Of cats and humans

We acquired a cat around Christmas. Never having had a pet before in my life (except for a puppy for a few days decades ago), what have I learned philosophically? Maybe this:

All cats by nature desire to know. An indication of this is the delight they take in their senses; for even apart from their usefulness they are loved for themselves; and above all others the sense of sight. For not only with a view to action, but even when they are not going to do anything, they prefer seeing (one might say) to everything else. The reason is that this, most of all the senses, makes one know and brings to light many differences between things.

This is, of course, what Aristotle says in the first paragraph of the Metaphysics, except he says it about humans. We tend to think of the pleasures of the mind as distinctively human. But a focus on pleasures of the mind is not distinctively human. Observing and exploring are our cat’s most driving pleasures.

The difference between humans and other animals may lie in the type of intellectual pleasure. Aquinas distinguishes the rightly ordered pursuit of understanding from the vice of curiositas. The main difference is that in the virtuous pursuit, one seeks an understanding of how the world explanatorily fits together, rather than a mere listing of facts of the sort one gets from mere seeing (here’s a tree, here’s a squirrel, etc.).

Calling for an explanation

If I am playing a board game and the last ten rolls of my die were 1, that calls out for an explanation. If only Jewish and Ethiopian people get Tay-Sachs disease, that calls out for an explanation.

It seems right to say that

1. a fact calls out for an explanation provided it is the sort of fact that we would expect to have an explanation, a fact whose nature is such that it "should" have an explanation, a fact such that we would be disappointed in reality in not having an explanation of.

But now consider two boring facts:

2. 44877 x 5757 = 258356889
3. Bob is wearing a shirt

These are facts that we all expect to have an explanation (e.g., the explanation of (2) is long and boring, involving many instance of the distributive law and the explanation of (3) presumably has to do with psychosocial and physical facts). They are, moreover, facts that "should" have an explanation. There would be something seriously wrong with logic itself if a complex multiplication fact had no explanation (it's certainly not a candidate for being a Goedelian unprovable truth), and with reality if people wore shirts for no reason at all.

So by (1), these would have to be facts that call out for an explanation. But I don't hear their cry. I am confident that they have explanations, but I wouldn't say that they call out for them. So it doesn't seem that (1) captures the concept of calling out for an explanation.

As I reflect on cases, it seems to me that calling out for an explanation has something to do with the intellectual desirability of having an explanation rather. Someone with a healthy level of curiosity would want to know why the last ten rolls were 1 or why only Jewish and Ethiopian people get Tay-Sachs. On the other hand, while I'm confident that there is a fine mathematical reason why 44877 x 5757 = 258356889, I have no desire to know that reason, even though I have at least a healthy degree of curiosity about mathematics.

This suggests to me an anthropocentric (and degreed) story like the following:

4. A fact calls out for an explanation to the degree that one would be intellectually unfulfilled in not knowing an explanation.

It is sometimes said that a fact's calling out for an explanation is evidence that it has an explanation. I think (4) coheres with this. That something is needed for our fulfillment is evidence that the thing is possible. For beings tend to be capable of fulfillment. (This is a kind of cosmic optimism. No doubt connected to theism, but in what direction the connection runs needs investigation.)

Omniscience

A standard definition of omniscience is:

• x is omniscient if and only if x knows all truths and does not believe anything but truths.

But knowing all truths and not believing anything but truths is not good enough for omniscience. One can know a proposition without being certain of it, assigning a credence less than 1 to it. But surely such knowledge is not good enough for omniscience. So we need to say: “knows all truths with absolute certainty”.

I wonder if this is good enough. I am a bit worried that maybe one can know all the truths in a given subject area but not understand how they fit together—knowing a proposition about how they fit together might not be good enough for this understanding.

Anyway, it’s kind of interesting that even apart from open theist considerations, omniscience isn’t quite as cut and dried as one might think.

Ineffability

Consider this argument against divine ineffability: Let p be the conjunction of all fundamental truths intrinsically about God (I'm thinking here of something like the Jon Jacobs account of ineffability, but the point should work on other similar accounts). Stipulate that the sentence "It divines" (a feature-placing sentence or zero-place predicate, like in "It rains") expresses p. It divines. It seems I have just said the conjunction of all fundamental truths intrinsically about God. Hence God is not ineffable.

