Tigers and Triangles

Locke held that the mind deals with abstractions by forming abstract ideas, by which he meant – or seems to have meant, or was interpreted to mean – mental images with less than fully determinate content. For example, on Locke’s view the abstract concept of a triangle is a generic mental image – an image whose content is a triangle, but not specifically an acute or obtuse or equilateral, not specifically a right or isosceles or ….

no triangle in particular To many of Locke’s empiricist successors – notably Berkeley and Hume – Locke’s solution was unacceptable, because, so they argued, all mental images are determinate. We can’t form an image of a triangle, they maintained, without its being the image of some specific kind of triangle. So the possession of an abstract concept, they concluded, must consist not in the contemplation of an indeterminate image but rather in what we do with our determinate images.

Now on the whole I’m on the side of Locke’s critics here (even if their conception of what sort of “doing” the possession of a concept consists in was rather impoverished). But I think they picked the wrong criticism to make of Locke’s position.

Here’s why. Locke’s critics were quite wrong in thinking we can’t form indeterminate mental images. On the contrary, our mental images generally are somewhat indeterminate; so, for that matter, are our very perceptions. When we see a tiger and observe that it has stripes, there is, I claim, no particular number of stripes we perceive it as having. If Locke’s critics thought otherwise, it was probably in part because they failed to see the difference between the indeterminate idea of a tiger and the idea of an indeterminate tiger, and partly because in typical representationalist fashion they thought of the field of vision (and the field of imagination too) as something like an internal viewing screen covered with pixels. Since there’s always more determinacy available to see if we look more closely, they implicitly figured such determinacy was already there on the internal screen (whereas for us direct realists it’s the external world we’re looking at to find the inexhaustible additional determinacy, so it needn’t be inside our minds already).

Here comes a tiger!  Run, run!  And then try to remember how many stripes you saw But while Locke is thus correct in holding we can form indeterminate mental images (if, again, that’s indeed what he means by abstract ideas), he’s surely wrong in thinking that these images can do the work of abstract concepts. For even if our mental images are not perfectly determinate, Locke’s critics were right to insist that they are more determinate than their associated concepts. When I think about tigers, the mental image that I form may not represent a determinate number of stripes, but it does represent the tiger as orange. My concept of a tiger, however, is not so determinate as to be restricted to orange tigers; it applies to white tigers too. So although I may form a mental image when I think about tigers, my concept is not identical with that mental image. Perhaps thinking about tigers involves, Aristotelean-wise, selective attention to certain generic features of my image, but it is not and cannot be simply a matter of having the image. Conceiving is an activity, not a static condition.

This raises the question: suppose there were an intelligent species capable (as we seem not to be) of forming mental images to any desired degree of indeterminacy, so that just as we can imagine a tiger without imagining any specific number of stripes, they could imagine a tiger without imagining anything more specific than tigerhood. (This might have to be a species with a special perpetual system just for detecting tigers.) Could their mental images serve as abstract concepts?

Again, no, methinks. For just as my mental image of an orange tiger could serve as the occasion either for thinking about orange tigers or for thinking about tigers generally, so our hypothetical Martian’s image of a tiger simpliciter might serve as the occasion either for thinking about tigers or for thinking about some still broader category, e.g., mammals. For Martians as for us, what a mental image means depends on what we do with it. (Wittgenstein made just this point when he noted that thinking of a visit from Mr. B and thinking of a visit from Mr. B’s identical twin brother, or thinking of Oxford on fire and thinking of a university that looks just like Oxford on fire, are distinct mental activities, yet the associated mental images are identical.)

12 Responses to Tigers and Triangles

  1. Gene Callahan October 2, 2007 at 5:29 am #

    But Berkeley did not hold that we were looking at a representation of reality! He was a “direct representational realist” of the best kind, i.e., an idealist. He was scathing in discussing the idea that what we perceive is not what is really there, but some “echo” of an unperceived stuff called “matter.”

  2. Sheldon Richman October 2, 2007 at 8:15 am #

    I thought Berkeley believe that to be is to be perceived. Great stuff, Roderick!

  3. Selfreferencing October 2, 2007 at 9:07 am #

    Ah, a philosophy post! Roderick hasn’t succumbed to the Sci-fi channel after all! All hail The Praxeologist!

