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Unicorn Meta Zoo #1: Why another podcast?How does one contradiction in argument makes the argument valid?In formal logic, how is it possible for an argument with a contradictory conclusion to be valid?The validity of the definition of a valid argumentHow to find redundant premises?Is this a valid argument?Determine if an argument is valid or invalidConcerning the definition of “valid”What is the difference between a conditional and material implication?How is “~A. Therefore A -> B” a valid argument?Is this argument valid?
If interest rates go down, then I will buy a house. If I buy a house, I will need
a loan. Therefore, I will not need a loan if I do not buy a house.
Is this argument valid?
logic
edited Apr 15 at 17:59
Frank Hubeny
10.6k51558
asked Apr 15 at 17:51
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
161
New contributor
Bruce Grayton Toodeep Muzawazi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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show 1 more comment
If interest rates go down, then I will buy a house. If I buy a house, I will need
a loan. Therefore, I will not need a loan if I do not buy a house.
Is this argument valid?
logic
edited Apr 15 at 17:59
Frank Hubeny
10.6k51558
asked Apr 15 at 17:51
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
161
New contributor
Bruce Grayton Toodeep Muzawazi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Proposed title edit: Is P → Q, therefore ~P → ~Q a valid argument?
– MiCl
Apr 16 at 14:22
@MiCl I think there is more than that going on in the question. There are two premises not just one. How does one show that the first premise about interest rates does not provide enough information for a valid argument?
– Frank Hubeny
Apr 16 at 14:29
What about: “Is P → Q, Q → R, therefore ~Q → ~R a valid argument?”
– MiCl
Apr 16 at 14:33
@MiCl Yes, "P → Q, Q → R, therefore ~Q → ~R" seems to symbolize the argument.
– Frank Hubeny
Apr 16 at 14:35
@MiCl I'm not sure OP knew this is the form of the argument in the post. Formalizing the argument is part of the answer in this case, so I don't think it should be edited into the question.
– Eliran
Apr 16 at 16:13
|
show 1 more comment
If interest rates go down, then I will buy a house. If I buy a house, I will need
a loan. Therefore, I will not need a loan if I do not buy a house.
Is this argument valid?
logic
edited Apr 15 at 17:59
Frank Hubeny
10.6k51558
asked Apr 15 at 17:51
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
161
New contributor
Bruce Grayton Toodeep Muzawazi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
If interest rates go down, then I will buy a house. If I buy a house, I will need
a loan. Therefore, I will not need a loan if I do not buy a house.
Is this argument valid?
logic
logic
edited Apr 15 at 17:59
Frank Hubeny
10.6k51558
asked Apr 15 at 17:51
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
161
New contributor
Bruce Grayton Toodeep Muzawazi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Apr 15 at 17:59
Frank Hubeny
10.6k51558
asked Apr 15 at 17:51
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
161
New contributor
Bruce Grayton Toodeep Muzawazi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited Apr 15 at 17:59
Frank Hubeny
10.6k51558
edited Apr 15 at 17:59
Frank Hubeny
10.6k51558
edited Apr 15 at 17:59
Frank Hubeny
10.6k51558
10.6k51558
asked Apr 15 at 17:51
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
161
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Check out our Code of Conduct.
asked Apr 15 at 17:51
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
161
asked Apr 15 at 17:51
Bruce Grayton Toodeep MuzawaziBruce Grayton Toodeep Muzawazi
161
161
New contributor
Bruce Grayton Toodeep Muzawazi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Bruce Grayton Toodeep Muzawazi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Bruce Grayton Toodeep Muzawazi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Proposed title edit: Is P → Q, therefore ~P → ~Q a valid argument?
– MiCl
Apr 16 at 14:22
@MiCl I think there is more than that going on in the question. There are two premises not just one. How does one show that the first premise about interest rates does not provide enough information for a valid argument?
– Frank Hubeny
Apr 16 at 14:29
What about: “Is P → Q, Q → R, therefore ~Q → ~R a valid argument?”
