Confused about the answers to two logic problemsA∧B-worlds and law of enrichment in Stalnaker semanticsValidity stemming from contradictory premissesAre “If P then Q” and “Q only if P” equivalent?“If p, then q” = “q unless ~p”?Why is the statement false: If (A⊃B)∨(A⊃C) is true, then A implies either B or CPutnam's argument against the possibility of nominalising 'distance-statements' in “Philosophy of Logic” (1972)Real World Example to break the logic of this SyllogismLogic. Having problems with interpretations
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Confused about the answers to two logic problems
A∧B-worlds and law of enrichment in Stalnaker semanticsValidity stemming from contradictory premissesAre “If P then Q” and “Q only if P” equivalent?“If p, then q” = “q unless ~p”?Why is the statement false: If (A⊃B)∨(A⊃C) is true, then A implies either B or CPutnam's argument against the possibility of nominalising 'distance-statements' in “Philosophy of Logic” (1972)Real World Example to break the logic of this SyllogismLogic. Having problems with interpretations
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
- True or False? If monkeys can fly, then 1 + 1 = 3.
- What is logically equivalent to all x (p(x) + ~q(x))?
For the first one I think it is False.
logic propositions propositional-logic
edited 2 hours ago
Frank Hubeny
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- True or False? If monkeys can fly, then 1 + 1 = 3.
- What is logically equivalent to all x (p(x) + ~q(x))?
For the first one I think it is False.
logic propositions propositional-logic
edited 2 hours ago
Frank Hubeny
13.9k6 gold badges17 silver badges67 bronze badges
asked 9 hours ago
MollyMolly
111 bronze badge
New contributor
Molly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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1) is true. Think about true conditionals as promises that were upheld. I promise you that if monkeys can fly, then 1+1 is equal to 3. Did I violate my promise? No, because I would violate it only if monkeys could fly, but 1+1 would still not be equal to 3. But this didn't happen.
– user161005
8 hours ago
Thank you. I changed it to True before I turned it in,
– Molly
5 hours ago
@user161005 - Are you assuming the "if A then B" formulation in English is equivalent to a logical proposition of the form A -> B? If this is a homework problem then probably that was the intent, but conditionals can also be interpreted in terms of modal logic which deals with possible worlds, David Lewis apparently developed a modal logic analysis of conditionals...it isn't true that in a possible world where monkeys can fly, 1+1=3, so I assume the statement wouldn't be true under this sort of translation.
– Hypnosifl
4 hours ago
add a comment |
- True or False? If monkeys can fly, then 1 + 1 = 3.
- What is logically equivalent to all x (p(x) + ~q(x))?
For the first one I think it is False.
logic propositions propositional-logic
edited 2 hours ago
Frank Hubeny
13.9k6 gold badges17 silver badges67 bronze badges
asked 9 hours ago
MollyMolly
111 bronze badge
New contributor
Molly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
- True or False? If monkeys can fly, then 1 + 1 = 3.
- What is logically equivalent to all x (p(x) + ~q(x))?
For the first one I think it is False.
logic propositions propositional-logic
logic propositions propositional-logic
edited 2 hours ago
Frank Hubeny
13.9k6 gold badges17 silver badges67 bronze badges
asked 9 hours ago
MollyMolly
111 bronze badge
New contributor
Molly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 hours ago
Frank Hubeny
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asked 9 hours ago
MollyMolly
111 bronze badge
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Molly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 2 hours ago
Frank Hubeny
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edited 2 hours ago
Frank Hubeny
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edited 2 hours ago
Frank Hubeny
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13.9k6 gold badges17 silver badges67 bronze badges
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MollyMolly
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asked 9 hours ago
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asked 9 hours ago
MollyMolly
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111 bronze badge
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Molly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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1) is true. Think about true conditionals as promises that were upheld. I promise you that if monkeys can fly, then 1+1 is equal to 3. Did I violate my promise? No, because I would violate it only if monkeys could fly, but 1+1 would still not be equal to 3. But this didn't happen.
– user161005
8 hours ago
Thank you. I changed it to True before I turned it in,
– Molly
5 hours ago
@user161005 - Are you assuming the "if A then B" formulation in English is equivalent to a logical proposition of the form A -> B? If this is a homework problem then probably that was the intent, but conditionals can also be interpreted in terms of modal logic which deals with possible worlds, David Lewis apparently developed a modal logic analysis of conditionals...it isn't true that in a possible world where monkeys can fly, 1+1=3, so I assume the statement wouldn't be true under this sort of translation.
