Rationalism Precludes Theism

I just had a long Facebook discussion about what it would take for a rationalist to believe in god.  I raised the question because the better we know exactly what sort of evidence would be required for rational theism, the more justified we are in not being theists.  It turned out to be very difficult to imagine what evidence would suffice.  In the end, I was able to prove that there are no conditions under which it would be rational to believe in god.  This surprised me, so I thought I’d share my argument.

I'll start with bunnies. One person said they’d believe in god given fossil evidence of Cambrian rabbits.  That seemed pretty weak to me at first, but I thought I should at least think it through.  I'm imagining that tomorrow morning I wake up to coffee and NPR, and find that the main story of the day is a claim that archeologists uncovered fossils from the Cambrian. My first thought is, "Simple mistake. Someone misrepresented information, got confused, fabricated evidence, etc." I do some research. It probably is a simple mistake. But suppose it isn't. Next, I think, "Earthquake anomaly." That seems pretty likely. More research. Along these lines, I entertain increasingly unlikely hypotheses (in careful order). "God did it" is nowhere near the beginning of the list. Part of that is because I'm not sure what it means, but I'll get back to that. I'd be getting near the neighborhood of god territory about the time I started hypothesizing that Earth is an alien science fair project and the rabbit fossil is left over from a test run that got a little messy and wasn't cleaned up all the way. That would indeed involve an intelligent creator of the human race, but it's quite a long way from, say, omnipotence, omniscience, omnipresence, and omnibenevolence.

The first problem with imagining sufficient evidence for belief in god is this: There are a whole lot of things we could mean when we say "god exists".  Not all of them are equally likely. Nor does one kind of evidence justify belief in all of them. "God" is fuzzy. Much like bunnies. It's semantically ambiguous and vague.  So if we want to know what it would take to reasonably believe in god, we’re going to have to figure out what it would take to reasonably believe in a pretty diverse range of entities individually.

That's one of the most frustrating things about talking with theists; they're quick to tell you what they don't mean once they've determined you're arguing for a god in whom they don't believe either, but they usually aren't so quick to pin down what they really do mean. When you try to reason with a theist, therefore, it’s a good idea to ask them explicitly what they mean by god even before you tell them that he doesn’t exist.  With many you get the impression that they themselves don't know that they mean. You'll talk with them for a long while, thinking you're getting somewhere, and then when you bring them to a conclusion they don't like but can't avoid, they say, "Well sure, but that's not what I mean by 'god'. What if god is really x?"

Legend has it that Paul Spade was once teaching a seminar on the philosophy of theology when someone pulled one of these. Another student gave an exasperated sigh, turned to the first student, and remarked, "Look, what if god is a garage in New Jersey?"

This succinctly expresses a rationalist’s frustrations with fuzzy notions of god, but let’s see what happens when we take the question seriously.  If god is a garage in New Jersey, convincing me of his existence is a fairly simple matter. I already have an awful lot of good reasons to think that there are garages in New Jersey, so showing me a picture of the particular one you're talking about would be plenty.  But this form of theism is neither interesting nor useful.  I really hope conceptions of god never get so boring as to be confined to garages in New Jersey.

So now let’s look at the somewhat more serious kinds of gods who are merely responsible for purposefully creating humans.  In light of the many observations about the universe we've so far made and systematically evaluated through science, it is tremendously unlikely that the human race was intelligently created.  Finding rabbit fossils would indeed be evidence for intelligent creation, because the probability of intelligent creation would be slightly higher after throwing large chunks of our model of biology into doubt.  But it's horribly weak evidence, especially relative to its strength for alternative hypotheses that are far more in line with the vast majority of what we've so far observed. It would be utterly irrational to believe even in the very weak meanings of god on the basis of Cambrian rabbits.  (Obviously, this isn’t evidence at all for garage-gods, since garages are equally likely to exist whether or not there were rabbits in the Cambrian.)

