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What is the difference between class and concept? − I am not sure whether, for instance, “chair” is typically a class or rather a concept, or both. I would say that it is only a class, though it is usual to say that it is a concept.

Some further reflections, in answer to the comments below, in order to expound the question:

If one reads the interesting comments by Mauro ALLEGRANZA below, one would think: So, the concept is the intension, and the class is the extension?

It has been hinted in the source, mentioned in my answer to virmaior (in the comments below) that the difference between “class” and “concept” were the following (I explain it a bit more extended than in the source, as I understand it, adding examples, but without really changing it in essence):

  • concept: − The fact that certain properties have been empirically found, is the motivation to define a new concept (comprising objects with those properties). E.g. the concept "wood" for ubiquitously growing plants that are a suitable material to produce spears and arches. – This new concept has been created as intensional predicate. In this sense Aristotle used it in his syllogisms. This might be called logic of concepts.
  • class: − A certain empirically found, additional property is attributed to an existing concept, e.g. the property "combustible" to the concept "wood". Hence, all woods are now members of the new class “combustible object”. – This new class has been created as a extensional predicate. In this sense class is used in Venn diagrams, and G. Boole used it about in this sense, too. This may be called logic of classes.

But now, the really big question follows, to wit, whether a class like “combustible objects” is a concept, or not. And whether a concept like “wood” is a class. This is the real reason for my question, because this has never been discussed, as far as I know.

In the case of “chair”, I imagine that, while everybody was sitting on the floor, some king once said that he wants to sit down conveniently and someone designed something like a singleton of a chair. Subsequently, all objects that were similarly agreeable to sit, were also called chair.

Is chair now a class or a concept? An how is it for more abstract “things” as for instance “discernment” or “equality” (in the Masonic/communist/French Revolution sense)?

If it were true that concepts are different from classes, in the sense that concepts do not have assigned parallel classes, and vice versa; this would not merely be a theoretical issue, since it would imply that philosophy and science should increase its focus more on concepts, and less on classes.

A further question would also be, whether there exist special (intrinsically “aristocratic”) classes, which have been automatically upgraded to concepts and vice versa.

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  • In whose logic are these terms occurring in this way? – virmaior Jun 05 '17 at 05:19
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    Usually, a class is the "extension" of a concept, i.e. the colelction of all and only those objects that fall under the concept. The class of man (and women) is the extension of the concept humanity. – Mauro ALLEGRANZA Jun 05 '17 at 05:57
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    In the same way, the concept chair has as extension the class of all chairs. – Mauro ALLEGRANZA Jun 05 '17 at 11:03
  • @virmaior: The only text where I found really interesting discussions about this, was in German: Enzykopädie Philosophie und Wissenschaftstheorie, ed. Mittelstraß, vol. 1, 2005, p. 391: “Begriffslogik” and vol. 4, 2010, p. 229: “Klassenlogik”. –  Jun 05 '17 at 16:31
  • Classical logicians often conflated classes and concepts, or extensional and intensional terms, as they are now called. Even Frege, who distinguished them, sometimes lapsed. Only the rise of axiomatic set theory brought about the strict separation of extensional meanings (it was completed by Hausdorff in 1914). They are handy due to technical convenience, but the class of all things falling under a concept (i.e. its extension) is rarely referred to colloquially. – Conifold Jun 05 '17 at 23:18
  • @Zeus that information should have been included in your original question. Moreover, specifically what made the discussion interesting should be included too. We can't read your mind and there's 2500 years of philosophy which means words have been used in myriad ways over that time period. – virmaior Jun 05 '17 at 23:23
  • this has never been discusses, as far as I know. in a different vocabulary, this has been discussed since Aristotle and is a major component in the debates in medieval philosophy about conceptualism, realism, and nominalism (http://www.newadvent.org/cathen/11090c.htm , https://en.wikipedia.org/wiki/Problem_of_universals ). In the broadest sense, this has been discussed since Plato in the West. – virmaior Jun 06 '17 at 02:11
  • Morphing questions into something else is a bad practice, what you are asking now should be asked in a separate post. However, whether something is a class or a concept is not a big question, trivially nothing is. What you are describing is rather evolution of concept extension over time, which is also a well explored issue, see causal theory of reference and natural kinds, but very distinct from the original one. – Conifold Jun 06 '17 at 02:21
  • @virmaior and Conifold: But my question was: Is a chair a class or a concept? And Mauro ALLEGRANZA said that it is both. But if it is both then the whole question has never been really discussed! I knew the article "Problem of Universals" in my philosophy dictionary. They discussed it, completely sluggish. But intrinsically "this has never been discussed."
    If it had been really discussed, the result would be visible in philosophy and science. Thus, I will have to do it by answering the question myself, and then you may downvote me.     –  Jun 06 '17 at 02:52
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    That is not what Mauro said, he said that to the concept "chair" there corresponds the class of "all" chairs (and such class is not really well-defined due to vagueness, which is why classes are mostly confined to mathematics). The "whole question", the way you phrased it, is just whether to call two different things by a single name for brevity. Evolution of concept's extension, or reference, i.e. of the "class" it singles out, over time is a separate issue. There may also be "this" which was not "really discussed", but it is unclear from the current phrasing what that is. – Conifold Jun 06 '17 at 03:42
  • @Conifold: “call two different things by a single name”? – No, I just formulated the question a bit idiotically unless you subcribe that it must be [on hold / unclear asking]. – “What is the difference …?”, may surely be answered other than as unification. – You want to know in advance what “this” is, which not really discussed? I may tell it only enigmatically or else the surprise would be spoiled. It is a chain of projections of identity having started 2000+ years ago and pervading all areas, founded on oriental religions: personal identity – chemistry – philosophy – physics – politics. –  Jun 06 '17 at 04:51
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    This is not a site for enigmas and surprises, please see our Help Center, nor is it a site for discussions. Please try to formulate your questions more clearly and in a form with at least a hope for a more or less unique and non-subjective answer. – Conifold Jun 06 '17 at 05:01
  • Intrinsically "this has never been discussed." is not the same as this has never been discussed to my liking... Also, take this as a lesson to ask your question clearly enough the first time that people know what you're talking about. I'm not Athena; I didn't pop out of your head with wisdom as to what you're thinking -- I have to read the words and infer the question from there (which is exactly what Conifold, Mauro, and I all did not take away from the originally cryptic question). – virmaior Jun 06 '17 at 05:25
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    "Is [a] chair now a class or a concept? " Neither: it is an object belonging to the class of all chairs and falling under the concept chair. – Mauro ALLEGRANZA Jun 06 '17 at 06:26
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    Related to your question about the "origin", we may sketch two different approaches: (i) the Platonic one: the concept of chair is derived from the metaphysically "prime" Idea of chair and all individual chairs (objects) are chairs because they share the basic properties that are intrinsec to the original Idea. – Mauro ALLEGRANZA Jun 06 '17 at 06:28
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    (ii) the Aristotelian one: the concept chair has been "abstracted" from the individual chairs "collecting" together the common properties shared by all similar objects. – Mauro ALLEGRANZA Jun 06 '17 at 06:30