– Hypnosifl
4 hours ago
add a comment |
1) is true. Think about true conditionals as promises that were upheld. I promise you that if monkeys can fly, then 1+1 is equal to 3. Did I violate my promise? No, because I would violate it only if monkeys could fly, but 1+1 would still not be equal to 3. But this didn't happen.
– user161005
8 hours ago
Thank you. I changed it to True before I turned it in,
– Molly
5 hours ago
@user161005 - Are you assuming the "if A then B" formulation in English is equivalent to a logical proposition of the form A -> B? If this is a homework problem then probably that was the intent, but conditionals can also be interpreted in terms of modal logic which deals with possible worlds, David Lewis apparently developed a modal logic analysis of conditionals...it isn't true that in a possible world where monkeys can fly, 1+1=3, so I assume the statement wouldn't be true under this sort of translation.
– Hypnosifl
4 hours ago
1) is true. Think about true conditionals as promises that were upheld. I promise you that if monkeys can fly, then 1+1 is equal to 3. Did I violate my promise? No, because I would violate it only if monkeys could fly, but 1+1 would still not be equal to 3. But this didn't happen.
– user161005
8 hours ago
1) is true. Think about true conditionals as promises that were upheld. I promise you that if monkeys can fly, then 1+1 is equal to 3. Did I violate my promise? No, because I would violate it only if monkeys could fly, but 1+1 would still not be equal to 3. But this didn't happen.
– user161005
8 hours ago
Thank you. I changed it to True before I turned it in,
– Molly
5 hours ago
Thank you. I changed it to True before I turned it in,
– Molly
5 hours ago
@user161005 - Are you assuming the "if A then B" formulation in English is equivalent to a logical proposition of the form A -> B? If this is a homework problem then probably that was the intent, but conditionals can also be interpreted in terms of modal logic which deals with possible worlds, David Lewis apparently developed a modal logic analysis of conditionals...it isn't true that in a possible world where monkeys can fly, 1+1=3, so I assume the statement wouldn't be true under this sort of translation.
– Hypnosifl
4 hours ago
@user161005 - Are you assuming the "if A then B" formulation in English is equivalent to a logical proposition of the form A -> B? If this is a homework problem then probably that was the intent, but conditionals can also be interpreted in terms of modal logic which deals with possible worlds, David Lewis apparently developed a modal logic analysis of conditionals...it isn't true that in a possible world where monkeys can fly, 1+1=3, so I assume the statement wouldn't be true under this sort of translation.
– Hypnosifl
4 hours ago
add a comment |
1 Answer
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There are two questions.
- True or False? If monkeys can fly, then 1 + 1 = 3.
The antecedent of the conditional, "monkeys can fly" is false. So is the consequent, "1 + 1 = 3". In classical truth-functional logic the conditional connecting these two sentences also has a truth-value. Wikipedia describes this "material conditional" as follows:
The material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→".
This binary operator would return true, based on the truth table Wikipedia provides. This is because the material conditional is defined to be false only when the antecedent is true and the consequent is false. Otherwise, even when the conditional doesn't make sense, it is defined as true.
Because the antecedent and the consequent are unrelated there may be objections to assigning a truth-value to such a statement or to assigning the value true. See the Wikipedia entry for relevance logic or the SEP article on relevance logic for a discussion.
- What is logically equivalent to all x (p(x) + ~q(x))?
I assume the statement is ∀x(P(x) v ¬Q(x).
Using Wikipedia's list of logical equivalences suggests a conditional that would be logically equivalent to the disjunction.
p ⟹ q ≡ ¬p ∨ q
Since ¬p ∨ q is logically equivalent to p ⟹ q, p v ¬q should be logically equivalent to ¬p ⟹ ¬q. This suggest that ∀x(P(x) v ¬Q(x) is logically equivalent to ∀x(¬P(x) ⟹ ¬Q(x).
For added confirmation, one can use a tree proof generator to see if one could derive such an equivalence:
Wikipedia contributors. (2019, May 27). Material conditional. In Wikipedia, The Free Encyclopedia. Retrieved 18:44, August 11, 2019, from https://en.wikipedia.org/w/index.php?title=Material_conditional&oldid=898972669
Tree Proof Generator. https://www.umsu.de/logik/trees/
answered 2 hours ago
Frank HubenyFrank Hubeny
13.9k6 gold badges17 silver badges67 bronze badges
add a comment |
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There are two questions.