If god is simply any conscious thing that purposefully created the human race, then here is an example of what would convince me. A very long-lived alien could land on Earth, show us the blueprints, and explain how it did it and why. Well, that wouldn't quite be enough, because the alien could be lying. (I mean, come on, you're a brilliant alien who's run into an extremely credulous species that likes to worship even evil gods. Honesty, or godhood? I could see lying.) But if we took those blueprints, showed that they account for all pre-existing observations, and made some predictions based on them whose truth would be in direct contradiction with our current model, then we could test those predictions and the right results would convince me that we were in fact created intelligently by this alien. Which, by that definition, would mean I'd become a theist.

But for meanings of god that are bigger than this (for instance, a being that is omnipotent), I run into the following problem. It is much, much more likely that there exists a being who is capable of causing me to experience whatever it chooses, regardless of what's actually going on outside of my head, than it is that there's a being who really does possess such properties as omnipotence and omniscience. Why?  Because of conjunction. 

For any events x and y, the odds of x happening cannot be greater than the odds of x and y happening.  To figure out the base probability that x and y both happen, you multiply the odds of x by the odds of y.  Odds are expressed as percentages or fractions, so you’re multiplying something less than one by something less than one, which makes the product even smaller than either factor. 

It would take a definite, finite amount of power and/or knowledge to appear infinitely powerful or knowledgeable.  There’s a certain set of things you’d have to know or be able to do in order, say, to run a computer simulation of a lifetime’s worth of human experience.  There is probably a very large number of things you’d have to do, and many of them may be awfully improbable, but because the set isn’t infinite, the probability isn’t infinitesimal (provided the set is well founded—that is, no item on the list requires that you be able to do all the things on the list).

A being with those powers could cause me to experience what I would ordinarily take to be evidence of extraordinary things. There is a certain degree of extraordinaryness beyond which it becomes less likely that the thing I’m experiencing is actually happening than that someone is purposefully monkeying with my subjectivity. For instance, perhaps I am actually a program running on the hard drive of some human’s computer from the future.  Perhaps the future human is amused by the game of creating consciousnesses solely for the purpose of messing with them. That would have to be sort of an evil person, but I must admit it's exactly my kind of evil.

But is a creature with the power to create such a simulation rightly called a god? If so, then any experience (or group of experiences) beyond the subjectivity-monkeying threshold would make me a theist. But this god is infinitely less powerful than an omnipotent god, so again, that's a long way from the god most theists seem to believe in.  They want a god who can do anything.

I'd planned to claim next that only an a priori proof for any god less likely than the monkeying version would do, but it now occurs to me that even that would be insufficient  With a slight modification, the monkeying-god becomes Plato's evil demon.  

Plato described a demon whose only purpose in life is to make us miscount the number of sides on a triangle.  It could be that there are not actually three sides to a triangle, provided that every time we try to count the sides of a triangle, we make a mistake.  This problem is bigger than triangles.  If the monkeying god can control every aspect of my subjectivity by changing lines of computer code, he could cause me to reason incorrectly about even an apparently iron-clad mathematical proof.  And this, too, would be much more likely than anything even close to the god(s) of the theists.

Note, by the way, that even the first version of the monkeying god isn't necessary for experiences of direct revelation. If an experience could possibly be caused by a malfunctioning (or strangely functioning) human brain, it's not sufficient evidence for theism. Simple hallucination happens all the time. I came up with the monkeying god to account for experience that couldn't be pathological. Here's an example of the kind of experience I'm talking about (adapted from a splendid scene by Eliezer Yudkowsky in Harry Potter and theMethods of Rationality).

You hand a very large list of prime numbers to a friend and tell him to select two four digit prime numbers (without telling you what they are) and write down their product. He returns a paper on which is written "16285467". You walk outside directly afterward, grab a shovel, pick a random chunk of ground, and start digging. Five feet down, you hit a rock. Upon examining the rock, you find that it contains fossilized crinoid stems on the surface (and may or may not contain a rabbit in the middle, presumably from the Paleozoic this time). On one side, the crinoid stems are configured to write out "2213". On the other side, the crinoid stems say "7359".  Actually imagine that this has happened, and imagine how you would react.  “I must be hallucinating” probably wouldn’t satisfy you, for you lack the ability to factor eight digit numbers in your head.