But this argument cannot be sound, since God is in fact ineffable--divine ineffability is, for instance, part of the creed of the Fourth Lateran Council. So what goes wrong with the argument?

First, one might have technical worries about infinite conjunctions or arbitrary linguistic stipulations. I'll put those to one side, though they are worth thinking about.

More deeply, one might worry whether there are any fundamental truths intrinsically about God. Truths are true propositions. Perhaps the fundamental reality of God not only cannot be expressed in language, but cannot even be given propositional form. I am not sure about this, though it is a promising response to the argument. But, plausibly, propositions are divine thoughts. And God surely does express his fundamental reality in his thought (indeed, this is central to Augustine's Trinitarianism).

I want to try out a different response to the argument: question the last step in the argument, the inference "Hence God is not ineffable." This response allows that we can stipulate and assert a sentence that means the conjunction of all fundamental truths intrinsically about God, but denies that this is a problem for ineffability. Ineffability isn't a denial of the possibility of asserting a sentence whose semantic content is such-and-such truths about the divine nature. Rather, it is the denial of the possibility of linguistically communicating these truths. For me to linguistically communicate a truth to you it is required that my sentence give rise to your thinking that truth. But the truth expressed by "It divines" isn't a truth you can think. On this understanding, divine ineffability is an immediate consequence of divine incomprehensibility, and rather than being a doctrine about semantics, it's a doctrine about communication.

If this is right, then stipulation allows the semantics of our language to outrun communication and thought. You can think some deep philosophical truth that I don't know, and I can stipulate that "It xyzzes" means that truth, and I can sincerely assert "It xyzzes." But I don't thereby think that truth. I can, of course, think the second order thought that "It xyzzes" is true, but to do that is not the same as to think that it xyzzes. Similarly, I can think that "It divines" is true, but that's a thought about a piece of stipulated language rather than a thought about God. Indeed, it divines, but I don't understand the sentence "It divines" as I can't grasp the proposition it expresses.

Sometimes people are accused of a certain kind of insincerity like this: "You're just saying the words but don't really understand." This is a different kind of insincerity than when people are lying. A person who is "just saying the words" may believe that the sentence composed of the words is really true, and if so, then she isn't lying. (Corollary: One can say something one doesn't believe and yet not be a liar, as long as one believes that what one is saying is true.) The reason that there may be insincerity in "just saying the words" is that normally one implicates that one believes (and hence has a minimal understanding of) the content of what one says. But that's an implicature that can be canceled to avoid even this kind of insincerity: "I don't exactly know what 'God loves you' means, but I believe that it is true. God loves you." And when people are talking of a topic neither is close to being an expert on, the implicature of understanding one's words may be contextually canceled.

Mathematics and intellectual humility

The discipline where we have the greatest consensus of certainty is mathematics. Yet that discipline is also pretty close to being the one where we have least consensus as to what we're talking about. This should make us collectively humble.

Asserting what you don't grasp

Some people think that to assert a proposition you need to grasp it.

I think they are mistaken. Suppose my wife asks me: "Can you take the car to the garage to have xyz done to it?" I have no idea what "xyz" means. It's some complicated thing having to do with internal combustion engines. I ask her: "How long do you think it'll take them to do xyz?" She says: "It shouldn't take more than two or three hours." So I say: "OK, I'll have them do xyz." I take the car to the garage and ask them: "Could you do xyz to the car?" Two hours later they tell me: "We did xyz" and hand me a bill for $250. I call up my wife and say: "They did xyz and it cost $250."

I engaged in four speech acts where I used "xyz": a question to my wife about how long xyz takes, a promise to my wife to have xyz done, a request of the mechanic that xyz be done, and finally something that looks like an assertion that it cost $250 to have xyz done. Clearly, I asked my wife about how long xyz takes, I promised my wife to have xyz done and I requested of the mechanic that xyz be done. For it is under the supposition that I asked my wife how long xyz takes that her response that it takes an hour or two is salient, and plainly it is salient. That I promised to have them do xyz is also clear--if instead I ask them to change the oil (assuming xyz isn't in fact an oil change--the two to three hour time estimate suggests it's not), I haven't done what I promised, and I owe my wife an apology. And if I didn't ask the garage to do xyz, then they performed an unauthorized repair.

