But if smart Sammy constructs a case on a really difficult issue that requires, say, 7 steps (or seven intermediate conclusions), the odds of Sammy being right in his final position become rather small. They diminish by 10% at each move. Even for smart Sammy, the odds are increasingly against him.

For the rest of us, it’s probably even worse, which means we ought to be careful about believing some of the things we say seem true and plausible. (One more note about smart Sammy: while on some issues –like who won the World Series last year — Sammy is better than 90%; on others, like papal infallibility, apostolic succession, or which church — if any — ought to be followed, he will be worse.)

In other words, I’m talking about the noetic effects of sin, about the fallen intellect that each of us owns, and about how easily we are deluded — me included, this post included.

L isn’t glossed in terms of how it seems to me, but in terms of ‘very likely’, which presumably has something to do with evidential assessment, and thus something to which seeming-to-me would have to conform in order to be rational; but other than that, it’s what I had in mind — in a sense, [1] simply identifies howthe inconsistent tetrad is inconsistent. Given the difference, to say that [1] is false is to say that, when we are qualifying everything with a ‘it is very likely that’ operator, the tetrad is consistent. This is surely wrong. If, however, we understand the operator to be ‘it strongly seems to me that’, then the tetrad really is consistent — it’s logically possible for each of 1 through 4 to seem to me strongly — and if -> means implication then [1] is strictly speaking false (the only way it can be true is if we hold that strong seeming is in fact logically consistent, which would be a rather strong claim about psychology). It could still, perhaps, be a useful idealization, but it wouldn’t be rigorously true. However, if we say this, it shows equally that seemings, however strong, simply can’t rationally trump actual principles: even strong seemings can be irrational, in the sense that believing according to them would be irrational. And, indeed, we find this elsewhere; there are people who have vivid hallucinations who recognize that they are, in fact, hallucinations. Thus how things seem to you is simply not relevant, on its own, to how reasonable one’s beliefs are, no matter how strong the seeming is; seemings only become relevant by way of rational assessment of how reasonable it is to believe according to how things seem to be.

Let me see if I can repeat back to you what you’re arguing.

Suppose I’m a faithful Catholic. If so, your [1] will be something I reasonably believe. It is a plausible principle on the assumption that my (1) really is true, and that I’m a rational agent in a non-hostile epistemic environment.

[1] says that IF it strongly seems to me (roughly) that (1) the church is infallible, then it strongly seems to me that: IF it strongly seems to me both that (2) I’m required by it to believe that any properly blessed wafer is Jesus’ body, AND that (3) the wafer over there has been so blessed THEN it strongly seems to me that (4) that wafer over there isn’t a mere wheat product.

Now that I understand what you’re saying, it makes sense to me. Yes, I grant that it is reasonable to assume [1]. I think it is part of assuming one’s own epistemic competence, when assuming (1). (For the record, [1] doesn’t seem true to me.)

Here’s how your belief in [1] could come to be no longer rational. 2 and 3 still strongly seem true. But now so does 4. Imagine that you’re serving as altar boy, and through some mishap, a blessed wafer ends up falling into your shoe. When you get home, you discover it. First you’re horrified at the thought that you’ve been stomping Jesus all the way home, but as you turn the thing over in your hand, smell it, tap it, break a piece off it, outside the context of the mass, it strikes you that this is no human body, but a mere wafer after all. Now 2,3, and 4 all seem true. L~4 is false, and yet L2 & L3, and so the conditional (L2 & L3) -> L~4 is false. You “see” this, so then L((L2 & L3) -> L~4) is false. This brings us to a case where L1 is true but L((L2 & L3) -> L~4) is false – that is to say, the whole [1] is false. It is false when you’re in this state of tension described above.

I agree that if you’re functioning properly (and you’re not in some weird epistemic environment), this typically won’t last long – something will give in to the pressure, as it were.

But keep in mind that this needn’t involve inconsistent beliefs! You may come to agree with me that [1] is false, all the while believing 1-3 and not believing 4. [1] would be shown false just by occasional episodes like that described above.

[1] L1 -> L((L2 & L3) -> L~4)

with

[2] L1 -> (L2&L3) -> L~4.

If so, we are both in agreement that the second claim is wrong in this context; I’ve agreed to this more than once, in fact, because it is implied by my description of the relevance of [1] that [2] is false.

I’m not sure what you mean here. L1 -> L((L2 & L3) -> L~4) clearly doesn’t say that anything follows from 1 about how 2 or 3 seem; L2 and L3 are explicitly in an antecdent to a conditional.

