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Logic. Truth of a negation
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If I say:
If I am paid today I'll go to the party tonight
I am saying that if I receive a payment today I will go to the party tonight.
But if I am not paid, can we conclude that I am not going to the party tonight?
I think not, because I have not said anything about what I am going to do if I am not paid.
But if I say:
To go to the party I need money. At this moment I don't have any
money, but if I am paid today I am going to the party tonight.
In this case, can we affirm with absolute certainty, based only on the proposition, that if I am not paid I will not go the party tonight?
In the former case, there is no relation between being paid and going to the party. In the latter case there is.
logic
edited 3 hours ago
Frank Hubeny
8,72751549
asked 4 hours ago
Carlitos_30Carlitos_30
263
add a comment |
If I say:
If I am paid today I'll go to the party tonight
I am saying that if I receive a payment today I will go to the party tonight.
But if I am not paid, can we conclude that I am not going to the party tonight?
I think not, because I have not said anything about what I am going to do if I am not paid.
But if I say:
To go to the party I need money. At this moment I don't have any
money, but if I am paid today I am going to the party tonight.
In this case, can we affirm with absolute certainty, based only on the proposition, that if I am not paid I will not go the party tonight?
In the former case, there is no relation between being paid and going to the party. In the latter case there is.
logic
edited 3 hours ago
Frank Hubeny
8,72751549
asked 4 hours ago
Carlitos_30Carlitos_30
263
If your aunt gives you some money, would you go to the party ? :)
– rs.29
37 mins ago
add a comment |
If I say:
If I am paid today I'll go to the party tonight
I am saying that if I receive a payment today I will go to the party tonight.
But if I am not paid, can we conclude that I am not going to the party tonight?
I think not, because I have not said anything about what I am going to do if I am not paid.
But if I say:
To go to the party I need money. At this moment I don't have any
money, but if I am paid today I am going to the party tonight.
In this case, can we affirm with absolute certainty, based only on the proposition, that if I am not paid I will not go the party tonight?
In the former case, there is no relation between being paid and going to the party. In the latter case there is.
logic
edited 3 hours ago
Frank Hubeny
8,72751549
asked 4 hours ago
Carlitos_30Carlitos_30
263
If I say:
If I am paid today I'll go to the party tonight
I am saying that if I receive a payment today I will go to the party tonight.
But if I am not paid, can we conclude that I am not going to the party tonight?
I think not, because I have not said anything about what I am going to do if I am not paid.
But if I say:
To go to the party I need money. At this moment I don't have any
money, but if I am paid today I am going to the party tonight.
In this case, can we affirm with absolute certainty, based only on the proposition, that if I am not paid I will not go the party tonight?
In the former case, there is no relation between being paid and going to the party. In the latter case there is.
logic
logic
edited 3 hours ago
Frank Hubeny
8,72751549
asked 4 hours ago
Carlitos_30Carlitos_30
263
edited 3 hours ago
Frank Hubeny
8,72751549
asked 4 hours ago
Carlitos_30Carlitos_30
263
edited 3 hours ago
Frank Hubeny
8,72751549
edited 3 hours ago
Frank Hubeny
8,72751549
edited 3 hours ago
Frank Hubeny
8,72751549
8,72751549
asked 4 hours ago
Carlitos_30Carlitos_30
263
asked 4 hours ago
Carlitos_30Carlitos_30
263
asked 4 hours ago
Carlitos_30Carlitos_30
263
263
If your aunt gives you some money, would you go to the party ? :)
– rs.29
37 mins ago
add a comment |
If your aunt gives you some money, would you go to the party ? :)
– rs.29
37 mins ago
If your aunt gives you some money, would you go to the party ? :)
– rs.29
37 mins ago
If your aunt gives you some money, would you go to the party ? :)
– rs.29
37 mins ago
add a comment |
2 Answers
2
active
oldest
votes
That depends on your underlying logic, or how you interpret "If ... then". If understood as material implication/conditional (written A → B in logic), which corresponds to the usual mathematical use of "if" as found in mathematical theorems, then from
If I am paid today I'll go to the party tonight
you can not deduce that
If I am paid not today, I'll not go to the party tonight.