  4. Christian Hoffmann October 2, 2007 at 9:34 am #

    “…they could imagine a tiger without imagining anything more specific than tigerhood…”

    It is very well possible that I do not quite understand your understanding of an abstract or indeterminate image, but it seems to me that human beings are very capable of imagining tigerhood. If (and of course, that is a big if) we think of our ideas and perceptions as subjective constructions which are largely based on the usage of signs or symbols, then the idea of “tiger” is subjectively formed through a human’s interaction to any more or less determinate degree. Obviously, a child that only “knows” tigers from bed-time stories will have a much less specific idea of a tiger, then say a zoo-keeper responsible for the resident tigers.
    Since the concept of “tiger” is only a symbol and can basically carry any subjective meaning, it can also be more or less abstract – depending on how much effort a human being invests into constructing a specific or determinate understanding of this specific symbol. On the other hand, just as human beings are able to imagine abstract symbols (e.g. “bravery”), their image of an object can become thoroughly abstract as well.
    Therefore, if a reader might stumble on a phrase in a novel such as “Mike had the aura of a tiger”, the reader will understand what is written based on a very abstract understanding of “tigerhood” – he might, for example, imagine Mike to be a fierce and dangerous creature, or an elegant and mighty man – depending on his subjective concept of “tigerhood”.
    Of course, it is possible, that human beings are more or less good at manipulating signs and symbols, and therefore more or less good at thinking in the abstract. But I wouldn’t doubt a human being’s general ability to do so.

  5. Christian Hoffmann October 2, 2007 at 2:36 pm #

    I’m afraid my lack of understanding may be due to a lack of English language skills – I don’t quite understand your usage of certain terms (we have already used a variety of terms such as images, ideas and concepts). Quite frankly, I am not sure, what you mean by the term “concept”. I also don’t really see the difference between “conceiving” or “imagining”.
    The word “tiger” is (or to be more precise: can be) a sign or symbol (e.g. according to Peirce). The word is connected to an object and is open to an according interpretation. As such, it can potentially be related to any object or idea (someone could even use the term “tiger” in reference to what conventionally is thought of as a “dog” or “house”). The full meaning of the term “tiger” will always be thoroughly subjective – though it can partly be matched intersubjectively (e.g. we can agree on the notion that the second picture in your post displays a “tiger”).
    Now the term or symbol “tiger” can be used in reference to a specific object – but it can also be used in reference to an abstract idea. It seems to me that there are many terms that generally refer to abstract ideas – such as “greatness”, “generosity” etc. All of these terms, when brought to mind by an individual, can be mentally connected to a specific object (e.g. a specific generous person). But I don’t see why that should necessarily be the case.
    For example the term “chair” can be linked in the mind of the interpreting invididual to a specific chair. It can also be linked to an abstract idea (“something to sit on”). Now “tiger” is just another term which can be mentally linked to specific or non-specific objects.
    In my understanding, if we talk of the “concept” of “tiger”, we refer to the usage of the term or symbol “tiger” in reference to a non-specific object – i.e. any kind of tiger. Doesn’t the fact that we are able to use the term in this fashion prove that we are able to imagine the abstract idea of “tiger”?

  6. Gene Callahan October 2, 2007 at 7:24 pm #

    Sheldon wrote: “I thought Berkeley believe that to be is to be perceived.”

    That’s correct. So what we perceive is what is real, not some representation of what is real.

  7. Gene Callahan October 2, 2007 at 7:30 pm #

    Administrator: OK, But how can a world of ideas (our perceptions) be a direct mapping of any sort onto what is, by assumption, not a world of ideas? Or, how can an idea correspond to what is not an idea, when between them you have already postulated this vast gulf?

  8. Gene Callahan October 2, 2007 at 7:44 pm #

    This thread brings up an important opint that I have been convinced of for several years, which is that the usual dichotomy of realism vs. idealism is severely wrong-headed. What we actually have is a quadrant, with idealism vs. materialism (with dualism lying in the middle) and realism vs. scepticism. For instance, Rorty is a materialist sceptic — he believes reality is fundamentally material, but that we know crap all about it, outside of our cultural and personal preconceptions. Many recent philosophers of science are materialist realists — reality is material, and our ideas track it fairly well. Berkeley, Hegel, Bradley, and Oakeshott are idealist realists, and they hold that reality is a world of ideas, and that those ideas are real and not subject to our subjective whims. I’m sure there have been idealist sceptics, but no name is coming to me now.

    I’m curious as to what administrator thinks of this.

  9. Administrator October 2, 2007 at 11:25 pm #

    Christian,

    Quite frankly, I am not sure, what you mean by the term “concept”. I also don’t really see the difference between “conceiving” or “imagining”.

