Equivalent forms of “if p then q”
I'm wondering if "If p then q" is equivalent to "p unless q" or "p or not q" in regards to philosophy?
logic
asked 2 hours ago
Katie SummersKatie Summers
61
New contributor
Katie Summers is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I'm wondering if "If p then q" is equivalent to "p unless q" or "p or not q" in regards to philosophy?
logic
asked 2 hours ago
Katie SummersKatie Summers
61
New contributor
Katie Summers is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Absolutely. You may always evaluate truth tables, but consider the truth conditions of the conditional; what does it mean for the implication to be true? It CANNOT be the case that p is true and q is false, yes? Hence (so to speak), ~(p and ~q)
– Ryan Goulden
2 hours ago
We haven't learned truth tables or the symbolic meanings behind these conditionals so that's where I became confused. I'll try to take what you said and see what I find! Thank you
– Katie Summers
2 hours ago
Something is wrong here. "If p then q" is p → q, "p unless q" is q → ¬p, and "p or not q" is classically equivalent to q → p. They are not even equivalent in elementary logic.
– Conifold
2 mins ago
add a comment |
I'm wondering if "If p then q" is equivalent to "p unless q" or "p or not q" in regards to philosophy?
logic
asked 2 hours ago
Katie SummersKatie Summers
61
New contributor
Katie Summers is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I'm wondering if "If p then q" is equivalent to "p unless q" or "p or not q" in regards to philosophy?
logic
logic
asked 2 hours ago
Katie SummersKatie Summers
61
New contributor
Katie Summers is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
Katie SummersKatie Summers
61
New contributor
Katie Summers is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
Katie SummersKatie Summers
61
New contributor
Katie Summers is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
Katie SummersKatie Summers
61
asked 2 hours ago
Katie SummersKatie Summers
61
61
New contributor
Katie Summers is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Katie Summers is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Katie Summers is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Absolutely. You may always evaluate truth tables, but consider the truth conditions of the conditional; what does it mean for the implication to be true? It CANNOT be the case that p is true and q is false, yes? Hence (so to speak), ~(p and ~q)
– Ryan Goulden
2 hours ago
We haven't learned truth tables or the symbolic meanings behind these conditionals so that's where I became confused. I'll try to take what you said and see what I find! Thank you
– Katie Summers
2 hours ago
Something is wrong here. "If p then q" is p → q, "p unless q" is q → ¬p, and "p or not q" is classically equivalent to q → p. They are not even equivalent in elementary logic.
– Conifold
2 mins ago
add a comment |
Absolutely. You may always evaluate truth tables, but consider the truth conditions of the conditional; what does it mean for the implication to be true? It CANNOT be the case that p is true and q is false, yes? Hence (so to speak), ~(p and ~q)
– Ryan Goulden
2 hours ago
We haven't learned truth tables or the symbolic meanings behind these conditionals so that's where I became confused. I'll try to take what you said and see what I find! Thank you
– Katie Summers
2 hours ago
Something is wrong here. "If p then q" is p → q, "p unless q" is q → ¬p, and "p or not q" is classically equivalent to q → p. They are not even equivalent in elementary logic.
– Conifold
2 mins ago
Absolutely. You may always evaluate truth tables, but consider the truth conditions of the conditional; what does it mean for the implication to be true? It CANNOT be the case that p is true and q is false, yes? Hence (so to speak), ~(p and ~q)
– Ryan Goulden
2 hours ago
Absolutely. You may always evaluate truth tables, but consider the truth conditions of the conditional; what does it mean for the implication to be true? It CANNOT be the case that p is true and q is false, yes? Hence (so to speak), ~(p and ~q)
– Ryan Goulden
2 hours ago
We haven't learned truth tables or the symbolic meanings behind these conditionals so that's where I became confused. I'll try to take what you said and see what I find! Thank you
– Katie Summers
2 hours ago
We haven't learned truth tables or the symbolic meanings behind these conditionals so that's where I became confused. I'll try to take what you said and see what I find! Thank you
– Katie Summers
2 hours ago
Something is wrong here. "If p then q" is p → q, "p unless q" is q → ¬p, and "p or not q" is classically equivalent to q → p. They are not even equivalent in elementary logic.