In propositional logic, "If A then B" means that in all the situations where A is true, B will be true as well, i.o.w., there are no situations in which A is true but B is false; but this doesn't exclude the possibility that there might be situations where A is false but B is still true. So from (not A) you can not conclude (not B) when given A → B.
Such an inference would require a stronger statement, namely "if and only if":
If and only if I am paid today I'll go to the party tonight
This is called a bi-implication or bi-conditonal, written A ↔ B and means that the situations in which A is true are exactly the situations in which B is true. So if A is false, this will enable you to conclude that B can not be true either.
The question is now whether the usual mathematical interpretation of "if" is indeed the "if" that is used in an ordinary English sentence like yours, i.e. whether a straightforward translation of "If A then B" into A → B with said logical properties is appropriate. There has been heaps of philosophical discussion and psychological research about this, and the short answer is: Depends on the context, but in general interpreing natural language "if" strictly as material implication is too short-sighted, because there are many scenarios in which people use and understand "if" in different ways, and good reasons why they do so. In particular, there are many real-life contexts (and theories about why this is so) in which a natural language "if" is intended and understood as what a logician would call an "if and only if", in which case the inference "If not A, then not B" is valid and intended. W.r.t. to your example, such an interpretation seems plausible, because you presumably intend to say that you need the money to spend at the party, in which case it would by cognitively reasonable to draw the inference that if you don't receive your payment, you won't show up at the party.
So: From a classical logic point of view, no, this inference is not valid; from a psychological/natural language point of view, depends on context, because a natural language "if" is vague, and there can be reasons in favor of either interpretation as A → B (from which we can't make any conclusions about B given that A is false), A ↔ B (from which we could deduce that you're not going to the party given that you're not paid), or something completely different.
answered 50 mins ago
lemontreelemontree
1315
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Good answer. I think you might mean, in your last paragraph, that "if" is ambiguous, not that it's vague?
– Eliran
30 mins ago
@Eliran Linguistically speaking, "vagueness" in the sense of underspecification for a certain feature (like bi-/non-bi conditionality) is just a kind of ambiguity, next to ambiguities like homonymy (bank vs. bank etc.), so I'd see my claim as non-contradictory to your statement - what definition of "ambiguity" do you presuppose that contradicts a predication as "vague"?
– lemontree
22 mins ago
I was thinking of vagueness that is present in words like 'tall' and 'bald' that have borderline cases, and of ambiguity as in words like 'bank' or 'must' (i.e. epistemic, moral, etc). But I'm not familiar with how these terms are used in linguistics, only in philososphy. This captures what I mean: plato.stanford.edu/entries/ambiguity/#Vagu
– Eliran
11 mins ago
@Eliran I would refer to this specific property of adjectives like 'tall' as "relativity" (in the direction of "context-dependent"), but wouldn't object to dubbing this as a case of "vagueness" either. SEP is a respectable resource; there are hardly precise and universally agreed upon definitions of notions like "vagueness", or even what counts as a word. You could probably say that "vague" is vague (or ambiguous, if you want) itself :)
– lemontree
6 mins ago
add a comment |
The question asks if we are given more information, that is, more propositions describing the situation about whether someone will go to the party or not, can we say "with absolute certainty, based only on the proposition, that if I am not paid I will not go the party tonight?"
There may be other conditions that arise that have not been anticipated that may prevent someone from going to the party or allow that person to go to the party even if that person is not paid. We don't know that we have covered everything.
For example, that person might be very tired and not want to go to the party when it is time to go even if the person has been paid. Or friends may say that they will loan the person the money to go to the party or pay the person's way allowing the person to go even if the person has not been paid.
Even assuming we have covered all of the possibilities that might come up, if we assume the person has free will that person may choose not to go to the party even if the person has been paid because there are two alternate possibilities, (1) go to the party or (2) do not go to the party, and, by assumption, the person still has enough free will to choose to do either.
answered 2 hours ago
Frank HubenyFrank Hubeny
8,72751549
I meant assuming nothing, just pure logic. I think there is a difference with the proposition: "if x + a = 2 then x = 2-a" and "if x = 6 then y = 6". In the first case, the negation implies necessarily that that x != 2-a". In the second, the negation doesn't imply that y != 6, because there is no relation between x= 6 and y=6.