– MiCl
Apr 16 at 14:33
@MiCl Yes, "P → Q, Q → R, therefore ~Q → ~R" seems to symbolize the argument.
– Frank Hubeny
Apr 16 at 14:35
@MiCl I'm not sure OP knew this is the form of the argument in the post. Formalizing the argument is part of the answer in this case, so I don't think it should be edited into the question.
– Eliran
Apr 16 at 16:13
|
show 1 more comment
Proposed title edit: Is P → Q, therefore ~P → ~Q a valid argument?
– MiCl
Apr 16 at 14:22
@MiCl I think there is more than that going on in the question. There are two premises not just one. How does one show that the first premise about interest rates does not provide enough information for a valid argument?
– Frank Hubeny
Apr 16 at 14:29
What about: “Is P → Q, Q → R, therefore ~Q → ~R a valid argument?”
– MiCl
Apr 16 at 14:33
@MiCl Yes, "P → Q, Q → R, therefore ~Q → ~R" seems to symbolize the argument.
– Frank Hubeny
Apr 16 at 14:35
@MiCl I'm not sure OP knew this is the form of the argument in the post. Formalizing the argument is part of the answer in this case, so I don't think it should be edited into the question.
– Eliran
Apr 16 at 16:13
Proposed title edit: Is P → Q, therefore ~P → ~Q a valid argument?
– MiCl
Apr 16 at 14:22
Proposed title edit: Is P → Q, therefore ~P → ~Q a valid argument?
– MiCl
Apr 16 at 14:22
@MiCl I think there is more than that going on in the question. There are two premises not just one. How does one show that the first premise about interest rates does not provide enough information for a valid argument?
– Frank Hubeny
Apr 16 at 14:29
@MiCl I think there is more than that going on in the question. There are two premises not just one. How does one show that the first premise about interest rates does not provide enough information for a valid argument?
– Frank Hubeny
Apr 16 at 14:29
What about: “Is P → Q, Q → R, therefore ~Q → ~R a valid argument?”
– MiCl
Apr 16 at 14:33
What about: “Is P → Q, Q → R, therefore ~Q → ~R a valid argument?”
– MiCl
Apr 16 at 14:33
@MiCl Yes, "P → Q, Q → R, therefore ~Q → ~R" seems to symbolize the argument.
– Frank Hubeny
Apr 16 at 14:35
@MiCl Yes, "P → Q, Q → R, therefore ~Q → ~R" seems to symbolize the argument.
– Frank Hubeny
Apr 16 at 14:35
@MiCl I'm not sure OP knew this is the form of the argument in the post. Formalizing the argument is part of the answer in this case, so I don't think it should be edited into the question.
– Eliran
Apr 16 at 16:13
@MiCl I'm not sure OP knew this is the form of the argument in the post. Formalizing the argument is part of the answer in this case, so I don't think it should be edited into the question.
– Eliran
Apr 16 at 16:13
|
show 1 more comment
4 Answers
4
active
oldest
votes
Is the argument valid?
No.
"I will not need a loan if I do not buy a house" is the same as "If I do not buy a house, then I will not need a loan".
This is not implied by "If I buy a house, I will need a loan".
See Denying the antecedent.
answered Apr 15 at 18:19
Mauro ALLEGRANZAMauro ALLEGRANZA
30.1k22066
add a comment |
Wikipedia describes validity as follows:
In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
The argument we want to test for validity is the following:
If interest rates go down, then I will buy a house. If I buy a house, I will need a loan. Therefore, I will not need a loan if I do not buy a house.
This can be broken up into propositions with this symbolization key:
- R: "Interest rates go down."
- B: "I will buy a house."
- L: "I will need a loan."
If R then B. If B then L. Therefore, if not B then not L.
