton for the proof".
Rather than provide a skeleton, I will provide a completed proof but using a different proof checker. To make this work in the proof checker I renamed the statements.
You may not be able to use all of the inference rules as they are used here. I used conjunction elimination (∧E), contradiction introduction (⊥I), explosion (X), conditional introduction (→I), and disjunction elimination (∨E).
Klement's proof checker and information about the rules I used can be found in forall x referenced below.
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 14 '18 at 1:12
Frank HubenyFrank Hubeny
7,55151446
answered Nov 14 '18 at 1:12
Frank HubenyFrank Hubeny
7,55151446
answered Nov 14 '18 at 1:12
Frank HubenyFrank Hubeny
7,55151446
answered Nov 14 '18 at 1:12
Frank HubenyFrank Hubeny
7,55151446
7,55151446
Thanks, I managed to understand what was going on and able to apply it!
– J. Martinez
Nov 14 '18 at 8:53
add a comment |
Thanks, I managed to understand what was going on and able to apply it!
– J. Martinez
Nov 14 '18 at 8:53
Thanks, I managed to understand what was going on and able to apply it!
– J. Martinez
Nov 14 '18 at 8:53
Thanks, I managed to understand what was going on and able to apply it!
– J. Martinez
Nov 14 '18 at 8:53
add a comment |
Clearly you want a Conditional Proof to prove that conditional. Assume ~Tet(a) aiming to derive Dodec(e).
Now look at the to premises and the assumption and ask: how may I derive Dodec(e) from that disjunction, conditional, and negation?
| (Tet(a) ^ Tet(b)) v (Cube(c) ^ Cube(d)) Premise
|_ Cube(c) -> Dodec(e) Premise
| |_ ~Tet(a) Assume
| | :
| | Dodec(e)
| ~Tet(a) -> Dodec(e) Conditional Introduction
answered Nov 14 '18 at 0:57
Graham KempGraham Kemp
85918
add a comment |
Clearly you want a Conditional Proof to prove that conditional. Assume ~Tet(a) aiming to derive Dodec(e).
Now look at the to premises and the assumption and ask: how may I derive Dodec(e) from that disjunction, conditional, and negation?
| (Tet(a) ^ Tet(b)) v (Cube(c) ^ Cube(d)) Premise
|_ Cube(c) -> Dodec(e) Premise
| |_ ~Tet(a) Assume
| | :
| | Dodec(e)
| ~Tet(a) -> Dodec(e) Conditional Introduction
answered Nov 14 '18 at 0:57
Graham KempGraham Kemp
85918
add a comment |
Clearly you want a Conditional Proof to prove that conditional. Assume ~Tet(a) aiming to derive Dodec(e).
Now look at the to premises and the assumption and ask: how may I derive Dodec(e) from that disjunction, conditional, and negation?
| (Tet(a) ^ Tet(b)) v (Cube(c) ^ Cube(d)) Premise
|_ Cube(c) -> Dodec(e) Premise
| |_ ~Tet(a) Assume
| | :
| | Dodec(e)
| ~Tet(a) -> Dodec(e) Conditional Introduction
answered Nov 14 '18 at 0:57
Graham KempGraham Kemp
85918
Clearly you want a Conditional Proof to prove that conditional. Assume ~Tet(a) aiming to derive Dodec(e).
Now look at the to premises and the assumption and ask: how may I derive Dodec(e) from that disjunction, conditional, and negation?
| (Tet(a) ^ Tet(b)) v (Cube(c) ^ Cube(d)) Premise
|_ Cube(c) -> Dodec(e) Premise
| |_ ~Tet(a) Assume
| | :
| | Dodec(e)
| ~Tet(a) -> Dodec(e) Conditional Introduction
answered Nov 14 '18 at 0:57
Graham KempGraham Kemp
85918
edited Nov 14 '18 at 1:06
answered Nov 14 '18 at 0:57
Graham KempGraham Kemp
85918
answered Nov 14 '18 at 0:57
Graham KempGraham Kemp
85918
answered Nov 14 '18 at 0:57
Graham KempGraham Kemp
85918
85918
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.
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%2f57078%2fsymbolic-conditional-help%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