– Carlitos_30
2 hours ago
@Carlitos_30 In the first math example x = 2-a, but in the second we don't know about the relationship between x and y enough to tell what a change in x has to do with y. With the first example, we know everything there is to know and there is no free will involved. In the example about going to the party we don't know everything there is to know and there is free will involved so we can't say with absolute certainty if someone will go to the party.
– Frank Hubeny
1 hour ago
add a comment |
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2 Answers
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2 Answers
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That depends on your underlying logic, or how you interpret "If ... then". If understood as material implication/conditional (written A → B in logic), which corresponds to the usual mathematical use of "if" as found in mathematical theorems, then from
If I am paid today I'll go to the party tonight
you can not deduce that
If I am paid not today, I'll not go to the party tonight.
In propositional logic, "If A then B" means that in all the situations where A is true, B will be true as well, i.o.w., there are no situations in which A is true but B is false; but this doesn't exclude the possibility that there might be situations where A is false but B is still true. So from (not A) you can not conclude (not B) when given A → B.
Such an inference would require a stronger statement, namely "if and only if":
If and only if I am paid today I'll go to the party tonight
This is called a bi-implication or bi-conditonal, written A ↔ B and means that the situations in which A is true are exactly the situations in which B is true. So if A is false, this will enable you to conclude that B can not be true either.
The question is now whether the usual mathematical interpretation of "if" is indeed the "if" that is used in an ordinary English sentence like yours, i.e. whether a straightforward translation of "If A then B" into A → B with said logical properties is appropriate. There has been heaps of philosophical discussion and psychological research about this, and the short answer is: Depends on the context, but in general interpreing natural language "if" strictly as material implication is too short-sighted, because there are many scenarios in which people use and understand "if" in different ways, and good reasons why they do so. In particular, there are many real-life contexts (and theories about why this is so) in which a natural language "if" is intended and understood as what a logician would call an "if and only if", in which case the inference "If not A, then not B" is valid and intended. W.r.t. to your example, such an interpretation seems plausible, because you presumably intend to say that you need the money to spend at the party, in which case it would by cognitively reasonable to draw the inference that if you don't receive your payment, you won't show up at the party.
So: From a classical logic point of view, no, this inference is not valid; from a psychological/natural language point of view, depends on context, because a natural language "if" is vague, and there can be reasons in favor of either interpretation as A → B (from which we can't make any conclusions about B given that A is false), A ↔ B (from which we could deduce that you're not going to the party given that you're not paid), or something completely different.
answered 50 mins ago
lemontreelemontree
1315
New contributor
lemontree is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Good answer. I think you might mean, in your last paragraph, that "if" is ambiguous, not that it's vague?
– Eliran
30 mins ago
@Eliran Linguistically speaking, "vagueness" in the sense of underspecification for a certain feature (like bi-/non-bi conditionality) is just a kind of ambiguity, next to ambiguities like homonymy (bank vs. bank etc.), so I'd see my claim as non-contradictory to your statement - what definition of "ambiguity" do you presuppose that contradicts a predication as "vague"?
– lemontree
22 mins ago
I was thinking of vagueness that is present in words like 'tall' and 'bald' that have borderline cases, and of ambiguity as in words like 'bank' or 'must' (i.e. epistemic, moral, etc). But I'm not familiar with how these terms are used in linguistics, only in philososphy. This captures what I mean: plato.stanford.edu/entries/ambiguity/#Vagu
– Eliran
11 mins ago
@Eliran I would refer to this specific property of adjectives like 'tall' as "relativity" (in the direction of "context-dependent"), but wouldn't object to dubbing this as a case of "vagueness" either. SEP is a respectable resource; there are hardly precise and universally agreed upon definitions of notions like "vagueness", or even what counts as a word. You could probably say that "vague" is vague (or ambiguous, if you want) itself :)
– lemontree
6 mins ago
add a comment |
That depends on your underlying logic, or how you interpret "If ... then". If understood as material implication/conditional (written A → B in logic), which corresponds to the usual mathematical use of "if" as found in mathematical theorems, then from
If I am paid today I'll go to the party tonight
you can not deduce that
If I am paid not today, I'll not go to the party tonight.