We could place the following into a truth table generator. For the truth table generator I am using I would enter the following string:
((R=>B)&&(B=>L))=>(~B=>~L)
This is the result I get:
Note the "F" in the third line of the table. This is a line where the premises are true but the conclusion false. Therefore the argument is invalid.
Stanford Truth Table Tool http://web.stanford.edu/class/cs103/tools/truth-table-tool/
Wikipedia contributors. (2019, March 28). Validity (logic). In Wikipedia, The Free Encyclopedia. Retrieved 18:05, April 15, 2019, from https://en.wikipedia.org/w/index.php?title=Validity_(logic)&oldid=889899195
answered Apr 15 at 18:19
Frank HubenyFrank Hubeny
10.6k51558
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
Apr 16 at 14:13
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
Apr 16 at 14:24
add a comment |
The last statement suggests that buying a house is the only reason you would need a loan. Not buying a house does not rule out other reasons for needing a loan. Therefore it's logically false.
If it were explicitly stated that you would only ever need a loan when buying a house, it would be logically correct, even though it would be potentially false in reality.
answered Apr 16 at 6:05
YoupTYoupT
636
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YoupT is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
All the upvoted arguments are valid. Here's just another way of phrasing the answer.
You start with this:
- (Lower interests) IMPLIES (purchase house)
- (Purchase house) IMPLIES (take loan)
You can drop the first one entirely.
Now you're asking : "Logically, are the following two statements equivalent?"
- (Purchase house) IMPLIES (take loan)
- (NOT purchase house) IMPLIES (NOT take loan)
No. They're not logically equivalent.
The logic concept that you SEEM to want to apply here would be Contraposition (cf. Wikipedia), but it's not applied correctly.
A correct contraposition of "(Purchase house) IMPLIES (take loan)" would be : "(NOT take loan) IMPLIES (NOT Purchase house)" (notice how they swapped position when adding the NOT)
answered Apr 16 at 12:55
jeancallistijeancallisti
312
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add a comment |
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
Is the argument valid?
No.
"I will not need a loan if I do not buy a house" is the same as "If I do not buy a house, then I will not need a loan".
This is not implied by "If I buy a house, I will need a loan".
See Denying the antecedent.
answered Apr 15 at 18:19
Mauro ALLEGRANZAMauro ALLEGRANZA
30.1k22066
add a comment |
Is the argument valid?
No.
"I will not need a loan if I do not buy a house" is the same as "If I do not buy a house, then I will not need a loan".
This is not implied by "If I buy a house, I will need a loan".
See Denying the antecedent.
answered Apr 15 at 18:19
Mauro ALLEGRANZAMauro ALLEGRANZA
30.1k22066
add a comment |
Is the argument valid?
No.
"I will not need a loan if I do not buy a house" is the same as "If I do not buy a house, then I will not need a loan".
This is not implied by "If I buy a house, I will need a loan".
See Denying the antecedent.
answered Apr 15 at 18:19
Mauro ALLEGRANZAMauro ALLEGRANZA
30.1k22066
Is the argument valid?
No.
"I will not need a loan if I do not buy a house" is the same as "If I do not buy a house, then I will not need a loan".
This is not implied by "If I buy a house, I will need a loan".
See Denying the antecedent.
answered Apr 15 at 18:19
Mauro ALLEGRANZAMauro ALLEGRANZA
30.1k22066
answered Apr 15 at 18:19
Mauro ALLEGRANZAMauro ALLEGRANZA
30.1k22066
answered Apr 15 at 18:19
Mauro ALLEGRANZAMauro ALLEGRANZA
30.1k22066
answered Apr 15 at 18:19
Mauro ALLEGRANZAMauro ALLEGRANZA
30.1k22066
30.1k22066
add a comment |
add a comment |
Wikipedia describes validity as follows:
In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
The argument we want to test for validity is the following:
If interest rates go down, then I will buy a house. If I buy a house, I will need a loan. Therefore, I will not need a loan if I do not buy a house.
This can be broken up into propositions with this symbolization key:
- R: "Interest rates go down."
