Trivium: Logic

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Term

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a concept communicated through a symbol

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Definition

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communicates the intension of the term

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Three parts of a definition

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Species = Genus + Differentia

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Species

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term to be defined

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Genus

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general category

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Differentia

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specific trait(s) differentiating the species from other species in the same genus

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Five Rules of a Definition

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must be convertible
must be positive, not negative
must be clear and univocal
can't be tautological
must have parallel grammatical structure

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Division

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communicates the extension of the term; explains all the different things which fall within that set

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Three Parts of a Division

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an identifiable whole
a single basis of division
dividing members

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Proposition

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relation of terms

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Subject of a proposition

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that about which something can be predicated

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Predicate of a proposition

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that which is predicated of the subject

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Copula of a proposition

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syncategorematic
like an equals sign

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The matter of a proposition

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provided by the terms

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The form of a proposition

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provided by the copula

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Distribution

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a characteristic of terms used in a proposition, not of a term standing alone
gives the extension of a term

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Logic

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the art of mapping thought
the art of thinking

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Contradictories: rule

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if one is true the other is false

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Contraries: rule

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both cannot be true, but both may be false

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Subcontraries: rule

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both cannot be false, but both may be true

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Subalterns: rule

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if the total proposition is true, the partial must be true
if the total is false, the partial is unknown
if the partial is true, the total is unknown
if the partial is false, the total is false

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Contradictories

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A-O
E-I

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Contraries

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A-E

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Subcontraries

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I-O

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Subalterns

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A-I
E-O

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Syllogism 1

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the act of reasoning by which the mind perceives that from the relation of two propositions having one term in common there necessarily emerges a new, third proposition in which the common term does not appear.

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Syllogism 2

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a formal relation of three terms in three propositions

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Premise

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a proposition in a syllogism

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Intension

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the sum of the term's essential characteristics--its meaning

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Extension

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the total set of objects to which that term applies

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For a division to be valid, its basis of division must be __

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exhaustive

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Enthymeme

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abbreviated syllogism

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Major premise

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the premise that contains the major term

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Minor premise

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the premise that contains the minor term

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Minor term

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the subject of the conclusion

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Major term

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the predicate of the conclusion

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Middle term

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the term which is common to the minor and major premises and is not found in the conclusion

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Categorical proposition

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asserts the relation of its terms as they are actually related, without expressing the mode of their relation

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Hypothetical proposition

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asserts the dependence of one proposition on another

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Disjunctive proposition

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asserts that, of two or more suppositions, one is true

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Nexus

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the dependence of the consequent upon the antecedent in an hypothetical proposition

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Fallacy #1 for an hypothetical proposition

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affirming the consequent in an hypothetical proposition

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Fallacy #2 for an hypothetical proposition

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denying the antecedent in an hypothetical proposition

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Modus ponens, way of affirmation

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affirming the antecedent in an hypothetical proposition

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Modus tollens, way of negation

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denying the consequent in an hypothetical proposition

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Ponendo tollens, affirming the negative

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when the minor premise posits one alternative and the conclusion denies another in a disjunctive syllogism

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Tollendo ponens, negating the positive

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when the minor premise denies one alternative and the conclusion affirms another in a disjunctive syllogism

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Imperfect disjunction

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fallacy in a disjunctive proposition in which the options are incomplete or not mutually exclusive

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What does the hypothetical syllogism express?

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a conditional relation of dependence

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What does the categorical syllogism express?

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a relationship without limitation

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Formal fallacy #1

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the fallacy of four terms

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Formal fallacy #2

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the fallacy of four propositions

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Formal fallacy #3

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the fallacy of the undistributed middle term

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Formal fallacy #4

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the fallacy of illicit process of the major or minor term

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Formal fallacy #5

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the fallacy of two negative premises

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Formal fallacy #6

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the fallacy of a negative conclusion without a negative premise

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Fallacies in dictione

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fallacies occasioned by ambiguity in language

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Fallacies extra dictionem

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fallacies occasioned by a hidden false assumption not warranted by the language used

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Equivocation

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a fallacy occasioned by the ambiguity of a word which symbolizes two or more different terms

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Amphiboly

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a fallacy produced by ambiguity of syntax or grammatical structure

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Composition (fallacy)

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a fallacy occurring when the properties of the parts are illicitly predicated of the whole

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Division (fallacy)

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a fallacy occurring when the properties of the whole are illicitly predicated of the parts

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Accent (fallacy)

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a fallacy occurring when a meaning different from that intended is conveyed through a special emphasis on certain letters, syllables, words, or ideas

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Arguing beside the point (fallacy)

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a fallacy that arises from falsely assuming that the point at issue has been disproved when one merely resembling it has been disproved; the point really at issue is consequently ignored

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Argument ad hominem

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a fallacy which confuses the point at issue with the people concerned; seeks to persuade by unsound ethos

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Argument ad populum

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a fallacy which substitutes an appeal to the passions and prejudices of the people for logical reasoning on the point at issue

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Argument ad verecundiam

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a fallacy which appeals to the prestige or respect in which a proponent of an argument is held as a guarantee of the truth of the argument

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False cause (fallacy)

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a fallacy in which something accidental to a thing is held to determine its nature, character, or value

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Post hoc, ergo, propter hoc

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a fallacy which makes a false assumption about the cause of being

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Begging the question

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a fallacy of assuming in the premises the very proposition to be proved, namely, the conclusion

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Logic 2

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the normative science which directs the operations of the intellect so as to attain truth

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Requirements of truth

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correspondence (the norm of induction)
coherence (the norm of deduction)

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Correspondence

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what is thought must represent what is

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Coherence

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thoughts must be consistent among themselves

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Induction, two definitions

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1) a mental act, preliminary and prerequisite to inference, which is an intuition of truth
2) the legitimate derivation of general propositions from individual instances

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Intuitive induction

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the psychological act of asserting a self-evident proposition as true

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In deduction we know the fact, the conclusion, through its causes, the premises.

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In induction we apprehend the cause common to a number of observed facts; that cause is a principle, a middle term, by which their relation can be understood.

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Five steps of scientific induction

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observation
analogy
hypothesis
analysis and sifting of data
verification of the hypothesis