In propositional logic, "If A then B" means that in all the situations where A is true, B will be true as well, i.o.w., there are no situations in which A is true but B is false; but this doesn't exclude the possibility that there might be situations where A is false but B is still true. So from (not A) you can not conclude (not B) when given A → B.
Such an inference would require a stronger statement, namely "if and only if":
If and only if I am paid today I'll go to the party tonight
This is called a bi-implication or bi-conditonal, written A ↔ B and means that the situations in which A is true are exactly the situations in which B is true. So if A is false, this will enable you to conclude that B can not be true either.
The question is now whether the usual mathematical interpretation of "if" is indeed the "if" that is used in an ordinary English sentence like yours, i.e. whether a straightforward translation of "If A then B" into A → B with said logical properties is appropriate. There has been heaps of philosophical discussion and psychological research about this, and the short answer is: Depends on the context, but in general interpreing natural language "if" strictly as material implication is too short-sighted, because there are many scenarios in which people use and understand "if" in different ways, and good reasons why they do so. In particular, there are many real-life contexts (and theories about why this is so) in which a natural language "if" is intended and understood as what a logician would call an "if and only if", in which case the inference "If not A, then not B" is valid and intended. W.r.t. to your example, such an interpretation seems plausible, because you presumably intend to say that you need the money to spend at the party, in which case it would by cognitively reasonable to draw the inference that if you don't receive your payment, you won't show up at the party.
So: From a classical logic point of view, no, this inference is not valid; from a psychological/natural language point of view, depends on context, because a natural language "if" is vague, and there can be reasons in favor of either interpretation as A → B (from which we can't make any conclusions about B given that A is false), A ↔ B (from which we could deduce that you're not going to the party given that you're not paid), or something completely different.
answered 50 mins ago
lemontreelemontree
1315
New contributor
lemontree is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Good answer. I think you might mean, in your last paragraph, that "if" is ambiguous, not that it's vague?
– Eliran
30 mins ago
@Eliran Linguistically speaking, "vagueness" in the sense of underspecification for a certain feature (like bi-/non-bi conditionality) is just a kind of ambiguity, next to ambiguities like homonymy (bank vs. bank etc.), so I'd see my claim as non-contradictory to your statement - what definition of "ambiguity" do you presuppose that contradicts a predication as "vague"?
– lemontree
22 mins ago
I was thinking of vagueness that is present in words like 'tall' and 'bald' that have borderline cases, and of ambiguity as in words like 'bank' or 'must' (i.e. epistemic, moral, etc). But I'm not familiar with how these terms are used in linguistics, only in philososphy. This captures what I mean: plato.stanford.edu/entries/ambiguity/#Vagu
– Eliran
11 mins ago
@Eliran I would refer to this specific property of adjectives like 'tall' as "relativity" (in the direction of "context-dependent"), but wouldn't object to dubbing this as a case of "vagueness" either. SEP is a respectable resource; there are hardly precise and universally agreed upon definitions of notions like "vagueness", or even what counts as a word. You could probably say that "vague" is vague (or ambiguous, if you want) itself :)
– lemontree
6 mins ago
add a comment |
That depends on your underlying logic, or how you interpret "If ... then". If understood as material implication/conditional (written A → B in logic), which corresponds to the usual mathematical use of "if" as found in mathematical theorems, then from
If I am paid today I'll go to the party tonight
you can not deduce that
If I am paid not today, I'll not go to the party tonight.
In propositional logic, "If A then B" means that in all the situations where A is true, B will be true as well, i.o.w., there are no situations in which A is true but B is false; but this doesn't exclude the possibility that there might be situations where A is false but B is still true. So from (not A) you can not conclude (not B) when given A → B.
Such an inference would require a stronger statement, namely "if and only if":
If and only if I am paid today I'll go to the party tonight
This is called a bi-implication or bi-conditonal, written A ↔ B and means that the situations in which A is true are exactly the situations in which B is true. So if A is false, this will enable you to conclude that B can not be true either.
