Posts tagged ‘inference’

January 25th, 2012

Word of the Week Wednesday: Existential Instantiation

by Max Andrews

The Word of the Week is: Existential Instantiation

Definition: A rule of inference that introduces existential quantifiers.  The symbol for an existential quantifier is (∃x).

More about the term: The existential quantifier indicates that there is at least one thing in a categorical reference.  Instantiation is an operation that removes a quantifier and replaces every variable bound by the quantifier with that same instantial letter.  There are eight rules of inference to derive a conclusion of an argument via deduction:

  1. Modus Ponens: p ⊃ q … p… .:q
  2. Modus Tollens: p ⊃ q … ~q … .: ~p
  3. Pure Hypothetical Syllogism: p ⊃ q … q ⊃ r … .: p ⊃ r
  4. Disjunctive Syllogism: p v q … ~q … .:p
  5. Constructive Dilemma: (p ⊃ q) & (r ⊃ s) … p v r … .: q v s
  6. Simplification: p & q… .: p
  7. Conjunction: p … q … .: p & q
  8. Addition: p … .: p v q

December 22nd, 2011

Inferential Reasoning in Foundationalism and Coherentism

by Max Andrews

Logically prior to inferential reasoning is intuition.  These intuitions may be basic beliefs. The belief that this glass of water in front of me will quench my thirst if I drink it is not inferred back from previous experiences coupled with an application of a synthetic a priori principle of induction.  Though this example is not how we form our beliefs psychologically or historically, it can be formed via instances of past experience and induction in the logical sense.  However, when it does come to inferential reasoning R.A. Fumerton provides two definitions for what it means to say that one has inferential justification.[1]

D1 S has an inferentially justified belief in P on the basis of E. = Df.

(1) S believes P.

(2) S justifiably believes both E and the proposition that E confirms P.

(3) S believes P because he believes both E and the proposition that E confirms P.

(4) There is no proposition X such that S is justified in believing X and that E&X does not confirm P.

D2 S has an inferentially justified belief in P on the basis of E. = Df.

(1) S believes P.

(2) E confirms P.

(3) The fact that E causes S to believe P.

(4) There is no proposition X such that S is justified in believing X and that E&X does not confirm P.

Given the explications of such definitions, both D1 and D2, there seems to be good grounds for believing that P must be inferentially justified.  It is most certainly that case that D2 is more amenable to having scientific knowledge in the sense that both (2) and (3) are confirmatory.  D2-(3) is certainly difficult to substantiate without begging the question.  Having E cause S to believe P is difficult to distance from some form of transitive relation.  Inferential justification may also be expressed probabilistically or determined probabilistically.[2]