    By imagining I literally mean forming something like a mental image or picture in your mind. So for example when I think of tigers various mental pictures of tigers flow through my mind. But those mental pictures don’t determine what I mean by the word “tiger,” because when I say, for example, “all tigers are mammals,” what I’m saying applies to all tigers, including white ones, even though none of the tiger images that flitted through my mind’s eye were white. Therefore the mental imagery that accompanies my thinking about tigers is not what determines what I mean by “tiger.” By the concept I mean whatever it is about me that does determine what I mean by “tiger.” Hence conceiving and imagining are very different.

    I’m afraid I didn’t understand how the rest of your comments were meant to oppose what I’d said.

    Doesn’t the fact that we are able to use the term in this fashion prove that we are able to imagine the abstract idea of “tiger”?

    It shows that we can form the concept, but I don’t see how it shows that we can form the mental image. Can you really form a picture in your mind that’s a picture of a tiger but is no particular colour?

    Gene,

    But how can a world of ideas (our perceptions) be a direct mapping of any sort onto what is, by assumption, not a world of ideas? Or, how can an idea correspond to what is not an idea, when between them you have already postulated this vast gulf?

    Who are you asking this question of? This seems like a challenge to the representationalist; but I’m not a representationalist. I agree with Berkeley that representationalism is a muddle (though I disagree with him about what to believe instead, and I think what led Berkeley to his version of idealism was his acceptance of too much of the representationalist picture).

    For instance, Rorty is a materialist sceptic — he believes reality is fundamentally material, but that we know crap all about it, outside of our cultural and personal preconceptions.

    But in that case he’s not a thoroughgoing skeptic, right? A thoroughgoing skeptic would say they didn’t know whether it was material or ideal or what. Thus it sounds to me like the real combination, for Rorty as you describe him, is not skepticism plus materialism but non-skepticism-about-materialism plus skepticism-about-everything-else.

    Incidentally, I think “idealism” is a seriously ambiguous term. Sometimes it means treating reality as fundamentally mental, consciousness-stuff (as in Berkeley); other times it means treating reality as being fundamentally composed of logical structures that serve as the contents of our mental thingies (as in Hegel). In Fregean terms the former is inner-realm idealism while the latter is third-realm idealism, and the two seem to me to have virtually nothing in common.

    I’m sure there have been idealist sceptics, but no name is coming to me now

    William Godwin might count as an idealist skeptic, but not in the same way that you describe Rorty as a materialist skeptic. Godwin is an idealist skeptic in that he thinks it’s reasonable to accept Berkeley-style idealism — or to put it another way, it’s unreasonable for us, given the evidence, to believe in anything besides minds and ideas — but unlike Berkeley he doesn’t think we can know whether idealism is true or false.

  10. Christian Hoffmann October 3, 2007 at 10:30 am #

    Roderick

    I see your point, thanks. Though I still wonder about the case of a purely abstract idea such as “bravery”: Since it is an abstract idea, it does not possess any bodily or physical features. Accordingly, we cannot “imagine” bravery (as in calling to mind a physical representation or picture). So how do we think about or manipulate the idea of “bravery”? Maybe our mental representation is less physical than in fact emotional?
    As to the concept of “tiger”: Our ability to “imagine” this concept would depend somewhat on our definition of the concept. If we define the concept “tiger” as an elegant but dangerous, cat-like wild animal. Wouldn’t we be able to imagine such a beast? Obviously, the less physical our definition of the concept becomes, the more difficult it would be to imagine. Thereby, if our definition of the concept “tiger” would be “a dangerous animal”, again, we would probably not mentally represent the concept as a picture, but as an emotion.
    But maby I am just babbling away – anyway, interesting topic, thanks for that.

  11. Administrator October 3, 2007 at 11:11 am #

    Accordingly, we cannot “imagine” bravery (as in calling to mind a physical representation or picture). So how do we think about or manipulate the idea of “bravery”?

    Well, that’s the sort of reason I had in mind for saying that although Hume et al. were right to think that having a concept was more about doing something with our images as opposed to just having them, they had an impoverished concpetion of what “doing” amounted to. For Hume, e.g., to think the concept red is to pass through a series of images that have only redness in common — a red bird, a red sign, etc. Obviously that’s not going to work with “bravery.”

    If we define the concept “tiger” as an elegant but dangerous, cat-like wild animal. Wouldn’t we be able to imagine such a beast?

    Sure, but the question is whether we can imagine an elegant but dangerous cat-like wild animal without imagining any more specific characteristics (such as colour).

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