The question is now whether the usual mathematical interpretation of "if" is indeed the "if" that is used in an ordinary English sentence like yours, i.e. whether a straightforward translation of "If A then B" into A → B with said logical properties is appropriate. There has been heaps of philosophical discussion and psychological research about this, and the short answer is: Depends on the context, but in general interpreing natural language "if" strictly as material implication is too short-sighted, because there are many scenarios in which people use and understand "if" in different ways, and good reasons why they do so. In particular, there are many real-life contexts (and theories about why this is so) in which a natural language "if" is intended and understood as what a logician would call an "if and only if", in which case the inference "If not A, then not B" is valid and intended. W.r.t. to your example, such an interpretation seems plausible, because you presumably intend to say that you need the money to spend at the party, in which case it would by cognitively reasonable to draw the inference that if you don't receive your payment, you won't show up at the party.
So: From a classical logic point of view, no, this inference is not valid; from a psychological/natural language point of view, depends on context, because a natural language "if" is vague, and there can be reasons in favor of either interpretation as A → B (from which we can't make any conclusions about B given that A is false), A ↔ B (from which we could deduce that you're not going to the party given that you're not paid), or something completely different.
answered 50 mins ago
lemontreelemontree
1315
New contributor
lemontree is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
That depends on your underlying logic, or how you interpret "If ... then". If understood as material implication/conditional (written A → B in logic), which corresponds to the usual mathematical use of "if" as found in mathematical theorems, then from
If I am paid today I'll go to the party tonight
you can not deduce that
If I am paid not today, I'll not go to the party tonight.
In propositional logic, "If A then B" means that in all the situations where A is true, B will be true as well, i.o.w., there are no situations in which A is true but B is false; but this doesn't exclude the possibility that there might be situations where A is false but B is still true. So from (not A) you can not conclude (not B) when given A → B.
Such an inference would require a stronger statement, namely "if and only if":
If and only if I am paid today I'll go to the party tonight
This is called a bi-implication or bi-conditonal, written A ↔ B and means that the situations in which A is true are exactly the situations in which B is true. So if A is false, this will enable you to conclude that B can not be true either.
The question is now whether the usual mathematical interpretation of "if" is indeed the "if" that is used in an ordinary English sentence like yours, i.e. whether a straightforward translation of "If A then B" into A → B with said logical properties is appropriate. There has been heaps of philosophical discussion and psychological research about this, and the short answer is: Depends on the context, but in general interpreing natural language "if" strictly as material implication is too short-sighted, because there are many scenarios in which people use and understand "if" in different ways, and good reasons why they do so. In particular, there are many real-life contexts (and theories about why this is so) in which a natural language "if" is intended and understood as what a logician would call an "if and only if", in which case the inference "If not A, then not B" is valid and intended. W.r.t. to your example, such an interpretation seems plausible, because you presumably intend to say that you need the money to spend at the party, in which case it would by cognitively reasonable to draw the inference that if you don't receive your payment, you won't show up at the party.
So: From a classical logic point of view, no, this inference is not valid; from a psychological/natural language point of view, depends on context, because a natural language "if" is vague, and there can be reasons in favor of either interpretation as A → B (from which we can't make any conclusions about B given that A is false), A ↔ B (from which we could deduce that you're not going to the party given that you're not paid), or something completely different.
answered 50 mins ago
lemontreelemontree
1315
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lemontree is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 44 mins ago
answered 50 mins ago
lemontreelemontree
1315
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lemontree is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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answered 50 mins ago
lemontreelemontree
1315
answered 50 mins ago
lemontreelemontree
1315
1315
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lemontree is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
lemontree is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
lemontree is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Good answer. I think you might mean, in your last paragraph, that "if" is ambiguous, not that it's vague?
– Eliran
30 mins ago
@Eliran Linguistically speaking, "vagueness" in the sense of underspecification for a certain feature (like bi-/non-bi conditionality) is just a kind of ambiguity, next to ambiguities like homonymy (bank vs. bank etc.), so I'd see my claim as non-contradictory to your statement - what definition of "ambiguity" do you presuppose that contradicts a predication as "vague"?
