The Two Branches of Logic

  1. Deduction - the conclusion follows necessarily from he premise(s)

    1. Categorical (Aristotelian) Logic - the logical relationship between the terms of categorical propositions

    2. Propositional (Sentential) Logic - the logical relationships between statements

    3. Predicate Logic - the logical relationships between quantifiable variables

    4. Modal Logical - The logical relationship between modally modified propositions

  2. Induction - a conclusion follows with a degree of probability from the premise(s)

    1. Arguments by Analogy (legal and moral reasoning)

    2. Arguments from Authority (deferring to expert consensus in a field/peer review)

    3. Arguments from Causation/Prediction (Mill’s Method)

    4. Arguments from Probability (How to Win in Vegas)

    5. Arguments from Statistical Evidence/Generalization (social scientific method)

    6. Arguments from Hypothesis (the scientific method)

    7. Arguments from Signs/Symbols

  3. Evaluating Arguments - what makes arguments “good” or “bad”?

    1. Deductive Arguments - a conclusion follows necessarily from the premise(s)

      1. Valid - the from of the argument is correct (i.e., if the premises are assumed to be true, then the conclusion cannot be false)

      2. Sound - the argument is valid (i.e., the form is correct) and the premises are true

    2. Inductive Arguments - a conclusion follows with a degree of probability from the premise(s)

      1. Strong - the premises are sufficient, relevant, and clear enough to make the conclusion more likely than not

      2. Cogent - the argument is strong (i.e., the premises are sufficient, relevant, and clear enough to make the conclusion more likely than not), and the premises are true

Note: Remember, arguments are never true or false. Only a proposition or statement can have a truth-value. Arguments are either valid and sound, or strong and cogent depending on whether they are inductive or deductive.

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