Term
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Definition
A set of two or more sentences, one of which is designated as the conclusion and the others as the premise
Example:
All Mammals are vertebrates
Some sea creatures are mammals
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Some sea creatures are verterbrates |
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Term
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Definition
An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false
Example: There are 3, and only 3, people in the room: juarez, sloan, and wang
Juarez is left handed
Sloan is left handed
Wang is left handed
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All the people in the room are left handed |
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Term
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Definition
An argument is deductiveli invalid if and only if it is not deductively valid. That is, it is possible for the premises to be true and conclusion false
Example:
Sloan is left handed
Wang is left handed
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Everyone is left handed |
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Term
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Definition
An argument is deductively sound if and only if it is deductively valid and all its premises are true
Example:
In 2000 Bush and Gore were the only major party candidates in the presidential election
A major party candidate won
Gore did not win
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Bush won the 2000 presidential election |
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Term
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Definition
An argument is deductively unsound if and only if it is not deductively sound
Example of a deductively valid argument that is not deductively valid:
France and Great Britain were the majors powers in the Napoleonic wars
France had the largest army, Great britain largest navy
the power with the largest army won
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France won |
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Term
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Definition
An argument has inductive strength to the extent that the conclusion is probable given the premises
-is not deductively valid but is a strong argument nonetheless
Example:
Juarez, Sloan, and Wang are all left handed
Juarez and Sloan both have trouble using can openers made for right handed people
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Wang also has trouble using can openers made for right handed people |
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Term
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Definition
A set of is logically consistent if and only if it is possible for all the members of that set to be true
Example: {Texas is larger than Oklahoma. The Phlogiston theory of heat has been disproven. The US congress consists of the senate and the house of representatives}
- no requirement that the members of the set have something to do with each other
-truth of sentences doesn't matter, as long as they do not keep, in their relations with one another, any of the others from being true |
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Term
| Logically inconsistent set of sentences |
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Definition
-if and only if it is not logically consistent, or if it is not possible for all the memebers of that set to be true
-when the truth of one sentence causes another one within the set to be untrue
Example:
{micheal and benjamin both applied for positions at the local fast-food outlet, and at least one of them got it. No one who applied for the position will get it} |
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Term
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Definition
a sentence is logically true if and only if it is not possible for the sentence to be false -some are due to their form or structure, such as 'either or sentences' Example: "either cynthia will get a job or she will not get a job" "If henry gets fired, he gets fired"
-aka a tautology |
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Term
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Definition
-is so only if it is not possible for the sentence to be true
Example:
"Sarah is an A student and she is not and A student"
"some dollar bills are not dollar bills" |
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Term
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Definition
Occurs if and only if it is neither true nor logically false
-sentences we encounter outside logic and mathematics
"Ivan is driving from Boston to New Orleans"
"Anyone who takes astrology seriously is foolish"= |
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Term
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Definition
The members of a pair of sentences are logically equivalent if and only if it is not possible for one of the sentences to be true while the other sentence is false Example: Not all tumors are cancerous Some tumors are cencerous
- usually mean the same thing
"sarah loves henry. Henry is loved by sarah" |
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Term
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Definition
sentence is such if it is possible for one of the sentences to be true while the other is false
Example:
Henry loves Sarah
Sarah loves Henry |
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