That The Evidence Of Insights Is Independent Of Arguments
July 31, 2009 — 13:21

Author: Trent Dougherty  Category: Uncategorized  Comments: 14

My position is that propositions become our evidence via the deliverances of basic faculties such as the senses, memory, introspection, and rational insight. Without the latter, we have little or no way of extending our basic knowledge beyond the testimony of the senses. The principles of inference according to which we extend basic knowledge are justified because of the testimony of rational insight. [Let’s bracket for now concerns about Carroll’s Paradox, because I don’t think that will affect my point.] Rational insight can be mistaken, as in the apparent self-evidence of the naÃ¯ve axiom of comprehension, but its reliability is entailed by our general reliability.
Rational insight sometimes gives testimony to simple facts–like the transitive property of equality–but sometimes to more complex items like the solutions to mathematical or metaphysical problems. You might seem to “see” that there could be a proof of a theorem, a solution to an equation via number theory, or a way to use probability to explicate justification.
Many readers will have had the experience of many failed attempts to make such apparent insights precise in a system of logic before apparently reaching success. At some point, of course, repeated failure is enough counter-evidence to undercut and defeat the evidence provided by the testimony of reason (or the deliverances of reason will be more clear for the negation, as in the case with Russell’s Paradox). When it does so is vague, but I think at times, given a plausible view of our resources, it would take a lot of failure to do so.
In fact, I think that sometimes repeated failure is evidence for the insight when it is repeated failure by multiple people. Think of the history of failure to prove Fermat’s last theorem. Personally, I never doubted the theorem for a second and I doubt I am alone in believing that the repeated failure to provide a proof did not provide much if any evidence that it was false. Or consider what a history to prove Goldbach’s conjecture would look like (I haven’t looked to see if there is an actual history of attempts to do so). The very fact that so many people have the insight that it is true is what is guiding all these (sadly failed) attempts, and the (partial) independence of the testimony can be surprisingly strong evidence when modeled probabilistically. And it helps when there is considerable conceptual similarity among the attempts, for the insights are often of the form “considerations pertaining to X support Y” (and we just can’t get the bridge in formal logic yet).
Now think of the history of attempts to prove God’s existence by, say, the Ontological Argument (OA). I think there is a sound OA, but suppose you don’t. There are OA’s in Augustine, Anselm, Descartes, Leibniz, Hartshorne, and Plantinga et al. And even if you think they are none of them so much as valid, I think their (hypothesized) failure would not mean that one lacked evidence for the existence of a sound OA. I think the fact that partially independent sources (not to mention what sources they are in terms of quality and otherwise disparity of conceptual framework!) have the testimony of reason that there is such an argument to be had is evidence that it is so, and I think that it is greater than any contrary evidence which might be provided by the failure to make precise that insight in the language of logic (much as that is to be desired). I think this is even more so with at least two versions of the cosmological argument. The question, for those of us seem to have the insight that considerations of causation, infinity, and contingency point to a supreme being isn’t so much whether the insight is or is not true–it maintains its luster of truth (too bad “truthiness” is taken!)–but just how to show that it is true. But knowing doesn’t require showing (much as that is to be desired).
I’m inclined to think that many ordinary beliefs by ordinary believers depend on this kind of scenario and that meditation on the history of math and science bear out this epistemological assessment via parallel examples. I’m also inclined to think that though there may be some atheological parallels, the theist has the advantage.

• Andrew Moon

Trent,
Some questions. First, are you endorsing something like the following?
1) If S has an insight that p is true, then S has some justification for believing that p is true.
Secondly, could you clarify what you are calling ‘insight’? Is it any different from ‘seemings’? Seemings have been discussed a lot recently by Swinburne, Conee, Huemer (especially), and others. Also, your examples could easily support a view like Huemer’s.