But if my apparent question, promise and request are what they seem, despite my lack of grasp of "xyz", surely the same should be said about my apparent assertion that they did xyz and it cost $250. Indeed, if instead I had the shop do an oil change, then I lied when I told my wife that they did xyz. But how could I have lied unless I asserted? Moreover, if I spoke sincerely but later a friend looked in the engine and told me: "They didn't do xyz!", then I should withdraw what I said to my wife. Again, the best explanation of why I should withdraw it is that it was an assertion that has since turned out to be incorrect.

Plurality of divine ideas

I've been suspicious of divine ideas, but now I like what St Thomas does in S. Th. I.15. St Thomas seems to be insisting that the sentence "There are many divine ideas" gets a semantics according to which it is made true not by some plurality in things, but by God's understanding himself in this way, and in that way, and so on, without these being separate acts of understanding. It is possible, I suspect, for an experienced physicist to understand light as a stream of particles and as a wave simultaneously and without there being two separate acts of understanding here. Likewise, then, God simultaneouosly, and without a multiplicity of acts of understanding, understands himself as something that can be participated in by a donkey, and as something that can be participated in by an oak tree, and as something that can be participated in by an angel, and he does this with a single indivisible (and the indivisibility may not be present in the physicist's case) act of understanding that suffices to make true all of these particular claims about what God understands. So the apparently quantified claim "There are many divine ideas" is made true by a single indivisible entity.

I see Aquinas' project here and in his discussion of the Trinity and the Incarnation as an attempt to provide a semantics compatible with divine simplicity for hard to avoid philosophical truths (this case) or orthodox theological doctrines (the other two cases). This semantics must make the right sentences true, and it must also be plausible.

Understanding a sentence

If you don't like centered propositions, drop the "centered" from the following. I am using the phrase "knowledgeably understand" to boost understanding to a level that requires the kinds of justification that knowledge does. Perhaps understanding already has that built-in, in which case "knowledgeably" can be dropped.

Now, consider the following inconsistent triad, each proposition of which is defensible:

1. To knowledgeably understand a sentence it suffices to know the language and to apply appropriate symbol recognition, symbol manipulation and logical skills to that sentence.
2. Necessarily, someone who knowledgeably understands a sentence knows what (centered) proposition that sentence expresses or else knows that the sentence does not express a (centered) proposition.
3. There are sentences s such that one cannot know whether s expresses a proposition simply by knowing the language, and by applying appropriate symbol recognition, symbol manipulation and logical skills to that sentence.

I think (1) and (2) are quite intuitively plausible, but (3) needs an argument. Here is a standard argument (Kripke came up with cases like this). I erase my board and write on it "No sentence on Jon's board expresses a true (centered) proposition." Let s be this sentence. Then I cannot know whether s express a (centered) proposition unless I know what Jon has on his board. For Jon, being a philosopher, might easily have written on his board "Every sentence on Alex's board expresses a true (centered) proposition." But if that is what is on his board, then the sentence on my board cannot express a (centered) proposition. (If it expresses a true (centered) proposition p, then plainly p is true if and only if p is not true.) But I cannot know what Jon has on his board simply by knowing the language and applying symbolic and logical skills to the sentence on my board. Hence, (3) is true.

Given the above really good argument for (3), we need to reject (1) or (2). I am inclined to reject (1), as (2) seems very, very plausible. Or, perhaps better yet, we might reject the notion of sentences that the paradox is predicated on.

Actually, everybody should reject (1) in the case of natural languages, simply because of the problems of homonymy, and that's not very interesting. But the argument against (1) (assuming the notion of sentences that the paradox is based on) continues to work even if we distinguish homonyms with subscripts, and similarly deal with other "standard" contextual ambiguities.

Intention and understanding

George, who is quite happy thinking that he has just aced his logic exam (actually, he failed miserably) sees a first-order logic proposition on a board:

1. (x)(~toothache(x) → ~(x = George))).

On a whim, he desires that this be the case. He rubs a lamp, the genie appears and George says to the genie: "Make it be the case that (x)(~toothache(x) → ~(x = George)))." To George's surprise, he immediately gets a toothache. The surprise isn't at the fulfillment of the wish—he fully expected the wish to be fulfilled—but at the toothache, since George did not see that (1) is logically equivalent to:

2. toothache(George).

Did George get what he intended? Well, yes: he wanted (1) to be true, and the genie did make (1) be true. But while George got what he intended, he also got a toothache, which he clearly did not intend to get. Thus, one can intend (1) without intending (2). Intention cuts more finely than logical equivalence.

