Here, I explain how we gain inferential justification, through appearances.*
[ *Based on “Inferential Appearances,” pp. 144-60 in Intellectual Assurance: Essays on Traditional Epistemic Internalism, ed. Brett Coppenger and Michael Bergmann (Oxford University Press, 2016). ]
Suppose you come to believe P by explicitly inferring it from some premise, E. In this case, your belief that E causes your belief that P. What else must be true for you to gain inferential justification for P?
I. Six Observations About Inferential Justification
Following are six interesting conditions on inferential justification:
1. You must have some attitude toward [E supports P].
Intuitively, you must see the connection between the premise and the conclusion, and that has to explain why you make the inference. It isn’t enough that the premise just causes you to believe the conclusion.
2. Justified belief is insufficient.
The “seeing the connection” cannot just amount to your believing for whatever reason that E supports P. For instance, suppose you can’t see any connection between E and P, but your logic professor tells you that E entails P. Since you already believe E, you then adopt the belief that P. In this case, you did not infer P from E. Rather, you inferred P from [E & my logic professor says that E entails P]. To infer P from E alone, you would have to have seen the logical connection for yourself.
3. [E supports P] is not a premise.
The preceding example also illustrates that there is a difference between inferring P from E and inferring P from [E & E supports P]. We want to explain the former. This means that whatever role is played by “seeing the connection” between premise and conclusion, this role can’t be the same as the role of a premise of the inference.
4. There is nothing more to put together.
In his story about Achilles and the Tortoise, Lewis Carroll imagines the tortoise agreeing that A and (A → B) are each true, but somehow not putting these things together to see that B must be true. Achilles helpfully points out that if A and (A → B) are both true, then B must be true. Whereupon the tortoise accepts the added premise ([A & (A → B)] → B). But the tortoise still doesn’t put all three premises together to see that B must be true. Etc.
An account of inference should exclude the tortoise’s oversight; it should guarantee that the subject has put together everything that needs to be put together.
5. Genuine support is unnecessary.
Suppose a mathematician goes through an apparent proof of P. He checks it over very carefully multiple times and finds no errors in it. Several other skilled mathematicians also check it, and no one sees anything wrong with it. The mathematician comes to accept P based on this proof. This seems justified. But suppose also (consistent with all of the above) that the proof actually contains a very subtle error, which renders it invalid.
In this case, the mathematician is justified in believing P, even though his premises do not genuinely support P. This shows that you can be justified in believing P on the basis of evidence that does not (genuinely) support P but merely seems to support P.
Objection: Maybe the mathematician is justified in believing P on the basis of E and [E supports P], rather than on the basis of E alone. [E supports P] in this case is false, but the mathematician is still justified in believing it, and [E supports P], when combined with E, really does support P.
Reply: Stipulate that the mathematician in fact bases his belief in P on E simply. It seems that this could be the case, and it seems, intuitively, that the mathematician would have a justified belief. This implies that E itself (and not merely “E & E supports P”) provides justification for P.
6. Skepticism is false.
Whatever we say about the conditions for inferential justification, they had better not be impossible to satisfy. For instance, we’d better not introduce conditions that create infinite regresses.
II. An Appearance-Based Theory
Appearances are mental states whereby something seems to one to be the case. They include sensory experiences, memory experiences, introspective awareness, and intellectual appearances. Intellectual appearances divide into two sub-species: intuitions, which are states in which a proposition directly seems true, and inferential appearances, in which a proposition seems to be necessitated by some other proposition, i.e., something seems true (or seems likely) in the light of something else that one believes.
An inferential appearance does not merely represent the relationship between E and P (that if E then P); that would leave us with Lewis Carrol’s problem. Rather the inferential appearance represents that P is (likely) the case, because E. This is how we satisfy condition 4 above.
So here are the conditions for being inferentially justified in believing P on the basis of E:
a) You must be justified in believing E;
b) You must have an inferential appearance that, in light of E, P must be (or is likely to be) the case;
c) Your justification for E must not depend on already having justification for P;
d) You must not have defeaters for your belief that P; and
e) Your belief in E must cause you to believe that P via the inferential appearance (by a nondeviant causal chain).
Some comments:
I assume (a) and (b) are self-explanatory.
Clause (c) is there to rule out question-begging inferences from generating justification.
Clause (d) is included since most inferences are defeasible (e.g., you could acquire evidence that your inference rule was unreliable).