July 31, 2009 — 14:54
• Joshua Thurow

Trent,
Here’s another example that seems to me to further support your claim that insights that “considerations pertaining to X support Y” justify us in believing (or, perhaps, give us some justification for believing which justifies us in the absence of defeaters) that considerations pertaining to X do support Y even if we have so far been unable to find a strong, generally persuasive, argument that considerations pertaining to X support Y.
The example: something about the features of my experience and my competence with concepts justifies me in believing that there is a computer in front of me. This seems true to me (and, I gather, to very many people, including reliabilists, who think there are other factors as well), even though it is hard to find a strong, generally persuasive, argument from some specific set of features to the conclusion that my belief that there is a computer in front of me is justified. This is so because people disagree about what it is about my experience and competence with concepts (and perhaps other factors) that matters for justification (and people disagree because they find problems with each others’ theories).
It’s not clear, though, that you can use this kind of claim to argue that there are considerations that in fact support theism because people’s intuitions differ more widely about whether, e.g., considerations pertaining to the simple existence of contingent entities support the existence of God. Some people have this intuition, others lack an intuition about it, and some have the intuition that such considerations do not support the existence of God. Now, we run into the problem of disagreement and, if you follow Feldman and Christensen, we should suspend judgment (assuming there are epistemic peers on all sides and one side doesn’t have many more advocates than the others). Maybe you don’t want to follow Feldman and Christensen, but the only point I’m trying to make is that your claim that I summarized in the first paragraph of this entry will not get us easily to the conclusion that there are considerations that support theism because we will have to deal with the problem of disagreement first which, at the very least, is a difficult problem. (Although I guess you could say that the problem of disagreement is a problem for everybody, so isn’t a special problem for the kind of argument you want to give; fair enough, but it still is an obstacle to getting this kind of argument to work).

July 31, 2009 — 15:54
• This is insightful and interesting.
Tell me a bit more about your FLT and GC insights. I myself have no direct insight into both (in this way, they differ from certain conjectures about harmonic measure that I have very strong direct intuitions about). That all integral positive solutions to x^n+y^n=z^n have n<3 is mildly surprising and very weakly counterintuitive. That every even number greater than two is the sum of two primes would be quite surprising to me. I check that this is so for 4, 6, 8, 10, 12, 14 and 16, and each one that comes out right is a bit of a surprise, except those that are of the form 2p where p is prime (and these get more rare later on).
My reason for believing GC is an instance of the argument schema:
1. F(n) all n up to something large.
2. There is no positive reason to think there is an n such that not F(n).
3. F(n) is a nice formula.
4. Therefore, probably, F(n) for all n.
In the case of GC, (1) is something I know by testimony, and (2) is largely based on testimony. Rational insight comes in in (3). For instance, compare the case of GC to that of GC*. Let GC*(n) = “n<10^100 or n is odd or n is the sum of two primes”. Then, GC*(n) for all n up to something large (namely for all n less than 10^100). There is no positive reason to think not-GC*(n) for any n. But these facts give me very little reason to affirm GC*(n) for all n. The culprit is that, clearly, GC*(n) is not a nice formula.
Niceness is, of course, entirely contextual–a formula is nice provided that it makes the argument schema (1)-(4) be a good argument schema. I have no idea how to explicitly formulate niceness. I just have a rational insight that GC(n) = “n< 4 or n is odd or n is the sum of two primes” is nice, while GC*(n) is not. I also have the rational insight that FLT(n) = “There are no positive x, y and z such that x^n+y^n=z^n, or n<3” is nice.
Is this how you’re thinking of your GC and FLT examples?
Another nice case for you is the isoperimetric inequality (the plane figure that maximizes area for a fixed circumference is the circle). This inequality has been correctly believed–and perhaps even known–since antiquity. But it was only in the first half of the 19th century that Steiner proved a conditional form of it (he proved that if D maximizes area for a fixed circumference, then D is a circle; he did not prove, however, that there is any figure that maximizes area of a fixed circumference), and only later was the full version proved. Yet loads of people seem to have had the rational insight that it was true. (One can make some headway towards rational insight by thinking about some transformations. For instance, if the figure is not convex, you can flip a portion of its edge outwards to increase area while leaving circumference unchanged.)

