Bad Dogs and Defective Triangles

Is a dog with three legs a bad dog? Is a triangle with two sides still a triangle or is it a defective triangle? Perhaps if we just expand the definition of triangle a bit we can have square triangles.

There is a point of view that holds that to define something we must say something definitive about it and that to say that we are expanding or changing a definition makes no sense if we don’t know what it is that is being changed.

It is of the essence or nature of a Euclidean triangle to be a closed plane figure with the straight sides, and anything with this essence must have a number of properties, such as having angles that add up to 180 degrees. These are objective facts that we discover rather than invent; certainly it is notoriously difficult to make the opposite opinion at all plausible. Nevertheless, there are obviously triangles that fail to live up to this definition. A triangle drawn hastily on the cracked plastic sheet of a moving bus might fail to be completely closed or to have perfectly straight sides, and thus its angles will add up to something other than 180 degrees. Even a triangle drawn slowly and carefully on paper with an art pen and a ruler will have subtle flaws. Still, the latter will far more closely approximate the essence of triangularity than the former will. It will accordingly be a better triangle than the former. Indeed, we would naturally describe the latter as a good triangle and the former as a bad one. This judgment would be completely objective; it would be silly to suggest that we were merely expressing a personal preference for straightness or for angles that add up to 180 degrees. The judgment simply follows from the objective facts about the nature of triangles. This example illustrates how an entity can count as an instance of a certain type of thing even if it fails perfectly to instantiate the essence of that type of thing; a badly drawn triangle is not a non-triangle, but rather a defective triangle. And it illustrates at the same time how there can be a completely objective, factual standard of goodness and badness, better and worse. To be sure, the standard in question in this example is not a moral standard. But from the A-T point of view, it illustrates a general notion of goodness of which moral goodness is a special case. And while it might be suggested that even this general standard of goodness will lack a foundation if one denies, as nominalists and other anti-realists do, the objectivity of geometry and mathematics in general, it is (as I have said) notoriously very difficult to defend such a denial.

– Edward Feser. Being, the Good, and the Guise of the Good

This raises a number of interesting questions, by no means limited to the following:

What is the fact/value distinction.

Whether values can be objective.

The relationship between objective goodness and moral goodness.

And of course, whether a three-legged dog is still a dog.

Meanwhile:

One Leg Too Few

469 thoughts on “Bad Dogs and Defective Triangles

  1. I find it interesting to contemplate the things we adapt to and the things we don’t adapt to. Switching from concave to convex lenses has gone rather easily (although it takes a lot longer than a few minutes.

    Other changes, such as the dramatic shift in color temperature, also adapt, but still feel strange after 10 weeks.

    But I have had a “floater” for about four years, and although it has become less disturbing, it is just as visible. Why do we ignore the lacuna produced by the fovea, but never fully lose awareness of floaters?

  2. Neil Rickert: Does an “x” really look blurry without your glasses?
    […]

    Constructing information is a creative act by an agent.

    […]
    As for consciousness — my view is that this is simply our experience of the information that our perceptual systems are constructing.

    Maybe I am just blurry on the concept of BLURRY, but I just take it to mean out of focus.

    On information: there are at least 4 kinds: thermodynamic, Shannon, Grice’s natural (eg tree rings=age), Grice’s non-natural (stop signs eg, I think).

    If you are a scientific realist, then you might say the thermodynamic types in real. Ditto for a math Platonist and the Shannon type. Natural information might be real in Dennett’s sense of Real Patterns. I’m not sure about Stop Signs; maybe if you think propositions are the type of abstractions that can be real in some sense then might apply.

    Now I’m not surprised that you would not accept any of the above. Someone who did might use “Detecting and modelling” rather than “constructing” as the first word in the phrase I quoted.

    On consciousness being experience: Isn’t the experience of something another way of saying that something is conscious? Also, isn’t’ there a lot of perceptional information that does not become conscious? So we do we “experience” some and not others?

  3. walto:
    Not without definitions (but you can use ubby-dubby).

    That was a brain fart on my part: I got realism and representationalism confused.

