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]

I have little contention with such definitions of inferential justification; my concern is whether this is most amicable within a foundationalist’s or coherentist’s noetic structure.

Both D1 and D2 offer, I believe, to be successful accounts of inferential justification.  However, I do find both definitions to be problematic for the empiricist on the bases of foundationalism, of which I will argue that such inferential justification and non-epistemological direct realism is more amicable to the coherentist and that a non-epistemological realist who adheres to foundationalism cannot successfully account for new beliefs.

Such inferential justification is certainly compatible with foundationalism but making all empirical claims to be inferential seems to be over-committing to inferential reasoning.  Suppose I am walking in the field and on the next hill over I see an object.  For all purposes, my phenomenological faculties indicate to me that there is something on the next hill.  This belief is held for a reason, primarily that my phenomenological faculties inform me that something is on the next hill over, but this is not a reasoned belief.  I may certainly infer certain properties consistent with D1 and D2 such as the belief that the object has a particular color or that it omits a certain sound or that it has a particular smell.  My belief that an object is on the next hill over from me seems to be quite basic.  I am not inferring its existence from other object-likenesses.  I am completely unaware as to the identity of this object, or better yet, whether this object is unique or unknown.  Suppose that this object has never been known before I experienced it.  This makes the situation quite different from Fumerton’s glass of water and is not a future tensed proposition nor is it a subjunctive conditional.

Inferential reasoning as described by D1 and D2 are certainly kind to empiricism when it comes to scientific knowledge.  Certain unknown entities may become known by inferential means.  We can infer the existence of protons, quarks, and other elementary particles by predicting what effects such entities may have in certain situations.  This may be causal in nature and may be confirmed by inference. However, it is not the case that we directly experience the existence of these particles (for all intents and purposes, it certainly is the case that we experience particles when we run in to a wall and even then we experience the strong nuclear force over the particles). Nevertheless, epistemological direct realism and new belief formation can be non-inferentially justified.[3]

With such a methodology for inferential reasoning it may be argued that the foundationalist framework requires a presupposing of coherentism.  This would bring inference to the best explanation into close contact with the holistic view of explanation.[4]  Philip Kitcher argued that this holistic view of inferential reasoning

holds that [scientific] understanding increases as we decrease the number of independent assumptions that are required to explain what goes on in the world… Explanations serve to organize and systematize our knowledge in the most efficient and coherent possible fashion.  Understanding, on this view, involves having a world-picture—a scientific Weltanschauung—and seeing how various aspects of the world and our experience of it fit into that picture.[5]

Inferentially justified empirical beliefs are more in sync with a coherentist noetic structure.  When making inferential claims the proposition being inferred from must cohere to a proposition already accepted as truth.  Inferential reasoning is not necessarily non-foundational, but if empirical claims are strictly inferential then coherentism is best suited.  No matter what the belief in question is to be it must be inferentially referred back to another experientially valid belief (within the scope of empirical discussion).

David Hume brought to our attention a problem with inferential reasoning, which is especially important to the present task given his empiricism.

As to past experience, it can be allowed to give direct and certain information of those precise objects only and that precise period of time which fell under it cognizance.  But why this experience should be extended to future times, and to other objects, which for all we know, may be similar in appearance…This, I must confess, seems to be the same difficulty…The question still recurs: on what process of argument this inference is founded?  Where is the medium, the interposing ideas which join propositions so very wide of each other?[6]

As Plantinga points out, Hume is right it does not follow.  There are plenty of possible worlds that match the actual world up to the present time, but then diverge wildly, so that inductive inferences would mostly fail in those other worlds.  It is by no means inevitable that inductive reasoning should be successful; its success is one more example of the fit between our cognitive faculties and the world.[7]  The criteria for the best inference are simplicity, beauty, and consilience (fit with other favored or established hypotheses).[8]  Inferentially justified new beliefs create less dissonance with coherentism than with foundationalism.  What is needed logically prior to the acceptance or justification of new belief is an evidence base.  This is the set of beliefs used, or appealed to, in conducting an inquiry.[9]  Recall Torrance’s onto-relations.  This onto-relation allows for inference to be a bridge between the ontological-epistemological divide.  It is the onto-relationship that serves as Hume’s missing medium.  It is this “web” of onto-relations and consilience that function best with coherentism.  Thus, to think rightly and in terms of inference and a posteriori reasoning means to connect things up with other things, thinking their constituent interrelations, and thus it is important for thinking to determine what kind of relation that exists between the realities contemplated.[10]

[1] R.A. Fumerton, “Inferential Justification and Empiricism,” The Journal of Philosophy 73 no. (1976): 564-65.

[2] This may be expressed by Thomas Bayes’ theorem for conditional probability or by his rule for belief change: PE(H) = p(H|E).  If my belief p is going to be justified probabilistically then it must be 0 < p ≤ 1 where p is > .5.  Suppose that after all the evidence that is available is possessed and I have come to a value of precisely .5 for p.  If I reject p as being true then I have just as much of a chance of being wrong about that as I do as being right.  When p has a value of .5, all things considered, then I believe it would be acceptable to believe p, ~p, or to be agnostic.  For more on the role of probability in inferential reasoning see Igor Douven’s “Inference to the Best Explanation Made Coherent,” Philosophy of Science 66 (1999): S424-S435.

[3] This is not to ignore other experiential data such as spiritual or religious experience.  Other propositional beliefs may be basic but non-empirical such as mathematical truths.  My concern is oriented towards empirical basic beliefs.  Additionally, suppose that today is Friday.  I cannot change my belief to believe that it is now Sunday or Monday.  Some beliefs are non-inferentially justified and involuntary. Richard Swinburne, Faith and Reason (Oxford: Oxford University Press, 1981) 25.

[4] Philip Clayton, “Inference to the Best Explanation,” Zygon 32 no. 3 (1997): 387.

[5] Philip Kitcher, “Scientific Explanation,” Minnesota Studies in the Philosophy of Science 13 (1989): 182.

[6] David Hume, An Enquiry Concerning Human Understanding, sect. IV, 2, in Philosophical Inquiry eds. Jonathan E. Adler and Catherine Z. Elgin (Indianapolis, IN: Hackett, 2007), 181-82.

[7] Alvin Plantinga, Where the Conflict Really Lies: Science, Religion, and Naturalism (Oxford: Oxford University Press, 2011), 295, 297.

[8] This criteria may certainly be unnecessary in the case of paradigm shift with warranted evidence (preservation of consilience).  Additionally, beauty and simplicity are certainly preferred but as long as the inference is in relation to reality then these two criterions may be inapplicable.  Consilience is the most important criterion.

[9] Plantinga, 167.

[10] John Morrison, Knowledge of the Self-Revealing God in the Thought of Thomas Forsyth Torrance (Eugene, OR: Wipf and Stock, 1997), 106. Thomas Torrance, God and Rationality (Oxford: Oxford University Press, 1971), 107.


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