Now, this isn't a perfect example, because it wouldn't be impossible to hallucinate this of your own accord. But it would indeed be incredibly unlikely (literally), far more so than anything people experience when they claim to communicate directly with god.  I'm not sure whether it would be more likely that an external agent is messing with your mind than that you happened to hallucinate it accidentally.  Or that you're actually that damn good at prime factorization.  Or that you multiplied every set of pairs of four digit numbers with one member less than half of 16285467 without noticeably aging and then promptly forgot about it.  But if it happened several times in a row, or many similar things happened, at some point the pathology position becomes untenable and it's time for the monkeying god hypothesis to step in.

Therefore, it's never rational to believe in an Allah or New-Testament-style god, because whatever your reason for suspecting that god is responsible, it’s more likely one of the less powerful versions of a god is the cause.  

I'd originally intended to figure out exactly what it would take to convince me of the existence of something like the Catholic god, but it appears this really is a special case.  Even if god does exist, there simply are no conditions under which it's rational to believe in him (unless you're willing to give the name god to something more like a garage in New Jersey).

Testing Is Bad

My father is a high school science teacher in the US.  Today he was feeling a bit overwhelmed by work, so I helped him grade tests from Bio 1, an introductory biology course for kids in their 9^th or 10^th years.  It’s early in the course, so they haven’t moved on yet from attempts to make sure everyone’s familiar with very basic and central notions that they should have learned in earlier years but likely didn’t.  I only graded fill-in-the-blank and definition type questions—no essays or short answers that would require significant interpretation.  I’ve never met the kids in the class, and since I only graded page two of the tests I didn’t even see their names.  Neither is this a common occurrence: I believe I’ve helped Dad with grading one other time in my whole life.  Just in case some readers wanted those disclaimers.  Anyway.

It was an enlightening experience.  It was very clear that the vast majority of the students were far more focused on exploiting the system during class and homework than on understanding the material at hand.  They were trying to learn what they needed to pass the test, and didn't feel at all that the test is merely evidence of what they've so far understood or failed to understand.  Their whole purpose as students is to pass the test.  

This is how I ended up grading one test on which the student defined "element" as "part of an atom which makes up an element".  I thought for a long time about what would have to happen in a child’s head for him to give an answer like this on a test.  When I was in high school myself, I never thought very hard about the minds of other students, and assumed people did poorly in school because they are stupid and lazy.  But now, I see that something else is going on here, something caused not by the stupidity or laziness of individual students but by a grave systemic flaw in US education.

There are two correct answers in this context to "define element".  The first is something along the lines of, "something without parts" (Dad often teaches via the history of science, so this would come from the ancient Greek notion), and the second is, "a substance made up entirely of one kind of atom".  I took Dad’s intro chemistry class way back when, and I remember his wording.

Here is the real problem.  It is threefold.  First, the students don't understand the goal of their lessons—they don’t know how to know what the teacher wants them to understand.  Second, they don’t know how to assess the content and level of their current understanding—they don't know how to know what they don't understand.  These combine to create the third part of the problem: they cannot identify the gap between what they don’t know and what they’re meant to know, so they can’t focus their academic efforts on closing it.  

As it stands, high school students know what tests tend to look like and how to streamline the process of passing them.  They are rewarded for good performance and punished for poor performance, and no one has ever tried to explain to them the internal mechanisms of learning beyond that.  The reason they run into such huge problems with Dad's classes in particular is that his tests require a great deal more understanding as a prerequisite for good performance than do the tests they’ve encountered previously.  

