Abstract
Infinitism claims that a belief is justified only if it stands at one end of an infinite series of available reasons. I argue that this condition cannot be satisfied by any human mind. In general, as one expands the list of propositions that a subject is said to believe, one must either add new basic evidence, add increasingly complex propositions, or include propositions that are ever more similar to each other. But I argue that (a) for a proposition to be available to one as a reason, one must either believe it or be disposed to acquire the belief without the need of acquiring new evidence, (b) there is a limit to the complexity of the propositions that a human mind can grasp, and (c) there is a limit to the capacity of a human mind to distinguish propositions. Thus, no human being can have infinitely many propositions available as reasons.
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Notes
- 1.
He further distinguishes ordinary dispositional beliefs that involve already-formed dispositions to (occurrently) believe something, from dispositional beliefs that involve second-order dispositions to form the first sort of dispositions. He proposes that the infinitist may rely on the latter sort of dispositional beliefs. For more on the nature of dispositional belief, see Sect. 11.2.1 below.
- 2.
See the recent papers in Turri & Klein 2014, which, despite many criticisms of infinitism , only briefly mention the finite mind objection. Fumerton (2014, 77), though otherwise critical of infinitism, seems to grant that the finite mind objection fails. But note that Kvanvig (2014, 137–141) and Podlaskowski and Smith (2011) advance variants of the finite mind objection.
- 3.
In Huemer 2016, I argue that it is metaphysically impossible for anything to possess an infinite intensive magnitude. I think having infinitely many available reasons might require one to instantiate an infinite intensive magnitude (for instance, infinite intelligence, or infinite information density). But I shall not pursue that suggestion here. Here, I am content to argue that having infinitely many available reasons is psychologically impossible for actual human beings.
- 4.
- 5.
One might think that “availability” should be treated normatively—e.g., perhaps a reason should be considered available only if it is justified, or even known. I leave this point aside, since I want to focus on the unsatisfiable psychological demands of infinitism . As Fumerton (2014, 80–81) observes, normative conditions on availability create additional problems for an infinitist.
- 6.
Assertive mental states are those that represent their contents as true or actual. For instance, perception, intuition, memory, and belief are all assertive; however, imagination and desire are non-assertive (see Huemer 2001, 53–54).
- 7.
More precisely, the conclusion is that given a square ABCD, the square constructed on the diagonal AC has twice the area of the original square.
- 8.
This is a slight misstatement, since having non-inferential justification for p is compatible with also having inferential justification for p. But consider an allegedly foundational belief that does not have any inferential justification. That belief, according to Klein , is arbitrary.
- 9.
One way to appreciate this point is to read about Graham’s Number, once said to be the largest finite number ever used in a serious mathematical proof. I won’t here try to explain what this number is, since doing so requires considerable time (see Gardner 1977). The considerable work required to describe Graham’s Number helps to bring home how increasingly large numbers demand greater cognitive resources to refer to them.
- 10.
Don’t worry about the apparent self-referential paradox, i.e., that I have apparently just referred to numbers that I can’t refer to. I mean that I can’t refer to these numbers individually, i.e., I can’t pick out specific ones. I can only refer to this general category of numbers. You might also wonder about the paradox generated by the expression “the smallest number that I can’t individually refer to.” I don’t know the solution to this sort of paradox, but I assume that the solution is not to declare that I can individually refer to every number.
- 11.
- 12.
I here make use of the character/content distinction, as explained in Kaplan (1989, 500–507).
- 13.
Armstrong (1978, 20) rejects such arbitrary disjunctive properties.
- 14.
Klein (1999, 308–309) suggests that “when our vocabulary and concepts fall short of being able to provide reasons, we can develop new concepts.” I assume that he has in mind new simple concepts, since the possibility of new complex concepts constructed out of concepts one already possesses would not help.
- 15.
Qualia (singular: “quale”) are the intrinsic, qualitative features of experience, the features that define what the experience feels like to the person having it.
- 16.
Klein communicated this during an exchange at the conference where this paper was first presented, at Rutgers University, April 29, 2016.
- 17.
I would like to thank Peter Klein, Cherie Braden, and the participants of the conference honoring Peter Klein at Rutgers University in April, 2016, for their many thoughtful and helpful comments on this chapter. Peter Klein is not responsible for any errors in this chapter. He and I have agreed that all responsibility for any mistakes falls on Cherie Braden.
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Huemer, M. (2019). Finite Minds. In: Fitelson, B., Borges, R., Braden, C. (eds) Themes from Klein. Synthese Library, vol 404. Springer, Cham. https://doi.org/10.1007/978-3-030-04522-7_11
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