  4. walto:
    Funny that this issue about blurriness–and related things like the number of speckles on hens–has been written about for-freaking-ever.One of my thesis advisors, Rod “the God” Chisholm, wrote a paper on it in 1942:

    http://philpapers.org/rec/CHITPO-7

    Yes, I’ve seen some Tye and others on that but it just hurts my brain too much to work through the entirety of the arguments and counterarguments.

    The speckled hen did help me with the idea of non-conceptual content for perceptual representation. Or was that the too many color shades to name argument that I’m thinking of?

  5. BruceS: On information: there are at least 4 kinds: thermodynamic, Shannon, Grice’s natural (eg tree rings=age), Grice’s non-natural (stop signs eg, I think).

    I’m assuming “Shannon information.” That’s the appropriate one for questions related to cognition. It took me a long time to realize that. My initial view was that semantics is important and Shannon information is syntactic so not important. But I came to realize that Shannon information can be full of semantics, depending on how it is generated.

    Stop signs — I’d accept those as a special case of Shannon information.

    Tree rings — those are natural physical things, but they are not information. We can use them to create our own information about tree age. But we still have to work at it.

    In particular, I am opposing a common view that there is natural information in signals that happen to strike sensory receptors, and all we need is for the brain to be a Bayesian inference engine. That idea is never going to work. Our use of information is far more creative than that.

  6. Neil Rickert: In particular, I am opposing a common view that there is natural information in signals that happen to strike sensory receptors, and all we need is for the brain to be a Bayesian inference engine. That idea is never going to work. Our use of information is far more creative than that.

    Defining human perception is about as likely task as defining what life is.

    Perceiving is something that brains do. What that “something” is is determined by the evolutionary history of the perceiver.

  7. Neil Rickert: I’

    In particular, I am opposing a common view that there is natural information in signals that happen to strike sensory receptors, and all we need is for the brain to be a Bayesian inference engine.That idea is never going to work.Our use of information is far more creative than that.

    Science is not about whether information or anything is else is real and “out-there”; that is topic for philosophy.

    Science is about creating models meeting the usual scientific criteria: testable predictions, verification by experiment, novel predictions, cogency of explanation, breadth, consistency with other relevant science, transparency and detail for review by the scientific community, and so on.

    On this basis, the Bayesian model has had success: for example, in predicting learning behavior, illusions, fMRI patterns. But there are also gaps, eg direct confirmation of the model’s two neural sub-populations with distinct functional roles (error versus representation).

    Also, I don’t think Bayesian models will be the only level of explanation. For humans, we need to understand how cognitive prosthetics, like language and number, fit in. Perhaps we will also need a different level of explanation for cognitively-complex animals like chimps, dolphins, crows, and octopuses.

    I don’t understand your ideas about measurement and continual re-calibration. Hence, I cannot evaluate how they meet the scientific criteria I listed.

  8. petrushka:
    Defining human perception is about as likely task as defining what life is.

    Perceiving is something that brains do. What that “something” is is determined by the evolutionary history of the perceiver.

    Granted. But there is still the separate question of what perception is now. (Separate from how it got that way).

    I don’t see why one would give up on that question without even trying.

    Also, I would not answer the question by trying to create a dictionary definition of perception, but rather by creating successful scientific models.

  9. BruceS: On this basis, the Bayesian model has had success: for example, in predicting learning behavior, illusions, fMRI patterns. But there are also gaps, eg direct confirmation of the model’s two neural sub-populations with distinct functional roles (error versus representation).

    Bayesian inference is done using existing concepts. So it can explain change of belief but it cannot explain conceptual change.

    I see conceptual change as highly important for human learning and for the advance of science. And it sure seems as if Bayesian inference cannot explain it.

    I don’t understand your ideas about measurement and continual re-calibration.

    I see them as involved in conceptual change.

  10. Neil Rickert: Bayesian inference is done using existing concepts.So it can explain change of belief but it cannot explain conceptual change.

    I see conceptual change as highly important for human learning and for the advance of science.And it sure seems as if Bayesian inference cannot explain it.

    I see them as involved in conceptual change.

    Bayesian methods can be used to estimate the parameters of a generative model (eg Gaussian mixture). When applied to a set of natural images, this can be viewed a doing a cluster analysis or as picking a sparse set of (hidden) causes for those images.

    That inference process can be implemented by a recurrent neural network. The Predictive Coding idea has a set of these networks linked in a hierarchy.

