Deduction (Classical) Flashcards
To know content of point five.
Define: deductive argument.
An argument whose premises are claimed to provide conclusive grounds for the truth of its conclusion.
Define: validity.
a characteristic of any deductive argument whose premises, if they were all true, would provide conclusive grounds for the truth of its conclusion. Such an argument is said to be valid.
Define: classical or Aristotelian logic.
The traditional account of syllogistic reasoning, in which certain interpretations of categorical propositions are presupposed.
Define: modern of modern symbolic logic.
The account of syllogistic reasoning accepted today. It differs in important ways from the traditional account.
Define: class.
The collection of all objects that have some specified characteristic in common.
Define: categorical proposition.
A proposition that can be analyzed as being about classes, or categories, affirming or denying that one class, s, is included in some other class, p, in whole or in part.
What are the four kinds of categorical proposition?
- universal affirmative propositions (all s is p), or A propositions
- universal negative propositions (no s is p), or E propositions
- particular affirmative propositions (some s is p), or I propositions
- particular negative propositions (some s is not p), or O propositions
Define: quality.
An attribute of every categorical proposition, determined by whether the proposition affirms or denies class inclusion. Thus every categorical proposition is either affirmative in quality or negative in quality.
Define: quantity.
An attribute of every categorical proposition, determined by whether the proposition refers to all members or only some members of the class designated by its subject term. Thus every categorical proposition is either universal in quantity or particular in quantity.
Define: copula.
Any forms of the verb “to be” that serve to connect the subject term and the predicate term of a categorical proposition.
Define: distribution.
An attribute that describes the relationship between a categorical proposition and each one of its terms, indicating whether or not the proposition makes a statement about every member of the class represented by a given term.
Predicate term Predicate term
undistributed distributed
Subject term distributed w x
Subject term undistributed y z
w=A
x=E
y=I
z=O
Define: opposition.
The logical relation that exists between two contradictories, two contraries, or in general between any two categorical propositions that differ in quantity, quality, or other respects. These relations are displayed on the square of opposition.
Define: contradictories.
Two propositions so related that one is the denial or negation of the other. On the traditional square of opposition, the two pairs of contradictories are indicated by the diagonals of the square: A and E propositions are the contradictories of O and I propositions, respectively.
Define: contraries.
Two propositions so related that they cannot both be true, although both may be false.
Define: contingent.
Being neither tautologous nor self-contradictory. A contingent statement may be true or false.
Define: subcontraries.
Two propositions so related that they cannot both be false, although they may both be true.
Define: subalternation.
The relation on the square of opposition between a universal proposition (an A or an E proposition) and its corresponding particular proposition (an I or an O proposition, respectively). In the relation, the particular proposition (I or O) is called the “subaltern,” and the universal proposition (A or E) is called the “superaltern.”
Define: square of opposition.
A diagram in the form of a square in which the four types of categorical propositions (A, E, I, O) are situated at the corners, exhibiting the logical relations (called “oppositions”) among these propositions.
The ___altern implies the truth of the ___altern.
a) super
b) sub
Define: immediate inference.
an inference that is drawn directly from one premise without the mediation of any other premise. Various kinds of immediate inferences may be distinguished, traditionally including conversion, obversion, and contraposition.
Define: mediate inference.
Any inference drawn from more than one premise.
Define: conversion.
A valid form of immediate inference for some but not all types of propositions. To form the converse of a proposition the subject and predicate terms are simply interchanged. Thus, applied to the proposition “No circles are squares,” conversion yields “No squares are circles,” which is called the “converse” of the original proposition. The original proposition is called the
“convertend.”
Conversion is valid for all __ and __ propositions.
E and I (A by limitation)