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In classical set theory, you are talking about dual representations of a collection via intension and extension. Each of these is equivalent to the other.

A concept selects the class of its applications, even if those are not very clearly defined or connected. And any defined class represents a concept, although it may be a complex one that is not very usable.

Developing semantics move fluidly back and forth between these two representations of the same thing, refining the boundary. We have almost no other way of refining or testing concepts than by choosing elements out of classes. So in 'nominalistic' worlds where these two things are distinguished instead of being unified, relatively little progress can be made reasoning about them.

'Chair' is neither of these. It is a noun. It represents both a thing meeting a definition, and therefore the class of such things, and the collection of criteria for being one.

If I say 'consider a chair' your mind might not immediately turn to a given site for sitting. You can be considering that chair in an abstract way defined entirely by the intent that it be able to serve the purpose of sitting. You might spontaneously generate test cases later.

But if your mind does immediately call up an inventory of test cases, this is not wrong either, as long as you can adapt the inventory as reasoning about the chair in question continues.

So the word does not necessarily demand either of these representations exclusively.

At the same time, ultimately, classical set theory fails us. It is a model, and not a fact.

If we take the unity of a definition, a class and its concept too seriously we end up with deductions like Berkeley' proof that there are no new concepts: Once we have the notion of being conceivable, every concept is in that class, so it is concept that already existed. By this logic we already know everything by virtue of imagining the state of knowing everything.

But this is not necessarily best addressed by discarding our tools. We need to think more deeply about how the abstract tool is embedded in reality, not invent nonexistent abstract distinctions that protect it into uselessness.

  • It was very valuable to see how you think. But the idea of a dual representation of a collection is strange, because a collection is a class. How can you be sure that an element of a class (or set) has really a concept? The problem which arises, is that the identity of a thing is not guaranteed merely by the fact that it is element of a class. ... –  Jun 09 '17 at 02:42
  • This Port-Royal method to see the world, suggests that non-identity and identity make no difference. But this is the dangerous Rumpelstiltskin’s principle. As you may see here the whole thing is not a question of nominalism, as you erroneously claim. –  Jun 09 '17 at 02:42
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    I am sorry I bothered to answer a question that is in no way in question for the person asking it. I will move to close the question as an attempt to push a personal philosophy. –  Jun 09 '17 at 14:26