Logic. Truth of a negationWhy would definition not be proposition?What paradoxes are there for deontic detachment?Propositions lacking referents, and their truth-valuesDoes any person truly need anything?Is there a logic of married bachelors?Regarding Logic and Reductio Ad AbsurdumThe sea battle paradox and the soundness criterionFOL and Tarski's world logic connectives questionWhy does Hume believe that ought brings a new relation?Why don't two equivalent propositions contribute to the same semantics?
Low budget alien movie about the Earth being cooked
What is the likely impact of grounding an entire aircraft series?
Should I tell my boss the work he did was worthless
Word for a person who has no opinion about whether god exists
If the Captain's screens are out, does he switch seats with the co-pilot?
Why don't MCU characters ever seem to have language issues?
Good for you! in Russian
Finding algorithms of QGIS commands?
Space in array system equations
Is there an equal sign with wider gap?
Why does the negative sign arise in this thermodynamic relation?
Is "history" a male-biased word ("his+story")?
The bar has been raised
Unreachable code, but reachable with exception
Offered promotion but I'm leaving. Should I tell?
How much stiffer are 23c tires over 28c?
Accountant/ lawyer will not return my call
Is it true that real estate prices mainly go up?
Algorithm to convert a fixed-length string to the smallest possible collision-free representation?
Do Bugbears' arms literally get longer when it's their turn?
A three room house but a three headED dog
Virginia employer terminated employee and wants signing bonus returned
Is there any way to damage Intellect Devourer(s) when already within a creature's skull?
Can someone explain what is being said here in color publishing in the American Mathematical Monthly?
Logic. Truth of a negation
Why would definition not be proposition?What paradoxes are there for deontic detachment?Propositions lacking referents, and their truth-valuesDoes any person truly need anything?Is there a logic of married bachelors?Regarding Logic and Reductio Ad AbsurdumThe sea battle paradox and the soundness criterionFOL and Tarski's world logic connectives questionWhy does Hume believe that ought brings a new relation?Why don't two equivalent propositions contribute to the same semantics?
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
21 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
21 mins ago
add a comment |
If your aunt gives you some money, would you go to the party ? :)
– rs.29
21 mins ago
If your aunt gives you some money, would you go to the party ? :)
– rs.29
21 mins ago
If your aunt gives you some money, would you go to the party ? :)
– rs.29
21 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 35 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
14 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
7 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
57 mins ago
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%2f61077%2flogic-truth-of-a-negation%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
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 35 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
14 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
7 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 35 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
14 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
7 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 35 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 35 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.
edited 29 mins ago
answered 35 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.
answered 35 mins ago
lemontreelemontree
1315
answered 35 mins ago
lemontreelemontree
1315
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.
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
14 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
7 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
14 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
7 mins ago
Good answer. I think you might mean, in your last paragraph, that "if" is ambiguous, not that it's vague?
– Eliran
14 mins ago
Good answer. I think you might mean, in your last paragraph, that "if" is ambiguous, not that it's vague?
– Eliran
14 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
7 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
7 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
57 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
57 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
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
57 mins 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
57 mins 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
57 mins 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
57 mins ago
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%2f61077%2flogic-truth-of-a-negation%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
If your aunt gives you some money, would you go to the party ? :)
– rs.29
21 mins ago