July 31, 2009 — 16:03
• Joshua:
I don’t think disagreement is a problem for Trent’s position. There is an asymmetry between:
1. x has the rational insight that p supports q.
2. y does not have the rational insight that p supports q.
(1) is much more evidence for p supporting q than (2) is for p not supporting q. Think of rational insight as an accomplishment. Some cases of rational insight are common accomplishments. Thus, the rational insight that no false proposition is true is quite common. But some cases of rational insight are rare accomplishments–it takes much thought, life and/or luck to get to that insight.
Compare the case of proofs. Steiner was no doubt a very smart mathematician, and his conditional proof of the isoperimetric inequality used quite a cool construction. But was he smarter, harder working or better informed than all his contemporaries who thought about the problem? I see no reason to say that. But he had an important insight (Steiner symmetrization), which no one else had. Now, his insight happened to be one that he could formalize and write down as a proof, albeit only of the conditional form of the inequality (though the idea could be extended to prove the full version). Insight is something variable, and we do not take the failure to have an insight to be evidence of being less smart, less knowledgeable, etc.
Here’s a different case. Amateur astronomy. A rather surprising fact is that it appears that two people can under the same conditions, with the same telescope, with equally good vision look at a patch of sky, and one will notice an object and the other will fail to notice.
Now, suppose that we take two equally experienced amateur astronomers, looking through the same telescope, at an area of sky that neither is familiar with (so we don’t have to deal with the problem that if I think M110 is there, my brain might just draw it in for me even if it’s not there). A sees a faint patch. B sees nothing. I think most amateur astronomers would take this pair of reports to support the claim that something was there. One would still have to rule out the hypothesis that it was an artefact of the eyes or an atmospheric disturbance. An easy way to rule these out would be for A to wiggle the scope and see if the patch moves in the way we would expect it to if it were in the sky, or else to ensure that tracking is turned off, and see if the patch moves out of the field of view due to the earth’s rotation (if not, then it’s in the eye or an atmospheric phenomenon). But that B did not see it might be slightly surprising if A and B are well-matched, and hence it would be some evidence against A’s claim to see, but it would be very little evidence, especially if A saw it moving appropriately.
Now, maybe I am being unfair. Maybe the symmetry is not between 1 and 2, but between 1 and:
2*. y has the rational insight that p does not support q.
However, note that this is still parallel to the amateur astronomy case. B sees blackness, i.e., the absence of a faint patch. A sees a faint patch. Nonetheless, we (i.e., amateur astronomers) credit A’s sight, say that B just missed it, and are not particularly surprised by the phenomenon, telling B: “Better luck next time!” The perception of an absence is rather less reliable than the perception of a presence.
I think the same is true in the rational case. There are many, many surprising logical connections between propositions. We would not be surprised if the range of logical connections that y saw did not include the one between p and q, and so it looked to y as if there was no connection there, even though there really was one there. y would report this is as the perception of an absence of connection, but the basis of it would still, probably, be a failure to cast the mental eye in a certain direction.
There would be a symmetry between 1 and 2**:
2**. y has the rational insight that p supports not-q.
But in the cases Trent gives, I doubt there is much in the way of competent folks who, say, have the rational insight that the existence of contingent things supports the non-existence of God.

July 31, 2009 — 16:37
• Hi Trent,
Very interesting line of thought. I wonder if you had any initial thoughts on how to distinguish the persistent apparent insight that God must exist (via the OA, or CA, or whatever) from, say, the perennial theme that, at bottom, life is meaningless. Other examples might include: perpetual motion is possible, reality is absurd, or (perhaps most importantly) that there absolutely must be something wrong with the OA, or that certain particularly horrible events disprove God’s existence.
Those last two are perhaps the atheological parallels you had in mind.
[P.S. I tried to post this comment a couple hours ago, but it apparently didn’t go through.]

July 31, 2009 — 16:48
• Andrew Moon

whoops, I just realized that you were talking about ‘rational insight’, and you were restricting yourself, it seems, to a priori knowledge. I guess I still have the same questions, though, whether insight is identical to seemings.
I also think that you might be talking about Conee and Plantinga’s “seeing the truth” phenomenon, which Conee devotes his 1998 PPR article “Seeing the Truth” to. Might that be what you are talking about by “rational insight”?
Josh,
Were you taking Trent’s ‘rational insight’ to express the same thing as ‘intuition’? I’m not sure he takes them to mean the same thing.