– lemontree
22 mins ago
I was thinking of vagueness that is present in words like 'tall' and 'bald' that have borderline cases, and of ambiguity as in words like 'bank' or 'must' (i.e. epistemic, moral, etc). But I'm not familiar with how these terms are used in linguistics, only in philososphy. This captures what I mean: plato.stanford.edu/entries/ambiguity/#Vagu
– Eliran
11 mins ago
@Eliran I would refer to this specific property of adjectives like 'tall' as "relativity" (in the direction of "context-dependent"), but wouldn't object to dubbing this as a case of "vagueness" either. SEP is a respectable resource; there are hardly precise and universally agreed upon definitions of notions like "vagueness", or even what counts as a word. You could probably say that "vague" is vague (or ambiguous, if you want) itself :)
– lemontree
6 mins ago
add a comment |
Good answer. I think you might mean, in your last paragraph, that "if" is ambiguous, not that it's vague?
– Eliran
30 mins ago
@Eliran Linguistically speaking, "vagueness" in the sense of underspecification for a certain feature (like bi-/non-bi conditionality) is just a kind of ambiguity, next to ambiguities like homonymy (bank vs. bank etc.), so I'd see my claim as non-contradictory to your statement - what definition of "ambiguity" do you presuppose that contradicts a predication as "vague"?
– lemontree
22 mins ago
I was thinking of vagueness that is present in words like 'tall' and 'bald' that have borderline cases, and of ambiguity as in words like 'bank' or 'must' (i.e. epistemic, moral, etc). But I'm not familiar with how these terms are used in linguistics, only in philososphy. This captures what I mean: plato.stanford.edu/entries/ambiguity/#Vagu
– Eliran
11 mins ago
@Eliran I would refer to this specific property of adjectives like 'tall' as "relativity" (in the direction of "context-dependent"), but wouldn't object to dubbing this as a case of "vagueness" either. SEP is a respectable resource; there are hardly precise and universally agreed upon definitions of notions like "vagueness", or even what counts as a word. You could probably say that "vague" is vague (or ambiguous, if you want) itself :)
– lemontree
6 mins ago
Good answer. I think you might mean, in your last paragraph, that "if" is ambiguous, not that it's vague?
– Eliran
30 mins ago
Good answer. I think you might mean, in your last paragraph, that "if" is ambiguous, not that it's vague?
– Eliran
30 mins ago
@Eliran Linguistically speaking, "vagueness" in the sense of underspecification for a certain feature (like bi-/non-bi conditionality) is just a kind of ambiguity, next to ambiguities like homonymy (bank vs. bank etc.), so I'd see my claim as non-contradictory to your statement - what definition of "ambiguity" do you presuppose that contradicts a predication as "vague"?
– lemontree
22 mins ago
@Eliran Linguistically speaking, "vagueness" in the sense of underspecification for a certain feature (like bi-/non-bi conditionality) is just a kind of ambiguity, next to ambiguities like homonymy (bank vs. bank etc.), so I'd see my claim as non-contradictory to your statement - what definition of "ambiguity" do you presuppose that contradicts a predication as "vague"?
– lemontree
22 mins ago
I was thinking of vagueness that is present in words like 'tall' and 'bald' that have borderline cases, and of ambiguity as in words like 'bank' or 'must' (i.e. epistemic, moral, etc). But I'm not familiar with how these terms are used in linguistics, only in philososphy. This captures what I mean: plato.stanford.edu/entries/ambiguity/#Vagu
– Eliran
11 mins ago
I was thinking of vagueness that is present in words like 'tall' and 'bald' that have borderline cases, and of ambiguity as in words like 'bank' or 'must' (i.e. epistemic, moral, etc). But I'm not familiar with how these terms are used in linguistics, only in philososphy. This captures what I mean: plato.stanford.edu/entries/ambiguity/#Vagu
– Eliran
11 mins ago
@Eliran I would refer to this specific property of adjectives like 'tall' as "relativity" (in the direction of "context-dependent"), but wouldn't object to dubbing this as a case of "vagueness" either. SEP is a respectable resource; there are hardly precise and universally agreed upon definitions of notions like "vagueness", or even what counts as a word. You could probably say that "vague" is vague (or ambiguous, if you want) itself :)
– lemontree
6 mins ago
@Eliran I would refer to this specific property of adjectives like 'tall' as "relativity" (in the direction of "context-dependent"), but wouldn't object to dubbing this as a case of "vagueness" either. SEP is a respectable resource; there are hardly precise and universally agreed upon definitions of notions like "vagueness", or even what counts as a word. You could probably say that "vague" is vague (or ambiguous, if you want) itself :)
– lemontree
6 mins ago
add a comment |
The question asks if we are given more information, that is, more propositions describing the situation about whether someone will go to the party or not, can we say "with absolute certainty, based only on the proposition, that if I am not paid I will not go the party tonight?"