- True or False? If monkeys can fly, then 1 + 1 = 3.
The antecedent of the conditional, "monkeys can fly" is false. So is the consequent, "1 + 1 = 3". In classical truth-functional logic the conditional connecting these two sentences also has a truth-value. Wikipedia describes this "material conditional" as follows:
The material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→".
This binary operator would return true, based on the truth table Wikipedia provides. This is because the material conditional is defined to be false only when the antecedent is true and the consequent is false. Otherwise, even when the conditional doesn't make sense, it is defined as true.
Because the antecedent and the consequent are unrelated there may be objections to assigning a truth-value to such a statement or to assigning the value true. See the Wikipedia entry for relevance logic or the SEP article on relevance logic for a discussion.
- What is logically equivalent to all x (p(x) + ~q(x))?
I assume the statement is ∀x(P(x) v ¬Q(x).
Using Wikipedia's list of logical equivalences suggests a conditional that would be logically equivalent to the disjunction.
p ⟹ q ≡ ¬p ∨ q
Since ¬p ∨ q is logically equivalent to p ⟹ q, p v ¬q should be logically equivalent to ¬p ⟹ ¬q. This suggest that ∀x(P(x) v ¬Q(x) is logically equivalent to ∀x(¬P(x) ⟹ ¬Q(x).
For added confirmation, one can use a tree proof generator to see if one could derive such an equivalence:
Wikipedia contributors. (2019, May 27). Material conditional. In Wikipedia, The Free Encyclopedia. Retrieved 18:44, August 11, 2019, from https://en.wikipedia.org/w/index.php?title=Material_conditional&oldid=898972669
Tree Proof Generator. https://www.umsu.de/logik/trees/
answered 2 hours ago
Frank HubenyFrank Hubeny
13.9k6 gold badges17 silver badges67 bronze badges
add a comment |
There are two questions.
- True or False? If monkeys can fly, then 1 + 1 = 3.
The antecedent of the conditional, "monkeys can fly" is false. So is the consequent, "1 + 1 = 3". In classical truth-functional logic the conditional connecting these two sentences also has a truth-value. Wikipedia describes this "material conditional" as follows:
The material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→".
This binary operator would return true, based on the truth table Wikipedia provides. This is because the material conditional is defined to be false only when the antecedent is true and the consequent is false. Otherwise, even when the conditional doesn't make sense, it is defined as true.
Because the antecedent and the consequent are unrelated there may be objections to assigning a truth-value to such a statement or to assigning the value true. See the Wikipedia entry for relevance logic or the SEP article on relevance logic for a discussion.
- What is logically equivalent to all x (p(x) + ~q(x))?
I assume the statement is ∀x(P(x) v ¬Q(x).
Using Wikipedia's list of logical equivalences suggests a conditional that would be logically equivalent to the disjunction.
p ⟹ q ≡ ¬p ∨ q
Since ¬p ∨ q is logically equivalent to p ⟹ q, p v ¬q should be logically equivalent to ¬p ⟹ ¬q. This suggest that ∀x(P(x) v ¬Q(x) is logically equivalent to ∀x(¬P(x) ⟹ ¬Q(x).
For added confirmation, one can use a tree proof generator to see if one could derive such an equivalence:
Wikipedia contributors. (2019, May 27). Material conditional. In Wikipedia, The Free Encyclopedia. Retrieved 18:44, August 11, 2019, from https://en.wikipedia.org/w/index.php?title=Material_conditional&oldid=898972669
Tree Proof Generator. https://www.umsu.de/logik/trees/
answered 2 hours ago
Frank HubenyFrank Hubeny
13.9k6 gold badges17 silver badges67 bronze badges
add a comment |
There are two questions.
- True or False? If monkeys can fly, then 1 + 1 = 3.
The antecedent of the conditional, "monkeys can fly" is false. So is the consequent, "1 + 1 = 3". In classical truth-functional logic the conditional connecting these two sentences also has a truth-value. Wikipedia describes this "material conditional" as follows:
The material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→".
This binary operator would return true, based on the truth table Wikipedia provides. This is because the material conditional is defined to be false only when the antecedent is true and the consequent is false. Otherwise, even when the conditional doesn't make sense, it is defined as true.