    One could say the hidden causes encoded in the upper, more abstract representations levels of the hierarchy are eligible to be called concepts. Isolated applications of the level in perception would be recognition using existing concepts. Long time changes to that level or or maybe higher ones would be learning new concepts or changing existing ones.

    With my definition of computation, I would say such neural networks are computing by Bayesian inference.

    I won’t pretend to understand the math well enough to rehearse it here, although I am planning to work on it. It’s the sort thing I studied a long time ago in a university not that far away.

    I believe you can find details in the Methods section of this paper: Predictive coding in the visual cortex. I have yet to study it in detail.

    I got my limited understanding of the math from a Coursera course which was co-led by the senior author of the paper.

  11. BruceS: Science is not about whether information or anything is else is real and “out-there”; that is topic for philosophy.

    Science is about creating models meeting the usual scientific criteria: testable predictions, verification by experiment, novel predictions, cogency of explanation, breadth,consistency with other relevant science, transparency and detail for review by the scientific community, and so on.

    On this basis, the Bayesian model has had success:for example, in predicting learning behavior, illusions, fMRI patterns.But there are also gaps, eg direct confirmation of the model’s two neural sub-populations with distinct functional roles (error versus representation).

    Also, I don’t think Bayesian models will be the only level of explanation.For humans, we need to understand how cognitive prosthetics, like language and number, fit in.Perhaps we will also need a different level of explanation forcognitively-complex animals like chimps, dolphins, crows,and octopuses.

    I don’t understand your ideas about measurement and continual re-calibration.Hence, I cannot evaluate how they meet the scientific criteria I listed.

    Neil is very attached to the philosophical enterprise, I think. It’s a love-hate relationship, but love is clearly winning.

  12. walto: Neil is very attached to the philosophical enterprise, I think.It’s a love-hate relationship,but love is clearly winning.

    Well, my last paragraph on Neil’s theories and their scientific status was meant as a polite way of saying that maybe his ideas, at least in the detail I have seen here, seem closer to philosophy than science.

    But is it polite to talk behind Neil’s back this way?

  13. BruceS: Well, my last paragraph on Neil’s theories and their scientific status was meant as a polite way of saying that maybe his ideas, at least in the detail I have seen here, seem closer to philosophy than science.

    I’m well aware of that.

  14. BruceS: Science is not about whether information or anything is else is real and “out-there”; that is topic for philosophy.

    Yet science manages to move forward while waiting for philosophers to agree on whether the discoveries of science are real or not. Science is metaphysics waiting on the philosophers to catch up.

  15. Mung: Yet science manages to move forward while waiting for philosophers to agree on whether the discoveries of science are real or not. Science is metaphysics waiting on the philosophers to catch up.

    Judging whether a field is moving forward requires a way of measuring progress.

    For science, the metric is the breadth and depth of the success in predicting and controlling the phenomena that interest scientists and the people who pay for their work. Measured this way, science makes progress without needing to draw any metaphysical conclusions.

    But what is the metric for philosophy? It’s not the same metric as science. So they are not in the same race and there is no issue of philosophers “catching up”.

    Perhaps progress in philosophy could be measured by the depth and breadth of the conceptual space that has been explored. If so, one could make an argument that philosophy is making progress.

  16. That’s a bit like evolution exploring phase space with no purifying selection. If there is no sieve of viability, there is no advance.

  17. petrushka:
    That’s a bit like evolution exploring phase space with no purifying selection. If there is no sieve of viability, there is no advance.

    Well, that just depends on how you define “advance”, doesn’t it? If you don’t want to conclude philosophy progresses, then define “advance” in a way that precludes it. Or conversely.

    The nice thing about science and progress is that there is an obvious pragmatic aspect to defining “advance” that makes it easy to judge various definitions of advancing. I’m not sure if there is any way to rank definitions for advancing in philosophy, except possibly by consensus of philosophers.

    On evolution: if you wanted to have some analog to evolution, you’d need to define an appropriate fitness function for philosophy. But is fitness really a measure of progress? I think it is just the NS process for explaining some examples of evolutionary change. Fitness does not measure progress in evolution. In fact, my understanding is that we do not say things like “life progresses by evolution. “

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