Posts tagged ‘inferential reasoning’

September 8th, 2013

Q&A 33: Abductively Reasoned Religious Experience

by Max Andrews

Q&A GraphicQuestion:

Hi Max Andrews,
I’ve just discovered your articles at sententias.org. Well done! And thank you for the
time and thought you and Ms. Davis obviously took to create such quality!

May I ask for your help?

I noticed on the site that you favor abductive reasoning. I am new to this inferential method.
And I wondered if you had written your own abductively-reasoned account of coming to
know and trust God? 
read more »

October 5th, 2012

Inferential Justification and Empiricism

by Max Andrews

In this post I’ll be responding to R.A. Fumerton’s “Inferential Justification and Empiricism” in The Journal of Philosophy 73/17 (1976).

In this paper Fumerton argues for the empiricist’s version of foundationalism.  He draws important distinctions between senses of how one may be inferentially justified.  His argument is matched against another argument, which proceeds from observations about what we do and do not infer.  His primary contention is that is that one can never have a noninfterentially justified belief in a physical-object proposition.  One must always justify one’s beliefs in propositions about the physical world by appealing to other beliefs or basic beliefs; a thesis I disagree with.

I will be faithful to knowledge being defined as a justified true belief.  The task that is of concern in this paper is to examine the coherence of inferential reasoning in a foundationalist’s system.  A problem with inference to the best explanation (IBE) is that it has the potential to create an infinite regress.  With inferential reasoning, in an attempt to justify a belief in proposition P there may be an appeal to another proposition (or set of propositions) E, and by either explicitly or implicitly appeal to a third proposition, that E confirms or makes P probable.  The challenge of inferential justification challenges one of two propositions:

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]