Some General Concepts

Arguments vs. Argumentations Borrowing a distinction from CS Peirce, “An ‘Argument’ is any process of thought reasonably tending to produce a definite belief. An ‘Argumentation’ is an Argument proceeding upon definitely formulated premisses” (CP 6.456). In other words, most arguments rest upon unstated premises, or may not be stated at all, as in the case of a photograph, even though a photograph can obviously change someone’s mind. Thus, much of critical thinking involves turning arguments into argumentations.

Features of an argument(ation) A proposition is a sentence that is either true or false; more specifically, the meaning of a sentence, regardless of its presentation. For example, if it is in fact raining, it is not false to say, “Il pleut” or “Es regnet,” instead of “It is raining.” Propositions typically take the form of declarative sentences. An argument(ation) consists of a set of propositions ordered by form of inference, with some propositions – the premises – intended to support another proposition – the conclusion. Evaluation of an argument(ation) An argument is valid if and only if the truth of the premises guarantees the truth of the conclusion. An argument is sound if the argument is valid and the premises are in fact true. An argument is cogent if it is valid & sound, as well as clear and relevant to the issue at hand. Strictly, only deductions may be valid and sound; inductions are more or less strong because the truth of the premises only support, but do not guarantee, the truth of the conclusion. Abductions trade in plausibility.

Principle of Charity This is a fundamental methodological approach to interpreting the arguments/positions of another which involves rendering their argument in the best, strongest form possible. This is similar to the principle of humanity, which involves assuming that another speaker’s beliefs are related to each other and to reality in some way.

Three general forms of inference Abduction/Hypothesis: The process of explaining a phenomenon by postulating a general rule of which it is a specific instance; also known as inference to the best explanation Deduction: The process of inferring from a general proposition to another general or particular proposition Induction: The process of inferring a general proposition from a particular one; alternatively, the process of testing a general proposition through sampling instances of that proposition or its corollaries

Three fundamental principles of logic Identity: A ≡ A A equals A, or A if and only if A Contradiction: ¬ [A ^ ¬A] It is not the case that both A and not-A Excluded Middle: [A  ¬A] Either A or not-A Traditional deductive logic also assumes the principle of bivalence, meaning that a proposition must be either true or false, never both or neither. This is similar to, but distinct from, the principle of excluded middle.

Deduction I: Categorical Logic (Syllogisms)

Varieties of Categorical Statements Affirmative Negative
Universal A: All S are P [(x)(Sx  Px)] E: All S are not P [(x)(Sx  ¬Px)]
Particular I: Some S are P [(x)(Sx ^ Px)] O: Some S are not P [(x)(Sx ^ ¬Px)]
Singular Treated as universal affirmations or negations: All/No [individuals identical] to S are P
The letters for derives from the Latin words AffIrmo (“I affirm”) and nEgO (“I deny”).

A: All, Every, Any E: No, None, Nothing I/O: Some, Few, Several, at least x, Majority, Many, Most, Almost All

Immediate Inferences These “immediate inferences” are ways to turn one categorical statement into another logically equivalent (always has the same truth value) categorical statement without the use of another proposition.
Contraposition: Valid for A and O statements -- Switch the S and P terms and negate each
A: All S are P ≡ All non-P are non-S
O: Some S are not P ≡ Some non-P are not non-S
Conversion: Valid for E and I statements -- Switch the S and P