- B: "I will buy a house."
- L: "I will need a loan."
If R then B. If B then L. Therefore, if not B then not L.
We could place the following into a truth table generator. For the truth table generator I am using I would enter the following string:
((R=>B)&&(B=>L))=>(~B=>~L)
This is the result I get:
Note the "F" in the third line of the table. This is a line where the premises are true but the conclusion false. Therefore the argument is invalid.
Stanford Truth Table Tool http://web.stanford.edu/class/cs103/tools/truth-table-tool/
Wikipedia contributors. (2019, March 28). Validity (logic). In Wikipedia, The Free Encyclopedia. Retrieved 18:05, April 15, 2019, from https://en.wikipedia.org/w/index.php?title=Validity_(logic)&oldid=889899195
answered Apr 15 at 18:19
Frank HubenyFrank Hubeny
10.6k51558
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
Apr 16 at 14:13
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
Apr 16 at 14:24
add a comment |
Wikipedia describes validity as follows:
In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
The argument we want to test for validity is the following:
If interest rates go down, then I will buy a house. If I buy a house, I will need a loan. Therefore, I will not need a loan if I do not buy a house.
This can be broken up into propositions with this symbolization key:
- R: "Interest rates go down."
- B: "I will buy a house."
- L: "I will need a loan."
If R then B. If B then L. Therefore, if not B then not L.
We could place the following into a truth table generator. For the truth table generator I am using I would enter the following string:
((R=>B)&&(B=>L))=>(~B=>~L)
This is the result I get:
Note the "F" in the third line of the table. This is a line where the premises are true but the conclusion false. Therefore the argument is invalid.
Stanford Truth Table Tool http://web.stanford.edu/class/cs103/tools/truth-table-tool/
Wikipedia contributors. (2019, March 28). Validity (logic). In Wikipedia, The Free Encyclopedia. Retrieved 18:05, April 15, 2019, from https://en.wikipedia.org/w/index.php?title=Validity_(logic)&oldid=889899195
answered Apr 15 at 18:19
Frank HubenyFrank Hubeny
10.6k51558
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
Apr 16 at 14:13
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
Apr 16 at 14:24
add a comment |
Wikipedia describes validity as follows:
In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
The argument we want to test for validity is the following:
If interest rates go down, then I will buy a house. If I buy a house, I will need a loan. Therefore, I will not need a loan if I do not buy a house.
This can be broken up into propositions with this symbolization key:
- R: "Interest rates go down."
- B: "I will buy a house."
- L: "I will need a loan."
If R then B. If B then L. Therefore, if not B then not L.
We could place the following into a truth table generator. For the truth table generator I am using I would enter the following string:
((R=>B)&&(B=>L))=>(~B=>~L)
This is the result I get:
Note the "F" in the third line of the table. This is a line where the premises are true but the conclusion false. Therefore the argument is invalid.
Stanford Truth Table Tool http://web.stanford.edu/class/cs103/tools/truth-table-tool/
Wikipedia contributors. (2019, March 28). Validity (logic). In Wikipedia, The Free Encyclopedia. Retrieved 18:05, April 15, 2019, from https://en.wikipedia.org/w/index.php?title=Validity_(logic)&oldid=889899195
answered Apr 15 at 18:19
Frank HubenyFrank Hubeny
10.6k51558
Wikipedia describes validity as follows:
In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
The argument we want to test for validity is the following:
If interest rates go down, then I will buy a house. If I buy a house, I will need a loan. Therefore, I will not need a loan if I do not buy a house.
This can be broken up into propositions with this symbolization key:
- R: "Interest rates go down."
- B: "I will buy a house."
- L: "I will need a loan."
If R then B. If B then L. Therefore, if not B then not L.
We could place the following into a truth table generator. For the truth table generator I am using I would enter the following string:
((R=>B)&&(B=>L))=>(~B=>~L)
This is the result I get:
Note the "F" in the third line of the table. This is a line where the premises are true but the conclusion false. Therefore the argument is invalid.