This : L1 -> L((L2 & L3) -> L~4) is false. If 1 strongly seems true to me, nothing follows about how either 2 or 3 seem to me. If 1 is true, it might also strongly seem to me that 2 is false (I’ve been misinformed) and that 3 is false (I’ve been told on good authority that that priest is an imposter).

I don’t follow what you’re asserting about the irrationality of changing charts, i.e. of one’s seemings changing from this:

1. XXX
2. XX
3. XX
4. XX

to this

1. XX
2. XXX
3. XXX
4. XXX

Here’s a guess – you’re reading the charts as if they were of belief-strength – i.e. 1.XXX means you very strongly believe 1, whereas 2.XX means that you only somewhat strongly mean 2. But these charts are only meant as snapshots of how things seem at a time. Seemings can shift involuntarily (also, I think, indirectly voluntarily) but if one’s seemings have shifted as above, that doesn’t mean one has made any inference. Or maybe you’re thinking of “evidence” as something mind-independent – I’m not sure.

You say “it is not possible, in a rational case, to diminish the seeming-true of 1 by increasinging the seeming-true of 4″ But who needs that claim? Not me. 1′s seeming could change *because* 4′s does, or they may just happen to change at the same time.

“Unlike the other propositions, 1 is a meta-level principle that establishes as certain an entire field of evidence; if 2 and 3 are held constant, then no considerations that might usually be brought for 4 are relevant — by 1 they are misleading and illusory.” Sorry, but this is just wrong. 1 will still be trumpable. There’s no way to make it untouchable – it might be defeated / trumped even if it seems as strongly as anything does. I don’t see how you can, as it were, remove 1 from the game.

As for testimonial evidence, I think your position is untenable. I take a Reidian view of it as a basic source of evidence; it’s just part of our design plan that when someone strongly asserts something, it to some degree seems true to us. This can be and often is easily trumped, but it is important that we are like this. We don’t have to wait until we’ve conducted some sort of study of the causal history of the testimony, or the reliability of the speaker on that sort of subject, etc.

I think I should withdraw my comment in comment #5 above: “unless the agent is malfunctioning”. When I said this I was confusing seemings with beliefs. The agent may be functioning perfectly, be if she’s in an unfortunate epistemic situation, she may find herself having these seemings, without suffering any malfunction or irrationality:

1. XXX
2. XXX
3. XXX
4. XXX

e.g. suppose that she’s a ten year old, and new to all of this, and that she deeply trusts her parents, who strike her as equally credible. One is a Catholic (and tells her 1 & 2) and the other is a atheist (who tells her 3 & 4). She may or may not believe all of 1-4; even if she withholds on all four, she’ll still be in the state above.

The switch from the first X-graph to either of the last two X-graphs is possible only for someone who is irrational. This follows directly from the logical structure of the inconsistent tetrad, i.e., from the fact that 1,2, and 3 combined imply that 4 is false. The switch from the first X-graph to the one with 3 X’s in each row shows someone to whom both conjuncts of a contradictory conjunction seem very likely. So that’s an obvious case of irrationality, unless seeming is non-adjunctive, in which case it’s difficult to see how your X-graphs tell us anything at all.

The second one is more subtle, because it is possible for a rational person to be in the state depicted in the X-graph, but it is not possible for a rational person to make the switch from your first X-graph to your last X-graph in the way you suggest. Unlike the other propositions, 1 is a meta-level principle that establishes as certain an entire field of evidence; if 2 and 3 are held constant, then no considerations that might usually be brought for 4 are relevant — by 1 they are misleading and illusory. Thus it is not possible, in a rational case, to diminish the seeming-true of 1 by increasinging the seeming-true of 4; if 2 and 3 are held constant 4 will necessarily seem false to any rational person unless 1 begins to seem less likely — and this follows from the logical structure of the problem because in this context 1 is an inference rule that tells you that 2 and 3, which are held to be highly likely, guarantee the falsehood of 4 regardless of other considerations.

We can put it this way. Let L be a modal operator that can be glossed as meaning something like ‘very likely’ — XXX’s or above. Then the logical structure of the seemings at the beginning is

L1 -> L((L2 & L3) -> L~4)

L~4 is implied by L2 & L3 under the scope of an L that follows from L1. It is the only one that cannot logically be changed independently of the others — whether or not L~4 depends on L1, L2, and L3, not vice versa. L1 is in an antecedent. L2 and L3 can change because they are in the antecedent of the hypothetical, and are each only one conjunct of the antecedent. But if L2 and L3 are given, L~4 can only be false if L((L2 & L3) -> L~4) is false, as a logical precondition. But L((L2 & L3) -> L~4) follows from L1. So it can’t be false unless L1 is false, as a logical precondition.

