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
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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
1 hour 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
1 hour 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
1 hour 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
1 hour 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
1 hour 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
1 hour 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
1 hour 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
1 hour 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
1 hour 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
1 hour ago
add a comment |
1 Answer
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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 53 mins ago
BumbleBumble
7,62921133
add a comment |
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1 Answer
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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 53 mins 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 53 mins 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 53 mins 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 53 mins ago
BumbleBumble
7,62921133
answered 53 mins ago
BumbleBumble
7,62921133
answered 53 mins ago
BumbleBumble
7,62921133
answered 53 mins 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.
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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
1 hour 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
1 hour ago