Is it Maps All the Way Down?

Is it Maps All the Way Down? April 15, 2012

Yesterday, I went to the Dominican House of Studies for a symposium on Creation and Modern Science, and one of the speakers was Edward Feser, author of The Last Superstition (the book that got me started exploring Aquinas and hanging out with the DC Dominicans).  His lecture was on the immaterial nature of thought, and there’s one facet of it I’d like to highlight here.

Feser was talking about the distinction between concepts and phantasms.  As briefly as possible (i.e. blame me, not Feser, if I’m oversimplifying):

A phantasm is an instantiation of a concept.  It’s a particular triangle, or a specific group of trees.  It doesn’t have to be a picture of something that exists — you can have a phantasm of a unicorn.

A concept is clear and distinct.  A concept of a triangle isn’t isoceles, equilateral, or scalene because you’re not picturing any specific triangle — you’re just understanding what the nature of a triangle is.

One good example Feser gave: you can have a concept of a chiliagon (a figure with 1000) sides, and that concept will be clearly distinct from a circle, or a figure with 1001 sides.  But your phantasm of a chiliagon will ‘look’ the same as a figure with 999 sides or a circle.  Your phantasms aren’t granular or clear enough to hit these details, but your concepts encompass all scales.

I’ve been thinking a lot about map-territory problems lately, so I was really interested in this thread of his argument.  What I wanted to know was how we could be sure we were differentiating correctly between phantasms and concepts in the first place.  If I tell you that I have a clear and distinct idea of a circle: that it’s a set of points at a fixed distance from one point, it certainly doesn’t sound like I’ve got a tangled-up-in-specificity-and-concreteness phantasm.

But several years of chemistry classes have taught me to be suspicious when I think I’ve finally drilled down to Truth.  You see, in the first chem class I took, we learned about the orbitals electrons occupied in atoms.  We learned about electrons as mini-moons, orbiting the nucleus.  When we took AP Chem, our teacher told us, “Look, we lied to you about how orbitals worked, so you could have a reasonable approximation.  Now we’re going to teach you the VSEPR model.”  I immediately started wondering how many years of chem you had to take before your conceptual models of atoms stabilized, and your professors weren’t constantly telling you that everything you’d learned up to that point had been a noble lie.

But how good is my supposed concept of a circle in the first place?  Just stating that definition is enough to logically entail plenty of properties of circles, however, my clear and distinct idea isn’t good enough to make me instantly remember and understand that the perpendicular bisector of any chord in a circle passes through the center of the circle.  It doesn’t feel like I have a firm grasp of what a circle is, just that I have an approximation of it, or a partial listing of its properties, or that I’ve got a clear and distinct idea of one facet of the whole.

I posed this problem to Feser and he told me that my question had already presupposed that I had a sufficiently clear and distinct idea of a circle to know that I was ignorant of some of its properties.  To be able to start approximating it in the first place, I needed a concept that I could test phantasms against.  This sounded satisfying, but I’d be interested in your takes.


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  • deiseach

    “I immediately started wondering how many years of chem you had to take before your conceptual models of atoms stabilized, and your professors weren’t constantly telling you that everything you’d learned up to that point had been a noble lie.”

    From a biological viewpoint, I refer you to Cyanobacter; if you care to look up the Wikipedia entry, you will see the tactful phrase “The taxonomy is currently under revision”, which is a nice way of saying that there is still hair-pulling over is it blue-green algae or is it blue-green bacteria? This has been going on since at least back in the 80s, when the classification changed from one year to the next in the latest issue of “Bergey’s Manual of Determinative Bacteriology” (when I was gaining a qualification as a laboratory technician, the 1980 version called it blue-green algae, the 1981 classed it as blue-green bacteria, and the 1982 – you’ve guessed it: reverted to algae.)

    Even calling it Cyanobacter would get me into trouble, since it might/should be Cyanophyta. So no – it never stops 🙂

  • Joe

    The map territory gap is a problem I think (at least for me) in theology as well. The map of Divine Simplicity seems pretty solid, until you have to deal with the fact of the incarnation! Im not well read enough to know how theologians bridge the divide. I understand why Christ was a stumbling block to the Jews and folly to the greeks. When you go from reason to the material, things get confusing. No wonder gnosticism is always so popular.

  • Hit two things together. See what breaks. For example, what’s a human?

    Well, a human has legs —

    No! Animals also have legs!

    Well, a human has a human body …

    No! Amputees are also human!

    … and so on, until we get to the understanding of the characteristics of a human soul. Once we’ve imbibed these distilled properties, we can wax poetical about what it’s like to someone who has no understanding of what we’re talking about.

    Once we know our comprehension of a concept approaches the true concept itself, we may finally come up useful introductory analogies. “See, it’s like a rubber sheet …”

  • Dangerous, dangerous tangent: “Conceptual models stabilizing” seems like a good way to explain the multiple creation stories in Genesis, Noah and the Flood, et al. Our conceptual models of metaphysical claims were suddenly no longer that we are huddled and cold specks on the back of a giant turtle, which is another way of saying we are subject to capricious all-powerful forces beyond our comprehension, but rather that we are unique among the creatures and disobedient nonetheless, which is another way of saying we are subject to our own transgressions, that we were once originally good.