(As far as I can see, 2 doesn’t constitute any sort of testimonial evidence for the wafer being Jesus’ body unless there is reason to think that the testimony is reliable; wholly unreliable testimony is of no evidential value whatsoever, perfectly reliable testimony is of immense evidential value, and other kinds of testimony fall between the two. I would deny very vehemently the claim that just hearing someone soberly assert a claim gives me any sort of evidence for what is asserted. What gives me evidence for what is asserted is the causal history of the testimony; this is a different thing entirely. There are other claims besides 1 that would make 2 evidence against 4; but it does take another claim to make it (or 3) even relevant as evidence. But I think this is a tangential point.)

When it comes to optical illusions, yes the seeming that e.g. these lines are really the same length is stronger than the seeming that one is longer. “Not easily trumped” means that they are fairly strong, and so less “trumpable” than seemings based on vague hunches, dim memories, and far-off sights, etc.

Brandon, I, or my atheist colleague have about as much reason to believe 2 as the most faithful Catholic. I don’t see why you think 1 and 2 are logically related…

Neither do 1 and 2 imply anything about 4. You need to include 3. Yes, assuming 3, then as 1 & 2 increase, 4 must decrease (in how strongly it seems) – unless the agent is malfunctioning.

I think 2 constitutes testimonial evidence that the wafer is Jesus’ body, even for the unbeliever. I’d expect you to agree on that… Just hearing someone soberly assert a claim to someone else gives you evidence for what was asserted. Of course, if you find out that speaker is always right, that does change things.

I agree that 2 & 3 differ, in that they can seem strongly to anyone who merely looks into the matter.

But I don’t understand why you think 1 sort of insulates itself from defeat. I take it you’ll grant that it doesn’t seem true at the maximal level. If so, it is subject to defeat – for anyone whose epistemic situation is like either of my last two X graphs in the post (or other combos I didn’t take the time to spell out).

I find this a very puzzling claim; this is what happens with optical and auditory illusions all the time — it takes very little to convince someone that something is an optical or auditory illusion, since it just requires some positive reason to think that it is one. It doesn’t matter how “multiple, close up, steady, firm” your sensations of a magic trick are, how much they are without exception; if you have a positive reason to think that it is, in fact, a trick, that’s all you need to believe your senses. And as Hume argues in various places, and as cognitive science experiments often seem to show, much of our view of the world involves tendencies of imagination trumping sensible appearances because what sensible appearances seem to suggest is not something that can be read off of them — it depends much more on how we are disposed to read them. If you are arguing for an empiricism even stronger than Hume’s, it’s going to have to be defended; and if you are not, it’s hard to see why one would think this true.

I am even more puzzled about your X’s argument, though; the ‘strength of seeming’ of the four beliefs in question, assuming that they are actually commensurable, aren’t independent: if 1 is strongly believed, this would, if Bob is rational, increase the strength of 2; and the combination of 1 & 2, if Bob is rational, would necessarily reduce the strength of seeming of 4. You can’t hold 4 constant through a change of strength in the conjoint seeming of 1 and 2; that would be irrational. Any change in the strength of seeming of the conjunction (1&2) would change our assessment of inferences relevant to holding 4.

Both 2 and 3 — whether the Catholic Church does, in fact, require its members to believe something and that the priest did, in fact, follow the procedures he was supposed to — admit of independent and intersubjectively recognizable tests. If Bob really has a question on them he can look them up, and get even Dan to agree on them without much trouble. Their strength of seeming, if each is considered simply on its own, is irrelevant to the question. But 1. affects how Bob sorts evidence, and turns 2. into relevant evidence, when it was not even relevant before; and 1 and 2 combined makes 3 evidence against 4, when it had not previously been so.

In other words: If we were to suppose 1 and 2 true together reasons for accepting 3 are reasons for rejecting 4. 2 and 3 can be raised to a high degree of certainty simply by investigation. 1 is not on a level with the rest of the claims because 1 is a meta-level claim: it’s a claim about how claims can be evidentially connected given other claims. If 1 seems more obviously true it changes everything simply on its own, by changing the evidential links among 2-4.