– Conifold
2 mins ago
Something is wrong here. "If p then q" is p → q, "p unless q" is q → ¬p, and "p or not q" is classically equivalent to q → p. They are not even equivalent in elementary logic.
– Conifold
2 mins ago
add a comment |
1 Answer
1
active
oldest
votes
In classical propositional logic, "if P then Q" is equivalent to "not P or Q" and to "not (P and not Q) and to "P only if Q". 'Unless' is taken to be equivalent to the inclusive 'or'. So in your two examples, "if P then Q" is not equivalent to "P unless Q" nor is it equivalent to "P or not Q".
In classical logic this kind of conditional is called 'material implication' and it is a truth function, which is to say that the truth of the conditional depends only on the truth values of P and Q. In practice, ordinary English conditionals do not always, perhaps do not often, behave like this. Conditionals usually express some kind of connection between P and Q, so their truth depends in some deeper way on what P and Q mean. Treating conditionals as truth functions runs into highly counterintuitive examples that are sometimes called the paradoxes of material implication. In reality, they are not paradoxes at all, just examples of conditionals that are not material implications.
Another point to notice is that conditionals often carry an implicature that the antecedent part is a precondition for the consequent part. For example, we hear a difference between:
- If you learn to play the cello, I'll buy you a cello.
- You'll learn to play the cello only if I buy you a cello.
or between
- Mary will continue to love John unless he goes bald.
- John will go bald unless Mary continues to love him.
These examples are from David Sanford's book "If P then Q".
answered 1 hour ago
BumbleBumble
7,62921133
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
});
}
});
Katie Summers is a new contributor. Be nice, and check out our Code of Conduct.
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%2f60046%2fequivalent-forms-of-if-p-then-q%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
In classical propositional logic, "if P then Q" is equivalent to "not P or Q" and to "not (P and not Q) and to "P only if Q". 'Unless' is taken to be equivalent to the inclusive 'or'. So in your two examples, "if P then Q" is not equivalent to "P unless Q" nor is it equivalent to "P or not Q".
In classical logic this kind of conditional is called 'material implication' and it is a truth function, which is to say that the truth of the conditional depends only on the truth values of P and Q. In practice, ordinary English conditionals do not always, perhaps do not often, behave like this. Conditionals usually express some kind of connection between P and Q, so their truth depends in some deeper way on what P and Q mean. Treating conditionals as truth functions runs into highly counterintuitive examples that are sometimes called the paradoxes of material implication. In reality, they are not paradoxes at all, just examples of conditionals that are not material implications.
Another point to notice is that conditionals often carry an implicature that the antecedent part is a precondition for the consequent part. For example, we hear a difference between:
- If you learn to play the cello, I'll buy you a cello.
- You'll learn to play the cello only if I buy you a cello.
or between
- Mary will continue to love John unless he goes bald.
- John will go bald unless Mary continues to love him.
These examples are from David Sanford's book "If P then Q".
answered 1 hour ago
BumbleBumble
7,62921133
add a comment |
In classical propositional logic, "if P then Q" is equivalent to "not P or Q" and to "not (P and not Q) and to "P only if Q". 'Unless' is taken to be equivalent to the inclusive 'or'. So in your two examples, "if P then Q" is not equivalent to "P unless Q" nor is it equivalent to "P or not Q".
In classical logic this kind of conditional is called 'material implication' and it is a truth function, which is to say that the truth of the conditional depends only on the truth values of P and Q. In practice, ordinary English conditionals do not always, perhaps do not often, behave like this. Conditionals usually express some kind of connection between P and Q, so their truth depends in some deeper way on what P and Q mean. Treating conditionals as truth functions runs into highly counterintuitive examples that are sometimes called the paradoxes of material implication. In reality, they are not paradoxes at all, just examples of conditionals that are not material implications.
Another point to notice is that conditionals often carry an implicature that the antecedent part is a precondition for the consequent part. For example, we hear a difference between:
- If you learn to play the cello, I'll buy you a cello.