There may be other conditions that arise that have not been anticipated that may prevent someone from going to the party or allow that person to go to the party even if that person is not paid. We don't know that we have covered everything.
For example, that person might be very tired and not want to go to the party when it is time to go even if the person has been paid. Or friends may say that they will loan the person the money to go to the party or pay the person's way allowing the person to go even if the person has not been paid.
Even assuming we have covered all of the possibilities that might come up, if we assume the person has free will that person may choose not to go to the party even if the person has been paid because there are two alternate possibilities, (1) go to the party or (2) do not go to the party, and, by assumption, the person still has enough free will to choose to do either.
answered 2 hours ago
Frank HubenyFrank Hubeny
8,72751549
I meant assuming nothing, just pure logic. I think there is a difference with the proposition: "if x + a = 2 then x = 2-a" and "if x = 6 then y = 6". In the first case, the negation implies necessarily that that x != 2-a". In the second, the negation doesn't imply that y != 6, because there is no relation between x= 6 and y=6.
– Carlitos_30
2 hours ago
@Carlitos_30 In the first math example x = 2-a, but in the second we don't know about the relationship between x and y enough to tell what a change in x has to do with y. With the first example, we know everything there is to know and there is no free will involved. In the example about going to the party we don't know everything there is to know and there is free will involved so we can't say with absolute certainty if someone will go to the party.
– Frank Hubeny
1 hour ago
add a comment |
The question asks if we are given more information, that is, more propositions describing the situation about whether someone will go to the party or not, can we say "with absolute certainty, based only on the proposition, that if I am not paid I will not go the party tonight?"
There may be other conditions that arise that have not been anticipated that may prevent someone from going to the party or allow that person to go to the party even if that person is not paid. We don't know that we have covered everything.
For example, that person might be very tired and not want to go to the party when it is time to go even if the person has been paid. Or friends may say that they will loan the person the money to go to the party or pay the person's way allowing the person to go even if the person has not been paid.
Even assuming we have covered all of the possibilities that might come up, if we assume the person has free will that person may choose not to go to the party even if the person has been paid because there are two alternate possibilities, (1) go to the party or (2) do not go to the party, and, by assumption, the person still has enough free will to choose to do either.
answered 2 hours ago
Frank HubenyFrank Hubeny
8,72751549
I meant assuming nothing, just pure logic. I think there is a difference with the proposition: "if x + a = 2 then x = 2-a" and "if x = 6 then y = 6". In the first case, the negation implies necessarily that that x != 2-a". In the second, the negation doesn't imply that y != 6, because there is no relation between x= 6 and y=6.
– Carlitos_30
2 hours ago
@Carlitos_30 In the first math example x = 2-a, but in the second we don't know about the relationship between x and y enough to tell what a change in x has to do with y. With the first example, we know everything there is to know and there is no free will involved. In the example about going to the party we don't know everything there is to know and there is free will involved so we can't say with absolute certainty if someone will go to the party.
– Frank Hubeny
1 hour ago
add a comment |
The question asks if we are given more information, that is, more propositions describing the situation about whether someone will go to the party or not, can we say "with absolute certainty, based only on the proposition, that if I am not paid I will not go the party tonight?"
There may be other conditions that arise that have not been anticipated that may prevent someone from going to the party or allow that person to go to the party even if that person is not paid. We don't know that we have covered everything.
For example, that person might be very tired and not want to go to the party when it is time to go even if the person has been paid. Or friends may say that they will loan the person the money to go to the party or pay the person's way allowing the person to go even if the person has not been paid.