Because the antecedent and the consequent are unrelated there may be objections to assigning a truth-value to such a statement or to assigning the value true. See the Wikipedia entry for relevance logic or the SEP article on relevance logic for a discussion.
- What is logically equivalent to all x (p(x) + ~q(x))?
I assume the statement is ∀x(P(x) v ¬Q(x).
Using Wikipedia's list of logical equivalences suggests a conditional that would be logically equivalent to the disjunction.
p ⟹ q ≡ ¬p ∨ q
Since ¬p ∨ q is logically equivalent to p ⟹ q, p v ¬q should be logically equivalent to ¬p ⟹ ¬q. This suggest that ∀x(P(x) v ¬Q(x) is logically equivalent to ∀x(¬P(x) ⟹ ¬Q(x).
For added confirmation, one can use a tree proof generator to see if one could derive such an equivalence:
Wikipedia contributors. (2019, May 27). Material conditional. In Wikipedia, The Free Encyclopedia. Retrieved 18:44, August 11, 2019, from https://en.wikipedia.org/w/index.php?title=Material_conditional&oldid=898972669
Tree Proof Generator. https://www.umsu.de/logik/trees/
answered 2 hours ago
Frank HubenyFrank Hubeny
13.9k6 gold badges17 silver badges67 bronze badges
There are two questions.
- True or False? If monkeys can fly, then 1 + 1 = 3.
The antecedent of the conditional, "monkeys can fly" is false. So is the consequent, "1 + 1 = 3". In classical truth-functional logic the conditional connecting these two sentences also has a truth-value. Wikipedia describes this "material conditional" as follows:
The material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→".
This binary operator would return true, based on the truth table Wikipedia provides. This is because the material conditional is defined to be false only when the antecedent is true and the consequent is false. Otherwise, even when the conditional doesn't make sense, it is defined as true.
Because the antecedent and the consequent are unrelated there may be objections to assigning a truth-value to such a statement or to assigning the value true. See the Wikipedia entry for relevance logic or the SEP article on relevance logic for a discussion.
- What is logically equivalent to all x (p(x) + ~q(x))?
I assume the statement is ∀x(P(x) v ¬Q(x).
Using Wikipedia's list of logical equivalences suggests a conditional that would be logically equivalent to the disjunction.
p ⟹ q ≡ ¬p ∨ q
Since ¬p ∨ q is logically equivalent to p ⟹ q, p v ¬q should be logically equivalent to ¬p ⟹ ¬q. This suggest that ∀x(P(x) v ¬Q(x) is logically equivalent to ∀x(¬P(x) ⟹ ¬Q(x).
For added confirmation, one can use a tree proof generator to see if one could derive such an equivalence:
Wikipedia contributors. (2019, May 27). Material conditional. In Wikipedia, The Free Encyclopedia. Retrieved 18:44, August 11, 2019, from https://en.wikipedia.org/w/index.php?title=Material_conditional&oldid=898972669
Tree Proof Generator. https://www.umsu.de/logik/trees/
answered 2 hours ago
Frank HubenyFrank Hubeny
13.9k6 gold badges17 silver badges67 bronze badges
answered 2 hours ago
Frank HubenyFrank Hubeny
13.9k6 gold badges17 silver badges67 bronze badges
answered 2 hours ago
Frank HubenyFrank Hubeny
13.9k6 gold badges17 silver badges67 bronze badges
answered 2 hours ago
Frank HubenyFrank Hubeny
13.9k6 gold badges17 silver badges67 bronze badges
13.9k6 gold badges17 silver badges67 bronze badges
add a comment |
add a comment |
Molly is a new contributor. Be nice, and check out our Code of Conduct.
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1) is true. Think about true conditionals as promises that were upheld. I promise you that if monkeys can fly, then 1+1 is equal to 3. Did I violate my promise? No, because I would violate it only if monkeys could fly, but 1+1 would still not be equal to 3. But this didn't happen.
– user161005
8 hours ago
Thank you. I changed it to True before I turned it in,
– Molly
5 hours ago
@user161005 - Are you assuming the "if A then B" formulation in English is equivalent to a logical proposition of the form A -> B? If this is a homework problem then probably that was the intent, but conditionals can also be interpreted in terms of modal logic which deals with possible worlds, David Lewis apparently developed a modal logic analysis of conditionals...it isn't true that in a possible world where monkeys can fly, 1+1=3, so I assume the statement wouldn't be true under this sort of translation.
– Hypnosifl
4 hours ago