The kind of test you write if you don’t want to spend much time grading—that is, understanding the minds of individual students—is the same kind of test you pass by knowing how to take tests.  An expert at test taking can pass a test over very difficult material without actually understanding the material provided the test is written in a way that allows them to exercise their expertise.  This is how I got a B+ on a college level psychology final last year without ever going to class or studying.  There were many things on that test whose answers I didn't really know, and sometimes I didn’t fully comprehend the question itself, but I could deduce what would be counted as correct in most cases because I know how to take tests.  Multiple choice, for instance, hardly ever requires understanding in most contexts.  It only requires memorization of associated sets of terms.  It’s a skillset that takes a long time to develop, but nine or ten years is plenty long.

So the poor kid did exactly what he’d been conditioned over the course of a decade to do.  He threw together "part", "made up", "atom", and "element" into a grammatically well-formed sentence, and didn’t even notice that it was totally nonsensical.  It didn't occur to him to actually try to understand what "element" means.  

And why would he?  Imagine that you aren’t simply trying to be efficient so you can spend your time on other things that are more obviously worthwhile, which is itself understandable.  Imagine that experience has shown that you aren’t smart enough to understand complicated things even when you try.  This is a pet theory you pulled together after failing tests repeatedly early on.  It makes a lot of sense to spend what cognitive resources you know you do have on exploiting the rules of the system, getting by without anyone suspecting that you’re failing to learn (including yourself) and without being punished for your failure.  Your teachers believe that a good grade means you’ve learned, and you believe your teachers.  Because you’ve been doing this for as long as you can remember, you don’t even recognize anymore that there’s another way.  

This kid gave an answer that evidenced an almost total lack of understanding of anything that had happened in his biology class up to that point, but it's not because he’s dumb, and it's not because he isn't trying to succeed.  He definitely would have had to have studied to give that particular answer.  He's failing to learn because tests have taught him not to learn.

What if instead of doling out rewards and punishments in the forms of grades for being able to answer correctly on tests, we taught kids how to assess their own understanding?  What if we taught them that the first priority is to figure out what it is the teacher wants you to understand, the second is to figure out in what way and to what extent you currently understand it, and finally that the entire purpose of all of this class time and work and testing is to figure out how to close the gap between those two things?  There's no way anyone would be content with a nonsensical answer.  They’d have written what they did understand about the meaning of "element".

A few students seem to have done something similar: they defined element as something like, "all the things on the periodic table".  This is what I'd expect from kids who didn't know how to know what they were meant to understand, but did know what they understood.  They knew that they knew that the things on the periodic table are called "elements".  They knew that they knew what a definition is.  They failed to give a correct definition because they didn't know what they were meant to understand.

Here is an answer I would expect from someone who knows how to know what he's meant to understand, knows how to know what he currently understands, but hasn't quite completed the process of closing the gap.  "An element is a very tiny thing that builds bigger things and takes part in chemical reactions."  A kid who answered this way would have genuinely been learning about atoms, but wouldn't have finished refining his notion: he'd have yet to precisify his understanding enough to distinguish between elements and molecules.  

Not a single student gave this kind of answer.  In fact, I don't think anyone gave this kind of answer to any of the questions.  This suggests that even the kids who are getting the answers right probably don't actually understand the things the understanding of which the test is meant to assess.

People like me, people who love learning so much that they aspire to be professional academics, learn in spite of tests.  In most cases, we grew up believing ourselves to be so much smarter than everyone around us that we were always confident that if someone else was meant to understand, we sure as hell were going to understand as well.  We had confidence in our ability to learn better and faster than required, expected, or maybe imagined.  When faced with the prospect of a test that presented any sort of challenge, we stepped up our efforts, because we knew it would pay off.  By contrast, many students have little confidence not because of low ability but because of learned helplessness.  We did learn to exploit the system because often we just weren't interested in the material, but we never had to deal with a feeling of doubt about our abilities or intellectual worth. 

I think that not only have most people never been taught to apply what intelligence they possess, but they've been taught specifically to behave less intelligently than they would if left to their own devices.  They've thrown in the towel, they're flying blind, and the best they can do is to try to exploit the system, and to pray.