Stanford Truth Table Tool http://web.stanford.edu/class/cs103/tools/truth-table-tool/
Wikipedia contributors. (2019, March 28). Validity (logic). In Wikipedia, The Free Encyclopedia. Retrieved 18:05, April 15, 2019, from https://en.wikipedia.org/w/index.php?title=Validity_(logic)&oldid=889899195
answered Apr 15 at 18:19
Frank HubenyFrank Hubeny
10.6k51558
answered Apr 15 at 18:19
Frank HubenyFrank Hubeny
10.6k51558
answered Apr 15 at 18:19
Frank HubenyFrank Hubeny
10.6k51558
answered Apr 15 at 18:19
Frank HubenyFrank Hubeny
10.6k51558
10.6k51558
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
Apr 16 at 14:13
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
Apr 16 at 14:24
add a comment |
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
Apr 16 at 14:13
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
Apr 16 at 14:24
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
Apr 16 at 14:13
Do I understand the third line correctly as "in the event that interest rates don't go down (R=false), and therefore I don't buy a home (B=false), I may still need a loan (L=true)"? That makes sense, as the concrete case the OP seems to be missing is that people get loans for many other purposes.
– Jon of All Trades
Apr 16 at 14:13
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
Apr 16 at 14:24
@JonofAllTrades Yes, that would be a way to view the situation. Then the premises "(R=>B)&&(B=>L)" are true, but the conclusion "~B=>~L" is false. That valuation or assignment of truth values to the propositions makes the argument invalid.
– Frank Hubeny
Apr 16 at 14:24
add a comment |
The last statement suggests that buying a house is the only reason you would need a loan. Not buying a house does not rule out other reasons for needing a loan. Therefore it's logically false.
If it were explicitly stated that you would only ever need a loan when buying a house, it would be logically correct, even though it would be potentially false in reality.
answered Apr 16 at 6:05
YoupTYoupT
636
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The last statement suggests that buying a house is the only reason you would need a loan. Not buying a house does not rule out other reasons for needing a loan. Therefore it's logically false.
If it were explicitly stated that you would only ever need a loan when buying a house, it would be logically correct, even though it would be potentially false in reality.
answered Apr 16 at 6:05
YoupTYoupT
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The last statement suggests that buying a house is the only reason you would need a loan. Not buying a house does not rule out other reasons for needing a loan. Therefore it's logically false.
If it were explicitly stated that you would only ever need a loan when buying a house, it would be logically correct, even though it would be potentially false in reality.
answered Apr 16 at 6:05
YoupTYoupT
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The last statement suggests that buying a house is the only reason you would need a loan. Not buying a house does not rule out other reasons for needing a loan. Therefore it's logically false.
If it were explicitly stated that you would only ever need a loan when buying a house, it would be logically correct, even though it would be potentially false in reality.
answered Apr 16 at 6:05
YoupTYoupT
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answered Apr 16 at 6:05
YoupTYoupT
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answered Apr 16 at 6:05
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answered Apr 16 at 6:05
YoupTYoupT
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All the upvoted arguments are valid. Here's just another way of phrasing the answer.
You start with this:
- (Lower interests) IMPLIES (purchase house)
- (Purchase house) IMPLIES (take loan)
You can drop the first one entirely.
Now you're asking : "Logically, are the following two statements equivalent?"
- (Purchase house) IMPLIES (take loan)
- (NOT purchase house) IMPLIES (NOT take loan)
No. They're not logically equivalent.
The logic concept that you SEEM to want to apply here would be Contraposition (cf. Wikipedia), but it's not applied correctly.
A correct contraposition of "(Purchase house) IMPLIES (take loan)" would be : "(NOT take loan) IMPLIES (NOT Purchase house)" (notice how they swapped position when adding the NOT)
answered Apr 16 at 12:55
jeancallistijeancallisti
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All the upvoted arguments are valid. Here's just another way of phrasing the answer.
