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Being not a philosophy scholar, I am trying to get up to speed on the nature of statements about basic, established facts in human knowledge and how these relate to the existance of rare exceptions. For instance, consider the current Encyclopedia Britannica page for 'tetrapod':

All tetrapods share a variety of morphological features. These include a pair of bones (the ulna and radius and the tibia and fibula) in the epipodial segments of the forelimbs and hind limbs, digits on the end of each limb, an oval window (fenestra ovalis) in the skull opening into the middle ear, a stapes (ear bone), and several other skeletal features.

This taxonomic description clearly does not apply to all tetrapods in real life, such as those born missing limbs or with agenesis of the ossicles - failure of middle ear bones to develop. They are still tetrapods, and yet they may lack certain features that "all tetrapods share".

I gather this is sometimes described as the "exception that proves the rule" - as in an exception that proves the existence of a rule. But to this layperson it doesn't feel satisfactory as an epistemological explanation.

What formal resolutions to this problem of exceptions exist in epistemology or taxonomy? By this I mean how is it considered a valid statement that "tetrapods have four limbs" when in reality this is not true of all tetrapods?

geotheory
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  • FYI, "basic statement" is often used as a technical term in philosophy which isn't how you are using it here. Maybe you could change it to "statements that are generally true but have rare exceptions". – David Gudeman May 05 '23 at 21:41
  • @DavidGudeman thanks have reworded to reduce ambiguity – geotheory May 05 '23 at 22:31
  • Statements with exceptions are handled by [default logic](https://en.wikipedia.org/wiki/Default_logic) and [prototype theory](https://en.wikipedia.org/wiki/Prototype_theory). However, the example with tetrapods is better handled in terms of prototypical properties, or properties *ceteris paribus* (other things being equal), see [Delgrande](https://www.academia.edu/26256379/A_first_order_conditional_logic_for_prototypical_properties). Encyclopedia descriptions are taken to be abridged, with omitted stipulations (something like "barring malformation or mutilation") eliminating the exceptions. – Conifold May 05 '23 at 23:54
  • @Conifold Sorry I don't understand what cognitive theory has to do with epistemology. One is about the individual's sematic mapping. The other - this question - is about our collective knowledge as a society. How are these related, and how can a theory of the former address a question about the latter? – geotheory May 06 '23 at 00:25
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    Even if one of the properties attributed to "tetrapod" is missing in a given individual, there should be other properties, such as "has tetrapod parents". The property "has tetrapod parents" would have priority over "having 4 limbs". – Frank May 06 '23 at 00:32
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    Taxonomy is not an issue of epistemology, it is a about organizing knowledge, not access to it. And cognitive theory is not just about individuals, it applies to social knowledge as well. On the one hand, we want to avoid complicating category descriptions to fully rule out exceptions, especially if those rarely matter in practice. On the other hand, we do want to keep exceptions rare. The task of taxonomy is to balance those goals. With a taxonomy in place, the answer to "how is it considered a valid statement" is that it is valid prototypically (for core instances or dropping stipulations). – Conifold May 06 '23 at 01:11
  • @Conifold but isn't there a problem in defining _prototype_ or _core instance_? – Frank May 06 '23 at 02:11
  • @Frank That's what the prototype theory is for. – Conifold May 06 '23 at 05:59
  • @Conifold But if a _prototype_ is like an average chosen as a representative of a collection of numbers, the prototype itself may not have any actual instance. So statements about the prototype do not necessarily apply to any individual. For a very concrete example, if aspirin on average cures headaches, there might be individuals for whom it doesn't work due to quirks of their physiological make-up. The point being, it's not clear how statements made on the _prototype_ are actually valid for any instance of that prototype. Maybe something like a universal/particular issue here? – Frank May 06 '23 at 15:49
  • @Frank Prototypes are not sets, and prototypical verification is not done by quantification over instances. You could say that prototypical sentences are partially idiomatic: "every x is y" may well be prototypically true even if sentences with some instances substituted for x are not. There are books and papers on the prototype theory that lay out nuances and technicalities at length, we won't be able to go over them in comments. – Conifold May 07 '23 at 00:09
  • Leaving this question open because I'm not satusfied by prototype theory as the solution. This question must have been addressed by earlier scholars than cognitive scientists in the 1970s. – geotheory May 17 '23 at 08:37

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Let's start with an anecdote:

According to Diogenes Laërtius, when Plato gave the tongue-in-cheek[35] definition of man as "featherless bipeds", Diogenes plucked a chicken and brought it into Plato's Academy, saying, "Behold! I've brought you a man", and so the academy added "with broad flat nails" to the definition.

This issue again to the fore in philosophy in Philosophical Investigations; you have raised the question of Wittgensteinian family resemblance. Eleanor Rosch, inspired, contemplated family resemblance and put forth prototype theory:

Prototype theory is a theory of categorization in cognitive science, particularly in psychology and cognitive linguistics, in which there is a graded degree of belonging to a conceptual category, and some members are more central than others. It emerged in 1971 with the work of psychologist Eleanor Rosch, and it has been described as a "Copernican revolution" in the theory of categorization for its departure from the traditional Aristotelian categories. It has been criticized by those that still endorse the traditional theory of categories, like linguist Eugenio Coseriu and other proponents of the structural semantics paradigm.

It is, of course, a progressive philosophical explanation and is often not known to philosophers who refuse to admit facts of linguistics into their philosophy of language (which is analogous to rejecting natural epistemology and then debating philosophy of science, which is obviously problematic).