July 31, 2009 — 19:17
• John:
Sorry to be defending Trent, since he can do so better. 🙂
Perpetual motion is possible. In a frictionless isolated system. Which, as a contingent matter of fact, doesn’t seem to exist.
The insight that life is meaningless… I wonder if often that’s not really just a conditional: If that’s all there is to life, then life is meaningness. In that case, it might be true, depending on what “that” ostends to. What if it’s unconditional? Well, I suspect that there is a strong correlation between clinical depression and unconditionally believing life to be meaningless, and diagnosable disorders will weaken our confidence.
The intuition that there is something wrong with the OA… That’s a really interesting case. There seem to be two versions of the intuition. The first is with respect to a particular version of the argument: one reads it, and thinks there must be something wrong with it, though one can’t put one’s finger on it. This is unproblematic for Trent, because it’s compatible with what he said that there is something wrong with every explicit formulation of the OA. The second is an intuition that no argument of that sort could work. I think some people do have that intuition. It could actually be the case that both this is correct and it is correct that there is something to the OA. For it could be that there is a good OA, but it is beyond our intellectual powers to formulate it correctly. (This is, roughly, St. Thomas’s view of the OA.) If so, then we explain both the insight that leads folks to continually formulate versions of the OA, feeling that they are getting at something important and right, and the insight that leads folks to think that no good OA can be formulated. That would be neat.
The problem-of-evil intuition is going to be a more serious problem. That’ll be a good thing for him and me to address in our book on the problem of evil. 🙂

August 1, 2009 — 12:31
• John Turri

Hi, Alex. I welcome your thoughts!
On perpetual motion: good catch. I guess there’s something more specific that people are intuiting, which goes beyond the bare possibility. Perhaps it’s that they’re actually able to build a perpetual motion machine.
On your way of handling the “insight” that life is meaningless: I’ll have to think about that one. If the insight is unconditional, then I worry about appealing to the clinical diagnosis to handle it. If the disorder is supposed to be practical, then it leaves the intuition untouched (“Yeah, maybe humans function more efficiently if they don’t believe it’s all meaningless and consequently get all depressed. But so what?”). What sort of disorder were you imagining?
On your way of handling apparent disagreement over the OA: you’re right, it would be really cool if you could explain it that way.

August 1, 2009 — 13:45
• I don’t know how much Trent wants the rational insight to apply to empirical matters, like perpetual motion. But I think it’s not a big problem to say that people’s continued attempts to build such machines are some evidence that it’s possible, and then to say that our scientific data trumps this evidence.
Generally, we don’t think of people with clinical depression as thinking rationally. But there is a direction of causality issue here: Maybe they are depressed because they unconditionally think life is meaningless (I would be if I did!). In those cases, your point would go through. Still, the evidence from the rational insight of people who are now irrational is weak, because they and we ought to worry that the insight already came from the beginning of the disorder. Moreover, the fact that depression can have non-cognitive neurological roots weakens the evidence further.
Compare the case of paranoia. One might become paranoid because one has vague and correct sensations of there being a plot against one. Once one is paranoid, however, one’s sensations of there being a plot against one are epistemically of very low value, and one will worry that the paranoid person acquired the initial sensation of a plot due to the beginning of paranoia.

August 1, 2009 — 14:46
• Joshua Rasmussen

Trent,
Good thoughts. You shared something like this to me wrt cosmological arguments before, and it’s something I still think about from time to time… I might add that one’s rational insights are relative to one’s background concepts and thoughts (think: non-doxastic conceptual awarenesses). So, two people could consider a proposition–for example, the proposition that if there were no people, there would neither be things nor would there not be things–, and one of those people might see that it is true while the other not. Both could be completely rational from their perspective. Rational insight is perspectival, I suggest.
There is a delicate issue here of testimony: if I see that P is true, and James does not, can I give James testimonial support that P is true? Or can James always say, “P is cannot be self-evident, for it if were, then it would seem evident to me, too”?
My sense is that if theism is true, then there are people who not only have rational insight (weak and tentative, perhaps) that there is a sound cosmological argument, but there are also people who have rational insight into a sound cosmological argument. I say this with all due respect for those very rational dissenters.
Sometimes concepts, thoughts, and philosophizing can actually occlude rational insight that is natural to have. This may be so wrt to certain arguments for God based on causation, contingency, and design–arguments that often strike children as undeniable. (Ask an 11-yeal-old whether something could pop into existence without a god or anything else causing it to; find out what they see).