For a boatload of unequivocal empirical evidence that conventional testing is harmful, checkout this ginormous meta-study by Paul Black and Dylan William.  If you’re convinced and want to know what to do about it, I suggest reading up on formative assessment, a good overview of which by D. Sadler can be found here.

Proposal for a Course in Which Students Invent Science

Part One: Multiplayer Mode

Every class begins with problem solving.  The question posed in the most recent assignment is written on the board.  The students, as a class, must solve it.  No one is allowed to give an actual answer to the question until a quorum has agreed on the best way to solve the problem, then executed the plan and interpreted the results.  The teacher can participate in the problem solving by posing leading questions, encouraging certain directions of thought, and suggesting that they try using tools they already have, but for the most part the students run this part of the show.  There are two main goals here: to develop their scientific toolboxes, and to encounter the inherent bugs of human minds (cognitive biases) so they can learn to recognize and patch them, thus solving problems more efficiently in the future.  Questions early in the course will emphasize revealing biases, and the later problems will emphasize empirical methods of inquiry and testing.  Overall, we’re working toward inventing something like Bayes theorem or another broad philosophy of science.

Part Two: The Meta-quest

After the question is answered, the lecture begins.  The teacher recaps everything that just happened, pointing out which things worked and which didn’t.  The methods and biases involved are given short and simple names the students can remember, like “testable hypothesis” and “availability heuristic”.  This serves as an outline for the lecture.  Lecture materials for the next several weeks should be assembled beforehand to allow for maximum flexibility in presentation order.  The lecture explicitly covers only those methods discovered by the students, showing how they’ve been used historically and how they’ve improved overtime.  (There is a little leeway here for closely related methods that are particularly difficult to discover in a class setting.)  When biases are identified, the lecture includes descriptions of studies and/or anecdotes evidencing or pinpointing the bias, a discussion (perhaps with class participation) of why we tend to think in that particular way, how we can notice when it presents an immediate danger to reasoning, and how to cope when it does.

Part Three: Personal Quests

An assignment is given at the end of every class: the students learn what question they’ll be answering the next day, and must come up with a plan for finding the answer.  These competing methods will duke it out in class debate the next day.  They must also propose problems whose solutions could be found by methods learned in class, which can be hypothetical or drawn from their lives or stories they’ve heard.

Part Four: Leveling Up

Tests will be given periodically, but their frequency will depend on how much has been discovered how quickly.  They will include simple questions about the material covered in the lectures, and a problem that can be solved only by using several if not all of the tools acquired since the last test.

Part Five: Winning the Game

The final will be cumulative.  There will be an in-class portion that is similar to the basic question and answer portions of previous tests.  The take-home portion of the test will have two parts.  The students have a choice on the first part.  They can either choose to answer one particularly difficult question, or they can answer three easier questions.  They must write an essay explaining how they went about solving the problem and why.  For the second part of the test, they must propose and defend a definition of Science.

*******************

What I'd really like to see in the comments here is a brainstorming session in which we generate a whole bunch of useful project ideas for a class like this.  In particular I'd like to focus on things geared toward 8th graders, but other thoughts are also welcome.

In Defense Of Semantics, Or: Until You Can Say What You Mean, You Cannot Mean What You Say

Semantics matters.  In a debate, it is all that matters.  What matters when you’re talking with someone is what you mean by what you say, and what the other person takes you to mean by it.  That’s what communication is.  If I could just project my thoughts into your head all at once, my choice of words and the order in which I arrange them wouldn’t matter.  Words wouldn’t matter.  But I’m not a dolphin, so I have to use language if I want to communicate.

Language is a social behavior in which symbols such as sounds or gestures are agreed by participants to denote entities in the world.  The symbols are arranged according to structural guidelines of temporal progression to denote larger concepts in an organized way.  Thus, an image of a concept is projected from the mind of the speaker into the world for listeners to observe and replicate in their own minds.  This process is called communication.