You start with this:
- (Lower interests) IMPLIES (purchase house)
- (Purchase house) IMPLIES (take loan)
You can drop the first one entirely.
Now you're asking : "Logically, are the following two statements equivalent?"
- (Purchase house) IMPLIES (take loan)
- (NOT purchase house) IMPLIES (NOT take loan)
No. They're not logically equivalent.
The logic concept that you SEEM to want to apply here would be Contraposition (cf. Wikipedia), but it's not applied correctly.
A correct contraposition of "(Purchase house) IMPLIES (take loan)" would be : "(NOT take loan) IMPLIES (NOT Purchase house)" (notice how they swapped position when adding the NOT)
answered Apr 16 at 12:55
jeancallistijeancallisti
312
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All the upvoted arguments are valid. Here's just another way of phrasing the answer.
You start with this:
- (Lower interests) IMPLIES (purchase house)
- (Purchase house) IMPLIES (take loan)
You can drop the first one entirely.
Now you're asking : "Logically, are the following two statements equivalent?"
- (Purchase house) IMPLIES (take loan)
- (NOT purchase house) IMPLIES (NOT take loan)
No. They're not logically equivalent.
The logic concept that you SEEM to want to apply here would be Contraposition (cf. Wikipedia), but it's not applied correctly.
A correct contraposition of "(Purchase house) IMPLIES (take loan)" would be : "(NOT take loan) IMPLIES (NOT Purchase house)" (notice how they swapped position when adding the NOT)
answered Apr 16 at 12:55
jeancallistijeancallisti
312
New contributor
jeancallisti is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
All the upvoted arguments are valid. Here's just another way of phrasing the answer.
You start with this:
- (Lower interests) IMPLIES (purchase house)
- (Purchase house) IMPLIES (take loan)
You can drop the first one entirely.
Now you're asking : "Logically, are the following two statements equivalent?"
- (Purchase house) IMPLIES (take loan)
- (NOT purchase house) IMPLIES (NOT take loan)
No. They're not logically equivalent.
The logic concept that you SEEM to want to apply here would be Contraposition (cf. Wikipedia), but it's not applied correctly.
A correct contraposition of "(Purchase house) IMPLIES (take loan)" would be : "(NOT take loan) IMPLIES (NOT Purchase house)" (notice how they swapped position when adding the NOT)
answered Apr 16 at 12:55
jeancallistijeancallisti
312
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edited Apr 16 at 13:00
answered Apr 16 at 12:55
jeancallistijeancallisti
312
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answered Apr 16 at 12:55
jeancallistijeancallisti
312
answered Apr 16 at 12:55
jeancallistijeancallisti
312
312
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New contributor
jeancallisti is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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jeancallisti is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
add a comment |
Bruce Grayton Toodeep Muzawazi is a new contributor. Be nice, and check out our Code of Conduct.
Bruce Grayton Toodeep Muzawazi is a new contributor. Be nice, and check out our Code of Conduct.
Bruce Grayton Toodeep Muzawazi is a new contributor. Be nice, and check out our Code of Conduct.
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Proposed title edit: Is P → Q, therefore ~P → ~Q a valid argument?
– MiCl
Apr 16 at 14:22
@MiCl I think there is more than that going on in the question. There are two premises not just one. How does one show that the first premise about interest rates does not provide enough information for a valid argument?
– Frank Hubeny
Apr 16 at 14:29
What about: “Is P → Q, Q → R, therefore ~Q → ~R a valid argument?”
– MiCl
Apr 16 at 14:33
@MiCl Yes, "P → Q, Q → R, therefore ~Q → ~R" seems to symbolize the argument.
– Frank Hubeny
Apr 16 at 14:35
@MiCl I'm not sure OP knew this is the form of the argument in the post. Formalizing the argument is part of the answer in this case, so I don't think it should be edited into the question.
– Eliran
Apr 16 at 16:13