August 2, 2009 — 20:37

Alex, you wrote, The problem-of-evil intuition is going to be a more serious problem. That’ll be a good thing for him and me to address in our book on the problem of evil.
I think the apparent âinsightâ some have that evil is a consideration that there is no God is the real serious problem as this insight seems to escape the other criticisms and asymmetries you highlight.
Nevertheless, I am inclined to think that Trent can avoid it. Take the issue of disagreement that Joshua raises, it seems that (i) either the fact that symmetrical insights contradict is reason for rejecting the insights; or, (ii) it is not the case that the fact symmetrical insights contradict which provides a reason for rejecting the insight.
If (ii) is the case then the insight that some people have, viz a viz abhorrent evil as a consideration for atheism, does not provide a theist, who has Trentâs insight, with any reason for rejecting his insight.
The issue hinges on (i); suppose then (i) is true, the problem here is that one can neutralise the abhorrent evil insight. This is because it seems to me very plausible that many people have the insight that the existence of evil is a consideration for believing in God.
Just as people who attempt to formulate the cosmological argument have the insight that contingency, infinity, etc are considerations for Godâs existence, similarly, those who attempt to formulate moral arguments, divine command theories, and naturalists who formulate error theories often have the insight that morality in some way depends upon Godâs existence. If this is the case then we find that with the existence of evil some people have the insight that this is a consideration for theism and some think it is a consideration for atheism. Therefore by (i), the insight that evil provides evidence for atheism should be rejected; insights about God and morality then should not be trusted either if (i) is correct.
The insight about contingency, however, seems to be in a better position. As you note, no one seems to have the insight that contingency is a consideration for atheism, atheism is typically only based on insights about evil and God but these insights are clearly ones we should not accept if we accept (i); hence, the contingency insight is in the clear.

August 8, 2009 — 1:10
• That’s a nice point about the symmetry in the evil.
But there is a remaining problem. Start with the putative atheist insight:
1. The existence of evil shows that God does not exist.
The putative insight (1) may then nicely cancel off against the putative insight:
1*. The existence of evil shows that God exists
via the moral argument, or Aquinas’ argument that evil can only exist against a background of good and proper function (and then we run a teleological argument), vel caetera.
So, suppose we admit on the basis of the above that the existence of evil, by itself, doesn’t affect Trent’s case. But now add the following further atheist insight:
2. The existence of horrendous evils (defined however you like) shows that God does not exist.
Ordinary people who think that evil provides provide against the existence of God tend to think that horrendous evils provide more evidence. The parallel to this would be:
2*. The existence of horrendous evils shows that God exists.
But it is not at all clear that horrendous evils require more of a background of good (as in Aquinas’ thinking about (1*)) or that the moral argument is strengthened. So it would require significant work to defend as providing any evidence beyond (1*).
However, it seems to me that the insight in (2*) does go evidentially beyond that in (1*) in more than one way:
A. If all we were dealing with were non-horrendous evils like mosquito bites and unpunctuality, it wouldn’t be so hard to dismiss the thinking behind (1*), e.g., by saying that the badness of mosquito bites is merely subjective or that unpunctuality is inconvenient but not wicked. But these dismissive moves, plausible as they are for minor evils, are obviously wrong when applied to, say, genocide.
B. The really horrendous evils we meet with are evils that happen to persons. What makes them horrendous is the violation of the dignity of the person. But now we have a design argument from the existence of beings that have that sort of dignity.
So the insight behind (2*) does go beyond that in (1*), in the way that the insight behind (2) goes beyond that in (1), and parallelism seems to be restored. Shiny!

August 8, 2009 — 9:33
• Alex, I am not sure the example in your response to me works (perhaps I am misunderstanding you).
You suggest:
â2. The existence of horrendous evils (defined however you like) shows that God does not exist.â
And then note the parallel is:
â2*. The existence of horrendous evils shows that God exists.
âBut it is not at all clear that horrendous evils require more of a background of good (as in Aquinas’ thinking about (1*)) or that the moral argument is strengthened. So it would require significant work to defend as providing any evidence beyond (1*).â
I do not see why the moral argument would not be a parallel to this. Consider your examples;
âall we were dealing with were non-horrendous evils like mosquito bites and unpunctuality, it wouldn’t be so hard to dismiss the thinking behind (1*), e.g., by saying that the badness of mosquito bites is merely subjective or that unpunctuality is inconvenient but not wicked. But these dismissive moves, plausible as they are for minor evils, are obviously wrong when applied to, say, genocide.â
The problem is that the moral argument does not argue for Godâs existence on the basis of merely subjective evils. Typically those who push this argument appeal to actions that are objectively wrong, wrong for anyone regardless of their subjective preferences; cases like genocide seem to be, obviously, the least controversial paradigms of such actions.