Clause (e): the inferential appearance has to explain why you draw the inference. The “nondeviance” clause rules out silly cases, like one where a demon sees that you have an inferential appearance, and that causes the demon to implant the belief that P in your mind.
III. The Appearance-Based Theory Satisfies the Six Conditions
The above is a good theory of inferential justification. Notice how it satisfies the six conditions on inferential justification from section I:
1. You must have some attitude toward [E supports P].
This is the inferential appearance.
2. Justified belief is insufficient.
Appearances in general are distinct from beliefs. The state of “seeing the connection” between a premise and a conclusion is an appearance, not a belief.
3. [E supports P] is not a premise.
The premises of an inference are the propositions in the light of which the conclusion seems true. [E supports P] isn’t one of those; that E supports P is built into the inferential appearance.
4. There is nothing more to put together.
This is true because the inferential appearance represents the conclusion as true, given the premises.
5. Genuine support is unnecessary.
The “inferential appearance” theory only requires that your premises seem to support your conclusion, so it easily explains how the mathematician with the mistaken proof is justified in his belief.
6. Skepticism is false.
The inferential appearance theory makes it easy for people to gain inferential justification, which is as it should be, since we seem to be doing it all the time.
IV. Appearance vs. Acquaintance
Richard Fumerton holds that in order to be justified in believing P on the basis of E, one must be justified in believing that E supports (renders probable) P. The way one gets to be justified in believing that, in his view, is by being directly “acquainted” with the “making probable” relation that obtains between E and P.
I disagree; I think that the way one gets to be justified in believing that E supports P is by having an inferential appearance as of E’s supporting P.
These two accounts differ because acquaintance is inherently factive – i.e., it is conceptually impossible to be genuinely acquainted with something unless that thing really exists. By contrast, appearance is non-factive – false things can appear to you just as well as true things.
So in the case of the unfortunate mathematician from sec. 1 (observation 5), the mathematician is not acquainted with any making-probable relation since there is no genuine such relation present. He merely has an appearance as of such a relation.
So Fumerton’s theory implies that the mathematician’s belief is unjustified, whereas my theory implies that it is justified. I take the latter to be the intuitive verdict.
Another way to look at the point: Suppose the mathematician has also constructed a genuinely valid proof of another proposition, Q. He has checked both proofs equally carefully and thus has equal confidence in both. Intuitively, it seems that the mathematician is justified in believing P in the same way that he is justified in believing Q. But, as we’ve noted, his justification for P cannot consist in his acquaintance with a logical support relation. Therefore, his justification for Q also does not consist in his acquaintance with a logical support relation. It must be that in both cases, his justification derives from his inferential appearance.
V. Inexplicit Justificatory Dependence
A complication: most of the time, when we make an inference (or otherwise form a belief that depends on other beliefs), we have a large amount of background information that is relevant to why the inference is good but that we are not explicitly entertaining. Indeed, most people couldn’t even name all the relevant information.
Ex.: You see the corner of your couch in tatters, and you infer that your cat did it. This inference depends on a host of background knowledge about what cats are like, what couches are like, what various other things are like (e.g., house plants usually don’t shred your couch), and so on. You would not actually think about all these pieces of information, but they’re all part of the story of why it makes sense to blame the cat.
How does this work with inferential appearances? I suggest that (i) you have an inferential appearance that represents that [the cat shredded the couch] is likely given [the couch is shredded]; (ii) the “likelihood” in question means likelihood conditional on all your background knowledge (even though you don’t actually entertain all that background at the time). What makes this the meaning of “likely” is your dispositions – e.g., you would recognize all these pieces of background information as relevant to the “likelihood” of your conclusion, if the issue were raised.
VI. Conclusion
Inference involves a special kind of appearance, which represents the conclusion of the inference as being either necessarily or probably true given the premises, relative to the subject’s current background information. This appearance presupposes the truth of the premises while representing the conclusion as likely because of those premises. This explains the sense in which, in a successful inference, one sees the connection between the premises and the conclusion.
Sigh. I wish I was clearer on a couple of things.
Appearances are not beliefs. Are they both propositional? Do they intersect at all? I missed why this matters.
Justification isn’t just having good reasons. It isn’t certainty. I can be justified without being certain, and maybe even uncertain of a justified belief. Justification isn’t having enough confidence to act on a belief. What is it? What do I know about justified beliefs that is different from a lucky educated guess? Or are educated guesses justified?
Regarding the tortoise, what is it an argument seeks to justify? Is it the conclusion alone, or the hypothetical statement “ if premises then conclusion?”