1. Introduction to Deductive Logic Flashcards
Truth-preservation.
Never takes one from truths to a falsehood. The premises do not lead to false conclusions.
Valid reasoning.
Reasoning that is truth-preserving: the premises do not lead to false conclusions.
List (7) examples of systems of deductive logic:
(1) Euclid’s axiomatization of plane geometry (300 BCE; classical Greece); 5 fundamental assumptions/axioms;
(2) Giuseppe Peano; successfully axiomatized arithmetic (1889);
(3) Aristotle (350 BCE); developed “categorical” or “syllogistic” logic;
(4) Gottlob Frege; invented axiomatic predicate logic;
(5) David Hilbert; Hilbert-style deductive system; most suited for first-order logic;
(6) Bertrand Russell; axiomatic predicate logic;
(7) other logicians in the late nineteenth and early twentieth centuries.
What is the difference between “Roberta will pass if she completes all of her homework” and “Roberta will pass only if she completes all of her homework”?
If “Roberta will pass if she completes all of her homework” is true, then Roberta can still pass even if she does not complete her homework. Completing all of her homework may not be the only pathway for Roberta to pass. This is unless “Roberta will pass only if she completes all of her homework”.
What kinds of sentences have a truth value?
Sentences that assert something.
What truth values can a sentence have?
True, false, and indeterminate.
Argument.
A set of two or more sentences, one of which is designated as the conclusion and the others as the premises.
Sets.
Abstract objects that have members (zero or more).
Argument in standard form.
Lists premises with a horizontal line under the last premise, followed by a conclusion.
p1.
p2.
- - - - -
c.
Logically valid argument.
An argument is logically valid if and only if it is not possible for all the premises to be true and the conclusion false. An argument is logically invalid if and only if it is not logically valid.
A logical valid argument, by definition, is _____.
…truth preserving.
Logically sound argument.
An argument is logically sound if and only if it is logically valid and all of its premises are true. An argument is logically unsound if and only if it is not logically sound.
Provide an example of an argument that is logically valid but not logically sound:
p1. Italy is a country that is located in North America.
p2. Every country that is located in North America uses the United States dollar as its currency.
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c. Italy uses the United States dollar as its currency.
Provide an example of an argument that is logically valid and logically sound:
p1. The United States is a country that is located in North America.
p2. No country that is located in North America uses the euro as its currency.
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c. The United States doe not use the euro as its currency.
Provide (7) examples of conclusion indicator expressions:
(1) therefore,
(2) thus,
(3) it follows that,
(4) so,
(5) hence,
(6) consequently, and
(7) as a result,
Provide (6) examples of premise indicator expressions:
(1) since,
(2) for,
(3) because,
(4) on account of,
(5) inasmuch as, and
(6) for the reason that.
Does the formal definition of ‘argument’ allow for arguments in which the premise(s) provide no support whatsoever for the conclusion?
Yes, but it will be invalid if it is possible for the premise to be true and the conclusion false.
Logically true sentence.
A sentence is logically true if and only if it is not possible for the sentence to be false.
- All sentences of the form p or not p, where p has a truth-value and not p is a denial of p.
Logically false sentence.
A sentence is logically false if and only if it is not possible for the sentence to be true.
- All sentences of the form p and not p, where p has a truth-value and not p is a denial of p.
Logically indeterminate sentence.
A sentence is logically indeterminate if and only if it is neither logically true nor logically false.
- Whether the truth value is true or false, it depends upon how the world in fact is.
Provide an example of a logically true sentence:
Either June will pass Chemistry 101 or June will not pass Chemistry 101.
Provide an example of a logically false sentence:
Both June will pass Chemistry 101 and June will not pass Chemistry 101.
Provide an example of a logically indeterminate sentence:
It rained on July 6, 1309 in what is now San Francisco.
Logically equivalent sentences.
Sentences p and q are logically equivalent if and only if it is not possible for one of these sentences to be true while the other sentence is false.