The success of the project of language depends on two things: syntax and semantics.  Syntax, the rules by which symbols are organized to denote more complex concepts, is ultimately a servant of semantics.  It allows for the communication of thoughts far deeper and more intricate than the mere vocabluary.  But it has no purpose whatsoever in the absence of semantics.

In natural language, “semantics” is a set of correspondences, some between symbols and the things they denote, and others among entire sentences.  For instance, the relationship between the sentences “math is exciting and challenging” and “math is challenging” is one of semantic entailment, because the meaning of one entails the meaning of the other.  Suppose I formulate the following sentence and speak it aloud: “Oma cabeca djorglesnuff.”  Even if you know all the rules of the syntax I’m employing, my utterance will be completely useless as communication until I explain somehow that by “oma” I mean “cats”, by “cabeca” i mean “eat”, and by “djorglesnuff” I mean “mice”.  Only then can you understand what I’m trying to say, and respond with something equally meaningful that moves the discussion forward.  You can identify my declarative sentence as a specific claim.  “My oma,” you might say to me, “does not cabecca djorglesnuff.  I think you’re wrong to say they do.”

And here we’re at a point where the two of us might start “arguing semantics”, because the next thing I say is, “I didn’t mean that all oma cabecca djorglesnuff.  I only meant that some oma cabecca djorglesnuff.”  “Ah,” you say to me, “then you’re correct, but you should have specified that when you were explaining what you meant by ‘oma cabecca djorglesnuff’ in the first place.”  And you are perfectly right to call me out on that.

Why?  Because the sentence “some cats eat mice” entails the truth of different sentences than does “all cats eat mice”, and if I didn’t provide you with the tools to determine which sentences my utterances entail, then my words haven’t sufficiently meant and I’ve done a poor job of communicating.  

Consider the following conversation.

A: God exists.

B: No he doesn’t.

A: Yes he does, and I can support my claim.  Behold!

A holds up a spoon.

B: What does that have to do with God?

A: It is God.  See?  It exists.  God exists.

B: You think that God is a spoon?

A: Well... yeah.  That’s what I meant by “God”.  You’re not going to argue mere semantics with me are you?

B: You bet your boots I am.

The above two cases are perfectly legitimate grounds for substantial semantic disputes.  In both cases, one party has done a poor job of communicating, and the other rightly asked for more careful formulations of what is to be projected through language.  In the first case, the failure was a matter of ambiguity.  There were multiple propositions the speaker might have intended to convey, the distinction between the possible propositions was significant, and thus the misunderstanding was not the fault of the listener.  What the speaker actually said did mean something, but it didn’t mean as much as it should have.  What it meant was not precise enough for the purposes of the discussion at hand.  He did not mean what he said, because he did not say what he meant.

In the second case, the speaker meant by his words something outside of the standard, agreed-upon set of entities that might be denoted by them.  The reason the word “God” is mostly useless in discussions with people who are used to attending to fine conceptual distinctions is that the standard set of notions to which God might be taken to refer is very large and poorly defined; not only is there ambiguity, there is vagueness.  But in the case of a spoon, using the term “God” causes more confusion than usually comes with even that word.  The speaker did not mean what he said, because he did not say what he meant.  If A were to say “God exists,” and B were to say, “I think so too” but take “God” to mean “a porcupine”, the listener would also be making the same kind of mistake.

So you see, the more accurate and careful we are with our language, the more intricate, interesting, and useful will be our communications, and the more worthwhile will be our debates.  Clarity matters.  Precision matters.  Sensitivity to semantic distinctions is a valuable skill, as is the diligence to attend to them.  When philosophers argue semantics with you, the purpose is neither to annoy you nor to show off.  It’s to actually get somewhere with the conversation.  If we’re asking for precision and clarity, we’re doing so because we excel at identifying problems that derive from a lack of these, problems that would lead to frustrating, tiresome spirals of self-perpetuating confusion.  