    Consider: Creation revelation is intended as a helpful riff to untwist creation stories contemporary to Ancient Hebrews into something more closely approximating the true relationship men have between each other and between themselves and God. Just as it is more true that the universe revolves around the Sun than the universe revolves around the Earth, Genesis is more true than the competition. I also argue it revealed more things and more important things, but consider this a helpful analogy for the uninitiated. “See, it’s like a rubber sheet …”

  • Penultimate comment before heading off to Mass:

    Is it Maps All the Way Down?

    If it were, then why would the maps stabilize, seemingly on their own?

    • Anticipating a certain response: If this stabilizing of the map is merely because we want things to make sense, why do maps in differing, isolated cultures overlap so much?

      Anticipating a follow-up response: If the overlap merely reflects human physiology and the common threads of Indo-European culture, you’ve offered an essentially untestable hypothesis. We’re the only rational souls we know.

      Resolved: Rather than our maps be a reflection of us, perhaps we are a reflection of this map, this Grand Design.

      This is somewhat testable. Do we perceive order to the universe? (By which I mean, “are there natural laws that more or less work?”) This is little more than saying “Does abstracted science lead to practical engineering?” Then we must ask: Is the universe intelligible? If science can be made practical, and reliably, then yes, the material universe is intelligible. From here we must postulate one of two responses:

      1. It is intelligible because we make it, which is to say gravity didn’t exist before Newton, which is to say that it is only because we fall through phantasms that concepts exist. Or,
      2. It is intelligible before us and will be after us, despite our best efforts, which is little more than saying that no matter how we master The Secret, wishing a thing does not make it so. In other words, the bottom of a well existed before we fell down it.

      Which, Dear Reader, is the side of reason?

      The first step on the realist path is to recognize that one has always been a realist; the second is to recognize that, however hard one tries to think differently, one will never manage to,; the third is to realize that those who claim they think differently, think as realists as soon as they forget to act a part. If one then asks oneself why, one’s conversion to realism is all but complete. — Etienne Gilson

      If we are physiologically reflective of a grand design, it takes a kind of rebellion to suppose that despite this we are not metaphysically reflective also.

      Why would someone rebel, leaving the primordial garden of common sense? It would take more intelligence than I have to explain this, and more than that to explain it to me why it is still so common.

      Think of what we could do with such a fundamental insight about the nature of man! We could be freed from the back of the space turtle! And this thing, what would let us move to more profound truths, is so simple that everyone must be able to understand it, even prehistoric nomadic shepherds. All it would take is a little parable from someone who knows Man better than men can know Man.

      For if corrupt man merely manufactures some essential wisdom, it won’t work. That wisdom is going to be foundation of the tower of all human knowledge. If it even slightly fails, eventually our knowledge will teeter and fall. So this is foolhardy. How can an incorrupt truth come from corrupt humanity? It must come from elsewhere.

      It would take someone abstracted from time and space, if not a Creator than maybe even just someone with the practical knowledge of someone who knows the nature of our form to explain why. We won’t understand him at first, lacking as we do an essential understanding of ourselves. So this person, the ultimate source of all reason we’d ever have, would start very slowly —

      “See, it’s like a rubber sheet …”

    • Alex

      Why would the maps not stabilize? The whole point of a map is to give accurate directions.

      • Ash

        In fact, one could image an automatic map-stabilizing process. Start with an arbitrary map and test its accuracy. Make some slight changes at random, then test again. Keep the more accurate map and repeat.

        Of course you might eventually hit a dead end, and you wouldn’t know if the “best” map was perfect or just better than all slightly modified ones. Maybe a better solution is to start with a whole bunch of maps and …

        I’m sure I’ve heard this idea before somewhere.

        • Why would it stabilize unless it represented something stable? That’s the question.

          • Alex

            Could you give an example of what a non-stable territory might look like? Preferably something in the domain of physics or chemistry (which is usually where the maps we are referring to are located). It seems to me that we only ever bother to make maps of phenomenon that follow stable patterns.

          • Certainly you agree that when we make maps of the physical and maps become stable, it is reasonable to suppose that the maps represent a stable reality. Truths beyond our understanding may seem unstable, but we have every reason to suspect this is only a seeming. In fact, science assumes that maps of the physical stabilize. Necessarily.

            My point, summarized: Similarly, if we make maps of the metaphysical and at least some maps become progressively stable, it is reasonable to suppose that at least some metaphysical truths are also stable. Metaphysical truths beyond our comprehension or conscious insight may seem unstable, but we have every reason to suppose that this is only a seeming.

            Could you give an example of what a non-stable territory might look like?

            No. In fact, I take the position that there is no non-stable territory, only non-stable map-makers.

            I think you have me backwards. I believe the Universe is ordered by “number, weight, and measure.” Examples contrary to this have only ever seemed to exist in the penumbra of our current knowledge.

          • Alex

            Very interesting. That makes sense. It’s something like the definition of a limit. If the maps can be made arbitrarily close to empirical results then they must be converging towards a stable reality.