- You'll learn to play the cello only if I buy you a cello.
or between
- Mary will continue to love John unless he goes bald.
- John will go bald unless Mary continues to love him.
These examples are from David Sanford's book "If P then Q".
answered 1 hour ago
BumbleBumble
7,62921133
add a comment |
In classical propositional logic, "if P then Q" is equivalent to "not P or Q" and to "not (P and not Q) and to "P only if Q". 'Unless' is taken to be equivalent to the inclusive 'or'. So in your two examples, "if P then Q" is not equivalent to "P unless Q" nor is it equivalent to "P or not Q".
In classical logic this kind of conditional is called 'material implication' and it is a truth function, which is to say that the truth of the conditional depends only on the truth values of P and Q. In practice, ordinary English conditionals do not always, perhaps do not often, behave like this. Conditionals usually express some kind of connection between P and Q, so their truth depends in some deeper way on what P and Q mean. Treating conditionals as truth functions runs into highly counterintuitive examples that are sometimes called the paradoxes of material implication. In reality, they are not paradoxes at all, just examples of conditionals that are not material implications.
Another point to notice is that conditionals often carry an implicature that the antecedent part is a precondition for the consequent part. For example, we hear a difference between:
- If you learn to play the cello, I'll buy you a cello.
- You'll learn to play the cello only if I buy you a cello.
or between
- Mary will continue to love John unless he goes bald.
- John will go bald unless Mary continues to love him.
These examples are from David Sanford's book "If P then Q".
answered 1 hour ago
BumbleBumble
7,62921133
In classical propositional logic, "if P then Q" is equivalent to "not P or Q" and to "not (P and not Q) and to "P only if Q". 'Unless' is taken to be equivalent to the inclusive 'or'. So in your two examples, "if P then Q" is not equivalent to "P unless Q" nor is it equivalent to "P or not Q".
In classical logic this kind of conditional is called 'material implication' and it is a truth function, which is to say that the truth of the conditional depends only on the truth values of P and Q. In practice, ordinary English conditionals do not always, perhaps do not often, behave like this. Conditionals usually express some kind of connection between P and Q, so their truth depends in some deeper way on what P and Q mean. Treating conditionals as truth functions runs into highly counterintuitive examples that are sometimes called the paradoxes of material implication. In reality, they are not paradoxes at all, just examples of conditionals that are not material implications.
Another point to notice is that conditionals often carry an implicature that the antecedent part is a precondition for the consequent part. For example, we hear a difference between:
- If you learn to play the cello, I'll buy you a cello.
- You'll learn to play the cello only if I buy you a cello.
or between
- Mary will continue to love John unless he goes bald.
- John will go bald unless Mary continues to love him.
These examples are from David Sanford's book "If P then Q".
answered 1 hour ago
BumbleBumble
7,62921133
answered 1 hour ago
BumbleBumble
7,62921133
answered 1 hour ago
BumbleBumble
7,62921133
answered 1 hour ago
BumbleBumble
7,62921133
7,62921133
add a comment |
add a comment |
Katie Summers is a new contributor. Be nice, and check out our Code of Conduct.
Katie Summers is a new contributor. Be nice, and check out our Code of Conduct.
Katie Summers is a new contributor. Be nice, and check out our Code of Conduct.
Katie Summers is a new contributor. Be nice, and check out our Code of Conduct.
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%2f60046%2fequivalent-forms-of-if-p-then-q%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
Absolutely. You may always evaluate truth tables, but consider the truth conditions of the conditional; what does it mean for the implication to be true? It CANNOT be the case that p is true and q is false, yes? Hence (so to speak), ~(p and ~q)
– Ryan Goulden
2 hours ago
We haven't learned truth tables or the symbolic meanings behind these conditionals so that's where I became confused. I'll try to take what you said and see what I find! Thank you
– Katie Summers
2 hours ago
Something is wrong here. "If p then q" is p → q, "p unless q" is q → ¬p, and "p or not q" is classically equivalent to q → p. They are not even equivalent in elementary logic.
– Conifold
2 mins ago