There are important things to learn from people who shatter your semantic endeavors and ask you to rebuild them from the shards.  Developing the patience to face down the linguistic challenges of philosophers will lead you to wield language that is sharp and strong as the edge of a samurai blade.  And if you choose instead to dismiss such attempts at careful communication as tiresome nitpicking, do not meddle in the affairs of philosophers, nor seek what they have sought.  

If you’re too lazy to say what you mean, how are you ever to mean what you say?  And why should I believe that you do?

Who does Kant think he is?

Kant lays out his theory of apperception in “Of the Deduction of the Pure Conceptions of the Understanding”.  He does so in his usual style, which, as is widely known, includes a great deal of obfuscation, repetition, and tedious verbosity.  

A diligent and patient reader with some philosophy background and a good translation will discover, eventually, that the vast majority of the notions he means to convey in The Critique are remarkably simplistic and powerful.  I find it most unfortunate that his style has made the volume inaccessible to nearly everyone.

Below, I have attempted to render, paragraph by paragraph, Kant’s passages on apperception accessible to anyone who can handle the New York Times.  This task became much more difficult toward the end of the section on apperception, but I think it’s an important project.  There is certainly room for improvement in places, but I envision a collaborative effort to convert all of the Critique to simple English, so I intend for this to be more of a seed than a final proclamation on how best to convey these concepts.

My simple English paraphrases appear italicized, and my further explanations follow in regular font.  The paragraph numbered 1.1 corresponds to the first paragraph of the first topic in section II of chapter II, 3.2 to the second paragraph of the third topic, etc.  Without further delay, I give you the first installment of “Kant in Simple English”.

1.1

To combine a bunch of separate experiences into a single concept, there must be something outside of the experiences performing the combination.

When Kant writes “manifold content”, he’s referring to the stream of information constituting experience over time.  When we form concepts, we combine pieces of information gathered over some period of time.  It may be a short period, as when we listen to a sentence that takes two seconds to speak; or it may be a very long period, as when we come to understand what “Italian food”, as a whole, tastes like by ordering several different Italian dishes over the course of a few months or years.  Each experience is separated by time from all the other experiences.  There is nothing about the taste of garlic bread on October third that suggests it should have something to do with the smell of alfredo sauce on February second.  The relationship among experiences is not contained in the experiences themselves.  Instead, it is imposed on them artificially by something outside the experiences—by  us.

Kant calls the ability to gather diverse experiences into larger concepts “understanding”, and the gathering itself he calls “synthesis”.  The understanding can gather (or synthesize) not only experiences, but also concepts.  We might form the concept “three” by gathering together many experiences in which we sensed that number of sounds or sights, but we might also form the more abstract concept “number” by gathering together the concepts of one, two, three, four, etc.  All synthesis, writes Kant, is an act of the understanding.

1.2

“Combination” involves three things: 1)the concept of a bunch of separate things, 2) the concept of the action of gathering all those things together, and 3)the concept of unity—that the result of this process is a single whole.  (I don’t mean the category I’ve been calling “unity”; the concept of a category requires the concept of combination, so that would be circular.  This kind of unity is something more abstract still.)

Since the concept of “unity” must exist for there to be combination (or “conjunction”) in the first place, unity can’t come from combination itself.  The whole-ness of unified things must be a product of something beyond combination.

2.1

Inasmuch as my sensations are specifically my sensations, they presuppose the thing I call “me”; thus the act of sensing and the ability to sense also presuppose me.  Self-awareness cannot arise entirely from any of these things, because it is awareness of something presupposed by all of them.

All of my sensations and such presuppose exactly the same me.  

The only thing that my experiences have in common is that there is a subject who experiences all of them.  That doesn’t mean the experiencer is somehow embedded in its experiences—it is no part of the taste of garlic bread—but instead that there is a relationship that holds between the subject and its experiences.  When I reflect on this fact, I perceive unity of the subject across all of the experiences; it’s the same subject every time.  Moreover, it’s the same subject experiencing the reflection on the subject of experiences!  I call that unitary subject “me” (Kant calls it “apperception”).  