            Back to your previous comment though, I’m not sure about the jump from stability to “Grand Design”. Although it seems perfectly reasonable and self-consistent to posit some ultimate natural law as the source of stability I don’t see it as being particularly necessary.

      • Why would the maps not stabilize? The whole point of a map is to give accurate directions.

        … to a stable thing. If a thing really is not so stable, it cannot be said to exist. If we do find that our understanding of a thing is stable, there are, broadly, two possibilities:

        1. It is of itself.
        2. It is of the observer.

        I could be wrong, but this seems solid enough.

        • Alex

          Sorry I don’t understand what any of that means.

          • Translation: If our understanding of a thing is stable, there are, broadly, two possibilities:

            1. It seems stable and it is.
            2. It seems stable even though it isn’t.

            There’s the other half of the quadrilemma, too:

            3. It seems unstable and it is.
            4. It seems unstable even though it isn’t.

            Someone could write a mighty fine blog post on this!

  • Patrick

    I think that math is a pretty terrible choice of examples for his idea. You’re familiar with the definition of a circle, but Feser has you wondering whether you understand what a circle “is.” But there is no “is.” The definition is it! There is nothing more than this. There is no essence. There is no true nature. A circle is a set of points defined in a particular manner. End. Of. Story. Your ability to put all of the facts that derive from that definition into the front of your mind is irrelevant.

    Here, have a semi related webcomic.

    • g

      Digression: ZW’s explanation of “Polish hand magic” can, I think, be streamlined. Instead of giving names to the digits, name the “fingers down” counts a,b. Then the “fingers up” counts are 5-a,5-b; and the trick says that (10-a)(10-b) = 10(5-a+5-b) + ab, which is the same as (10-a)(10-b) = 100 – 10(a+b) + ab, which is just multiplying out the brackets. For me, at least, this is transparent enough to put an end to the “Yes, but why?” questions.

      (I agree with the actual point you’re making.)

    • I think you missed the point differentiating between concept and phantasm. Moreover, if your beef is only his analogy, it may easily be filed under “See, it’s like a rubber sheet …”

      Feser did not necessarily give an example so much as an illustration. The point is not to visualize circles but to understand how visualization sharpens, what the ultimate fruit of visualization feels like.

      • Patrick

        I was addressing Leah’s comments in the second to final paragraph of her piece, where she discusses her inability to put all data in existence on circles into the forefront of her brain at one time, causing her to feel as if she hasn’t fully formed a “concept” of “circle.”

        As for his selection of analogies… I think you’d get a very different argument if you required him to take out all references to mathematics and replace them with references to chickens. This is what a circle is: “a closed plane curve every point of which is equidistant from a fixed point within the curve c.” That’s the concept. Mentally imagining a circle is generating a phantasm under his terminology.

        Now do the same thing for a chicken.

        • Phantasm: Looking at a chicken.

          Concept: Knowing chicken-ness. Being able, therefore, to group chickens together without including ducks.

  • Ray

    I think the distinction between concept and phantasm is reasonable, but it’s presented misleadingly. A phantasm is something like raw sensory data. A concept is a mental circuit that is used to detect specific features in the raw data. Computers can do this too: a computer can check if two mathematical statements are related by one of the legal replacement rules in an axiomatic system, or more visually, image processing software can detect edges corners, etc. It appears to be this rather prosaic ability Feser is referring to when he’s talking about “concepts.”

    Likewise, your circle concept allows you to recognize, with some difficulty, true statements about “circles,” specifically those which can be reached by a small number of deductions from Euclid’s axioms and his definition of the circle. The axioms, the definitions, and the neural circuitry needed to process the language is the whole of the concept, but there is an unlimited number of statements you can test against it — just as a finite number of lines of Turing machine code will generate all the primes, but no computer in the world used to run the program will ever finish the list.

    Feser presents the concept/phantasm distinction misleadingly, partially, I think, because he only understands what he’s describing on the level of knowing what it feels like, not on the level of what’s going on (ironically he only has a phantasm, rather than a concept for the concept/phantasm distinction.) The other reason, of course is because Feser is not creating these distinctions for the love of knowledge, but to prop up the intellectual moribund doctrines of an obsolete, but still powerful, political institution.

    • Ray

      To clarify why Feser’s description is misleading: The phantasm is the territory, the concept is the map.

  • Maiki

    I guess I’d make the distinction between a concept and a model. A model is not the concept but a simplification of a concept. The phantasm is not a simplification of the concept but a mental instance of the concept.

    e.g. I have a concept of “gravity” in my head. I have imperfect knowledge of this concept, but I know basically it is the attractive force between massive objects. I have a few “models” of how to apply/describe/predict gravity in specific situations — e.g. the Newtonian model allows me to think about gravity in most everyday situations, and the Relativistic model allows me to think about it in the realm of space travel. Phantasms of gravity might be my mental image of how I expect objects to behave in known gravitational fields.

  • @b

    So the “concept” is the category (a Chiliagon) and the “phantasm” is the concrete example (THIS chiliagon).