Even assuming we have covered all of the possibilities that might come up, if we assume the person has free will that person may choose not to go to the party even if the person has been paid because there are two alternate possibilities, (1) go to the party or (2) do not go to the party, and, by assumption, the person still has enough free will to choose to do either.
answered 2 hours ago
Frank HubenyFrank Hubeny
8,72751549
The question asks if we are given more information, that is, more propositions describing the situation about whether someone will go to the party or not, can we say "with absolute certainty, based only on the proposition, that if I am not paid I will not go the party tonight?"
There may be other conditions that arise that have not been anticipated that may prevent someone from going to the party or allow that person to go to the party even if that person is not paid. We don't know that we have covered everything.
For example, that person might be very tired and not want to go to the party when it is time to go even if the person has been paid. Or friends may say that they will loan the person the money to go to the party or pay the person's way allowing the person to go even if the person has not been paid.
Even assuming we have covered all of the possibilities that might come up, if we assume the person has free will that person may choose not to go to the party even if the person has been paid because there are two alternate possibilities, (1) go to the party or (2) do not go to the party, and, by assumption, the person still has enough free will to choose to do either.
answered 2 hours ago
Frank HubenyFrank Hubeny
8,72751549
answered 2 hours ago
Frank HubenyFrank Hubeny
8,72751549
answered 2 hours ago
Frank HubenyFrank Hubeny
8,72751549
answered 2 hours ago
Frank HubenyFrank Hubeny
8,72751549
8,72751549
I meant assuming nothing, just pure logic. I think there is a difference with the proposition: "if x + a = 2 then x = 2-a" and "if x = 6 then y = 6". In the first case, the negation implies necessarily that that x != 2-a". In the second, the negation doesn't imply that y != 6, because there is no relation between x= 6 and y=6.
– Carlitos_30
2 hours ago
@Carlitos_30 In the first math example x = 2-a, but in the second we don't know about the relationship between x and y enough to tell what a change in x has to do with y. With the first example, we know everything there is to know and there is no free will involved. In the example about going to the party we don't know everything there is to know and there is free will involved so we can't say with absolute certainty if someone will go to the party.
– Frank Hubeny
1 hour ago
add a comment |
I meant assuming nothing, just pure logic. I think there is a difference with the proposition: "if x + a = 2 then x = 2-a" and "if x = 6 then y = 6". In the first case, the negation implies necessarily that that x != 2-a". In the second, the negation doesn't imply that y != 6, because there is no relation between x= 6 and y=6.
– Carlitos_30
2 hours ago
@Carlitos_30 In the first math example x = 2-a, but in the second we don't know about the relationship between x and y enough to tell what a change in x has to do with y. With the first example, we know everything there is to know and there is no free will involved. In the example about going to the party we don't know everything there is to know and there is free will involved so we can't say with absolute certainty if someone will go to the party.
– Frank Hubeny
1 hour ago
I meant assuming nothing, just pure logic. I think there is a difference with the proposition: "if x + a = 2 then x = 2-a" and "if x = 6 then y = 6". In the first case, the negation implies necessarily that that x != 2-a". In the second, the negation doesn't imply that y != 6, because there is no relation between x= 6 and y=6.
– Carlitos_30
2 hours ago
I meant assuming nothing, just pure logic. I think there is a difference with the proposition: "if x + a = 2 then x = 2-a" and "if x = 6 then y = 6". In the first case, the negation implies necessarily that that x != 2-a". In the second, the negation doesn't imply that y != 6, because there is no relation between x= 6 and y=6.
– Carlitos_30
2 hours ago
@Carlitos_30 In the first math example x = 2-a, but in the second we don't know about the relationship between x and y enough to tell what a change in x has to do with y. With the first example, we know everything there is to know and there is no free will involved. In the example about going to the party we don't know everything there is to know and there is free will involved so we can't say with absolute certainty if someone will go to the party.
– Frank Hubeny
1 hour ago
@Carlitos_30 In the first math example x = 2-a, but in the second we don't know about the relationship between x and y enough to tell what a change in x has to do with y. With the first example, we know everything there is to know and there is no free will involved. In the example about going to the party we don't know everything there is to know and there is free will involved so we can't say with absolute certainty if someone will go to the party.
– Frank Hubeny
1 hour ago
add a comment |
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If your aunt gives you some money, would you go to the party ? :)
– rs.29
37 mins ago