2.2

It’s interesting that there is sameness of the me presupposed by all those different sensations; the me who experiences sensations participates in of lots of different acts of experiencing, and there’s not anything about any one of those acts that ties it directly to the others.  Self-awareness is needed to combine all of these actions into a single concept of “me”.  So, for me to exist as an identity among experiences, I must be self-aware.

My awareness of myself is why my experiences can all be gathered together under the heading “my experiences”.  Without the unity in the combination described by that heading, there would be nothing tying all those experiences together; there might as well be a different experiencer for each experience.  They are, after all, each separated by time.  Since I am exactly the thing that experiences all of my experiences, the lack of unity would preclude my existence.  Unity, you’ll recall, can’t be a product simply of combination, so the combination of all those subjects does not itself account for selfhood.  There must be something above the experience/experiencer relation that makes the combination across times possible.  The self can’t exist without self-awareness (apperception).

2.3

Remember all that stuff I just said about unity and self-awareness?  Good.  It was important.

This paragraph is mostly repetition and emphasis of the concepts in the previous two paragraphs.

3.1

Earlier in this book, I talked about some other conditions presupposed by experience.  Specifically, I said that the kind of thing we usually count as “experience” can’t exist without Space and Time.  Those are both forms of what I called “sensibility”.

Self-awareness is another condition for experience just like Space and Time, but it involves the mind (or “understanding”) instead of sensibility.

Here, Kant is drawing a parallel between these passages on apperception and those on the transcendental aesthetic from earlier on.  He is also enumerating the conditions he’s so far determined are necessary for experience: space, time, and self-awareness.

3.2

A judgment about the relationship of a group of sensations to the particular object that caused those sensations is called a cognition.  The grouping of various sensations must be done by the self I’ve been talking about, because grouping is a kind of unity, and unity comes from self-awareness.  The relationship between sensations and objects is the objective validity of cognitions, so a self is required for there to be objective truth, cognitions, or anything else that goes on in minds (or “the understanding”).

When I see an aardvark in front of me and I judge it to be true that, “The thing in front of me is an aardvark,” what I’m really claiming is, “The object that caused the sensations that I grouped together into the concept ‘aardvark’ really is an aardvark, objectively speaking.”  It’s a claim about the relationship between the concept formed by my understanding and the object outside of my understanding (specifically in sensibility).  Because concepts are formed through combinations, combinations require unity, and unity is a product of self-awareness, the whole notion of objective truth would be meaningless without selfhood.

3.3

That the self is the same self across all experiences is a prerequisite for there being a mind.

This is already clear from 3.2 and earlier paragraphs.  Unity is a product of self-awareness; since unity is a product of self-awareness, everything that depends on unity also depends on the self.  The main jobs of a mind (or “the understanding”) are to form concepts and make judgments about them.  To make judgments about concepts, you first need concepts.  To form concepts, you first need to combine sensations.  Combination requires unity.  Unity requires self-awareness.  Therefore, the mind depends on self-awareness.

3.4

Read 2.2 again.  I really like what I said there.

3.5

I’m not saying that there’s a particular act of combining that must happen for there to be a mind; only that the mind must be able to combine things, and that the unity of the self is what makes that possible.

We wouldn’t even be able to conceive of a mind without self-awareness to ground it.

4

Objective unity of selfhood is different from subjective unity of selfhood.  Objective unity is the gathering up of all the different bits of self scattered across experiences into a whole.  Subjective unity is the ability of the little bits of self to be gathered up like that.  It’s necessary that the self is objectively unified, but it just so happens that it’s also subjectively unified.

Objective unity can exist if and only if there is subjective unity.  Objective unity is one of the prerequisites for experience, and that is true regardless of whether or not there really is experience.  That there is experience, however, is not logically necessary.