Logic 10

What is a complement?

"The negation of a term. The _complement class_ of a given class is the class of all things that are _not_ members of the given class." LP, 365

What is vagueness?

"To complain of vagueness is to complain that what has been said is unacceptably indeterminate in some relevant dimension." -Anthony Flew, _How to think Straight: An Introduction to Critical Thinking_ (Amherst, NY: Prometheus, 1998), 82.

What does it mean to say that a word or a statement is ambiguous?

"To say of some word or expression or of some whole statement that it is ambiguous is to say that it can be construed in at least two different ways." -Anthony Flew, _ How to Think Straight_, 81.

How is vagueness different from ambiguity?

"When a statement is ambiguous, you have a choice between different senses of a word. When it is vague, there is no doubt about the sense, only the degree." -Monroe C. Beardsley, _Thinking Straight_, 3rd ed (Englewood Cluff, NJ: Prentice-Hall, 1966), 172.

What is logical equivalence?

"When referring to truth-functional compound propositions, the relationship that holds between two propositions when the statement of their material equivalence is a tautology. A very strong relation; statements that are logically equivalent must have the same meaning, and may therefore replace one another wherever they occur." --Copi, Cohen, McMahon, _Intro. to Logic, 14th ed., 348

What is a subject?

The term of a proposition about which something is affirmed or denied. AH

In predicate logic, is a property constant the same as a predicate?

Yes. See Siu-Fan Lee, Logic: A Complete Introduction (Great Britain: Hodder & Stoughton, 2017), 268. -Logic and Philosophy: A modern Introduction, 13th ed., Alan Hausman, Frank Boardman, and HOward Kahane (Indianapolis: Hackett, 2020), 158.

Frege used the term "concept" to stand for what?

a property Yes. See Siu-Fan Lee, Logic: A Complete Introduction (Great Britain: Hodder & Stoughton, 2017), 268.

According to Frege, a predicate always needs what to satisfy it?

Objects: individual terms: individual constants and individual variables Yes. See Siu-Fan Lee, Logic: A Complete Introduction (Great Britain: Hodder & Stoughton, 2017), 268.

What is a predicate?

That part of a proposition that is affirmed or denied about the subject. AH

What is inference for Copi, Cohen, and McMahon?

"A process by which one proposition is arrived at and affirmed on the basis of some other proposition or propositions." _Introduction to Logic_, 14th, 5

What is a propositional function?

"A propositional function is an expression composed of a predicate and a variable; it has no truth-values and must be either bounded by a quantifier (universal or existential) or substituted with an individual constant to become truth-evaluable." Siu-Fan Lee, Logic: A Complete Introduction (Great Britain: Hodder & Stoughton, 2017), 268.

What is a proposition?

"A statement that affirms or denies something." _American Heritage Dictionary_ A statement that is true or false. -Robert L. Johnson & Charles R. McNerney, _Arithmetic: A text for elementary school teachers_ (New York: Macmillan, 1974), 5.

What is proposition, according to Copi, Cohen, and McMahon?

"A statement; what is typically asserted using a declarative sentence, and hence always either true or false--although its truth or falsity may be unknown." _Introduction to Logic_, 14th ed., p. 2

What is a well-formed formula?

"A well-formed formula is roughly the same as a proposition, i.e. something can be either true or false." Siu-Fan Lee, Logic: A Complete Introduction (Great Britain: Hodder & Stoughton, 2017), 269

What is distribution?

"An attribute that describes the relationship between a categorical proposition and each of its terms, indicating whether or not the proposition makes a statement about every member of the class represented by a given term." Irving M. Copi, Carl Cohen, and Kenneth McMahon, 622

What is a class (or set)?

"The collection of all objects that have some specific characteristic in common." Irving M. Copi, Carl Cohen, Kenneth McNahon, 620

What is existential fallacy?

"Any mistake in reasoning that arises from assuming illegitimately that some class has members." Irving Copi, Carl Cohen, Kenneth McMahon, 14th ed.,199.

What is the paradox of material implication?

"In standard systems of logic, A materially implies B is true if and only if it is not the case both A is true and B is false. This gives rise to the paradoxes of material implication: a false proposition materially implies any proposition, and a true proposition is materially implied by any proposition." _The Penguin Dictionary of Philosophy_, 2nd ed., 298 1. A false proposition implying (entailing) any proposition: If the earth orbits the moon, Donald Trump was born in Russia. 2. A true proposition implied by any proposition: If the earth orbits the moon, Donald Trump was born in the United States.

What is material equivalence?

"Material equivalence is the truth-functional connective that asserts that the statements it connects have the same truth value. . . . One straightforward definition is this: Two statements are materially equivalent when they are both true, or both false." --Copi, Cohen, McMahon, _ Introduction to Logic_, 14th ed., 344.

What is obscurity?

"Obscurity is difficulty of comprehension, in so far as that difficulty is due to clashes between implicit meanings of the words." -Monroe C. Beardsey, _Thinking Straight_, 169. "Of course, if a passage is nonsense--if it has no meaning as a whole-- then it is not obscure. We call a passage obscure if it has a meaning which the style makes troublesome to discern. An obscure passage may or may not be ambiguous--we can't tell whether it has two possible meanings until we have succeeded in finding at least one." -ibid, 170

What is "Fa" in predicate logic?

"So "Fa" is a proposition and it represents a complete thought. Fa is also called a singular proposition, which is defined as a proposition asserting that a particular individual has a specific attribute." Siu-Fan Lee, Logic: A Complete Introduction (Great Britain: Hodder & Stoughton, 2017), 268.

What is a categorical proposition? (my definition)

A categorical proposition is a proposition whose terms are about classes and that affirms or denies that the class represented by the subject term is included in the class represented by the predicate term, in whole or in part. (TSL)

What are the three types of well-formed formulas, propositions, can one-place predicates have?

Fa For all x, Fx For some x, Fx Siu-Fan Lee, Logic: A Complete Introduction (Great Britain: Hodder & Stoughton, 2017), 269

What are sentence constants and property constants?

Sentence constants: Capital letters such as A, B, C, and so forth that serve as symbols for actual sentences. Property constants: Capital letters such as A, B, and C used to denote properties. -Logic and Philosophy: A modern Introduction, 13th ed., Alan Hausman, Frank Boardman, and HOward Kahane (Indianapolis: Hackett, 2020), 20, 158.

"We may therefore say that an argument form is valid, if and only if, its expression in the form of a conditional statement (of which the antecedent is the conjunction of the premises of the given argument form, and the consequent is the conclusion of the given argument form)

is a tautology." --Copi, Cohen, & McMahon, _Intro. to Logic_, 14th ed., 346

According to Douglas Walton, "To say that an argument is deductively valid means

that it is logically impossible for all the premises to be true and the conclusion false. In other words, in a deductively valid argument, the claim that the premises are true and the conclusion false is inconsistent." _Fundamentals of Critical Argumentation_ (New York: University of Cambridge Press, 2006), 49