If you understand LW's passages on family resemblance, and then weigh the details of prototype theory, you'll find the bumbling speculations of those outside of philosophy of language wholly inadequate. A complicated but accessible explication of the act of what Robinson assesses as 'real definition' which is what enriches our discussion of concepts can be found in Women, Fire, and Dangerous Things, a book written by a Chomskian dissenter by the name of George Lakoff (who appears in Dennett's humorous dictionary of philosophy jargon).

J D
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  • My advice is explicitly prescriptive in that you should ignore the Aristotelian diehards and get with the times. ; ) Also relevant to taxonomical issues like clades, etc. https://plato.stanford.edu/entries/natural-kinds/ – J D May 05 '23 at 22:05
  • Nice anecdote! Does prototype theory not share something with Plato's ideal forms? I wonder how suitable its cognitive science pedigree makes it for of established human knowledge. – geotheory May 05 '23 at 22:23
  • @geotheory Well, prototype theory would be seen as [nominalism (SEP)](https://plato.stanford.edu/entries/nominalism-metaphysics/), where as Forms stems from realism. Whereas Plato knew nothing of contemporary science, Rosch's ideas come from psychology and neurology. Plato was 2000 years before LW, and Rosch came after. So Rosch's proposals have all the advantage of being consistent with modern philosophy and science. What good are proposals about how humans classify if they ignore or even contradict what is known about how our brains and minds work? – J D May 06 '23 at 14:19
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I've been thinking about this very question for the past couple of months. I haven't been able to find any literature that discusses it directly, although it seems to be related to the distinction between essential and accidental properties.

So here are my own thoughts on the issue: you have to distinguish the essential property of "being four-legged" from the closely related accidental property of "having four legs". The essential property is about classification. It is a property that is part of what it means to be a member of a certain species, or at least an essential consequence of being a member of that species. The accidental property is a matter of fact. It is a property that can be different from one individual of the same species to another, and from one time to another.

This observation isn't a complete solution to the problem, unfortunately because it leaves some important questions. In particular: what is the relationship between these two properties? They clearly are related in a fundamental way, but how do you describe that relationship? You could resort to teleology, which means you could resort to what is proper or correct for a species: "To say that a species S is four-legged (essential) is to say that it is proper for members of the species to have four legs (accidental). That if a member of the species doesn't have four legs, there is something wrong."

However, if this is the answer, then these essential/accidental pairs can only apply to teleological systems (basically, living systems and things made by living systems); such pairs cannot apply to things like rivers or mountains that aren't teleological. I can't think of an essential/accidental pair that applies to a non-teleological system though, so maybe that's right.

David Gudeman
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  • I agree this is a matter of classification. I wonder if there is something in how the statement _"tetrapods have four limbs"_ will be naturally interpreted as referring to the definition of a _class_ within a taxonomic system rather than classification of _individuals_ within the system. I.e. a higher level statement of knowledge. Accidental/essential might capture it - I'll have to research. – geotheory May 05 '23 at 22:37
  • This requires defining "proper" and "wrong", which seem to carry judgement. That shouldn't be needed here and it could be harmful especially when applied to humans. – Stef May 06 '23 at 08:22
  • @Stef, they are teleological judgments, not moral ones. And if you have an alternative, what is it? – David Gudeman May 06 '23 at 08:29
  • @Stef your morality is not relevant to this discussion. – geotheory May 08 '23 at 08:25
  • @geotheory That's my point exactly. The approach suggested in this answer requires defining "wrong" and "proper", which carry a moral judgement, which shouldn't be required for this problem. – Stef May 08 '23 at 08:53
  • @Stef, once again, "wrong" and "proper" are ambiguous. In this usage they are *not* moral judgment but teleological judgments. – David Gudeman May 08 '23 at 08:59
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I would encourage you to consider the question in the following way.

In nature there are very few kinds of objects which we might consider properly identical, in the sense that no known test could tell the difference between them. Electrons, protons, etc are identical in that sense.

The world is an enormous collection of those sorts of identical objects arranged in a way that is constantly changing.

Humans needed to make sense of the world, and share ideas about it, in order to survive, so we developed patterns of thought about subsets of the vast collection of particles that form the world. We developed notions such as food, tiger, stone, seed, cloud, to denote subsets of the world having common characteristics that were important to us in some way. Clearly, unlike the fundamental particles from which they are made, no instances of tigers, stones, clouds etc are exactly alike. However, using labels to denote objects that are broadly alike is a sensible strategy for two main reasons: 1) for most purposes it is not important to distinguish between objects more precisely; 2) carried to its extreme, labelling objects individually would soon exhaust our limited vocabularies and powers of recall. You would not consider it even remotely feasible to refer to all of the billions of tiny pieces of matter on a beach as anything other than just sand, regardless of the fact that every one of them will be different from every other.

The level of specificity with which one might bother to label an object will depend on the context. I might be happy to label any beetle-like insect I encounter as a beetle, whereas a coleopterist would be more careful and discriminating in their labelling of the little creatures.

What you call basic statements of knowledge are in fact conventional labels that we use to refer to subsets of the world having broadly similar characteristics. For the reasons I have outline above, the labels are necessarily applied coarsely, and the sets of objects they refer to are necessarily fuzzy. It is neither practical or desirable to create new labels to distinguish between tetrapods generally and the wide variety of what you call exceptions. Aside from the fact that we would complicate our classification system to an unworkable extent, and there would be no end to the upkeep as new exceptions were encountered and needed to be classified, you would be missing the point of a classification system, which is that the common characteristics of the objects in a class are more significant than their individual characteristics.

Marco Ocram
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