Suppose George were better at logic, so it was obvious to him that (1) and (2) are equivalent? Could he intend (1) without intending (2)? I am inclined to answer affirmatively. Belief does not automatically affect intentions—intentions are a matter of the will, not of the intellect. Of course, if he were better at logic, the toothache would not be a surprise.

Once we admit that intentions can cut this finely, we have to be really careful with Double Effect, lest we end up justifying the unjustifiable. We don't want to allow Janine to get away with murder by saying that she asked the genie to bring it about that either Fred is dead or 2+2=5, and so she never intended Fred to be dead. My way of doing that is to introduce the notion of accomplishment. As long as George intended (1), whether or not he knew that (1) entailed (2), George accomplished his toothache: the toothache was a part of the accomplishment of the action. As long as Janine intended the disjunction, the disjunct (or, more precisely, the truthmaker of the disjunct) which she (through the genie) accomplished is a part of her accomplishment.

Love of truth

You are a philosophical researcher who has concluded that the only four metaethical positions that have any serious plausibility are nihilism, Natural Law, Kantianism and utilitarianism. You plan to devote the rest of your life to figuring out which of these four theories is correct. But God speaks to you—and you know it's God speaking—and makes you an offer. First he tells you that you're right that the correct metaethical theory is one of the four you listed. But you must now choose between two options:

1. You continue on your career as before, and God makes no guarantee whether you'll come to an answer, and whether, should you come to an answer, the answer will be correct.
2. God will tell you which of the four theories is true, and will do so in such a way that you will know that it is God speaking, but the price you will have to pay is that you will lose the creative abilities that are necessary for good philosophical research. Nonetheless, God promises to ensure you will still be able to teach philosophy in a way that is just as beneficial to students and both renumerative and satisfying to yourself.

Never mind the epistemological question of how you know it's God speaking and how you will know the answer is from God. What should you do?

On the face of it, this is a question whether you love truth more than the search for truth, and my own gut reaction to a question like this is to say: "I want to know the truth, and I don't care about the means by which I get it (except insofar as I am a sinful and vain man, who wants to get it by his own power, but this sinful desire is one that I do not endorse)."

But this gut reaction is simplistic. Aquinas distinguishes faith from science (which includes philosophy, of course, in his terminology) as follows: faith gives one certainty of the truth, but science also gives one understanding of why something is so. Faith ensures that we know with greater certainty that God is a Trinity than we know that the planets move in approximately elliptical orbits; but while our knowledge that God is a Trinity is more certain, we have better understanding of the ellipticity of the orbits—we can say something about why the orbits are elliptical (something about the curvature of space or the law of gravitation). There are pluses and minuses of knowing by faith versus knowing by science: certainty versus understanding.

In choosing option (1), one may never get the right answer; however, one may also get the right answer plus an understanding of why it is the right answer. Option (2) gives one a certainty of knowing the right answer, but it is less likely that one will know why it is the right answer, because one will have lost the creative abilities needed to find that out. It seems, then, that there are incommensurable goods involved in the two options. It may be that both choices are rational.

But suppose now that the offer is different. Option (1) is as before. But in the case of option (2), God will not take away one's philosophical abilities—one will still be free to try to find out why the given metaethical theory is true. While one might worry that knowing the answer ahead of time will make one less good at figuring out the why question (e.g., more apt to glibly accept arguments for the answer one already knows is right), this does not seem to me to be a compelling worry. Barring that worry, it seems that the modified version of option (2) is what one should choose. To fail to opt for option (2) is likely to care more about searching for truth than about having truth, and that, I think, is to have one's priorities backwards.

If this is right, then likewise those philosophers who also know various doctrines by faith need not be shy about making use of this knowledge, about drawing out the entailments of this knowledge. I might work dozens of years trying to figure out if there is such a thing as substance, and fail. But significantly less effort might yield the conclusion that there is substance based on the my knowledge that transsubstantiation occurs (even there, some non-trivial philosophical work is needed to rule out non-substantival accounts of transsubstantiation). And to fail to make use of that knowledge, and instead to search for years, could be a case of loving philosophy more than truth. Of course some will dispute whether we have knowledge by revelation. Here I take my stance by faith: I believe (on the authority of the First Vatican Council, for instance) that faith yields knowledge and proper certainty. (I also have some philosophical stories about how this might happen.)