Frege famously said horse is not a concept (it is an object). When we consider the sentence 'Socrates is a philosopher', 'Socrates' is an object and 'philosopher' is a concept, and there is a copula, a linking word 'is'.

Hence we understand that horse is not a concept but an object.

But, now consider the sentence 'Socrates is a man'. 'Socrates' is as an object, but so is 'a man' - it is a genus as is horse; but also going by the example above, 'man' is a concept.

One might resolve this confusion in that 'man' when it acts as the subject of a sentence is an object, and when it is acting as the predicate it i a concept.

Is this right?

Then we should conclude that horse is both an object and a concept. Or a sublation of the two?

Is this right too?

Frege himself appears to address this in his On Concept and Object:

It must indeed be recognized that here we are confronted by an awkwardness of language, which I admit cannot be avoided, if we say that the concept horse is not a concept [. . . ] [O]ne would expect that the reference of the grammatical subject would be the concept; but the concept as such cannot play this part, in view of its predicative nature; it must first be converted into an object, or, more precisely, an object must go proxy for it

  • 1
    Can be of interest Kelly Dean Jolley, The Concept Horse Paradox and Wittgensteinian Conceptual Investigations (2007). May 27 '14 at 13:00
  • Concepts are not what we know, but whereby we know.
    – Geremia
    May 30 '14 at 14:53
  • @Geremia:Sure, thats the Kantian perspective. May 30 '14 at 15:22
  • @MoziburUllah: Wouldn't Kant would say concepts are what we know?
    – Geremia
    May 30 '14 at 15:30
  • @Geremia: There is quite a bit of technical vocabulary associated with the Kantian perspective. What are known as (conceptual) categories are whereby we know, then concepts synthesised by the intellect are what we know. The categories are (experiantially) a priori, whereas concepts are (experentially) a postereroi. May 30 '14 at 16:23

The question is a bit confusing, so let me separate the two issues that are being discussed.


First, there is Frege's concept horse problem. It has been a topic of much discussion and there is no one way of explaining exactly what the problem is. If I could summarize in a few sentences, I'd start by saying that Frege is committed to the idea that:

(1) definite descriptions (expressions of form 'the φ') denote objects of type ⟨e⟩, that is, individuals.

That is why, Frege's analysis of a sentence like "the concept horse is a concept", is the following:

(2) [the concept horse]⟨e⟩ + [is a horse]⟨e,t⟩

⟨e,t⟩ is the type of intransitive verbs like "walks", "is red", and so on. The two types ⟨e⟩ and ⟨e,t⟩ are combined to give an expression of type ⟨t⟩, a boolean. The problem is that the concept horse should be a concept (a thing of type ⟨e,t⟩) and not an object (a thing of type ⟨e⟩), but because of Frege's commitment to (1), he's forced to say that the concept horse is actually an object and not a concept.


Now, let's look at the other stuff you said, without talking about the above mentioned problem. Consider:

(3) Socrates is a philosopher.

You explain that in (3), 'Socrates' is an object (type: ⟨e⟩), 'philosopher' is a concept (type: ⟨e,t⟩), and there is a copula 'is' linking the two. That seems right. I'd add that 'a' in (3) is semantically vacuous, and that 'is' is an identity function from concepts to concepts (from ⟨e,t⟩s to ⟨e,t⟩s), so (3)'s structure is:

(3') (([is]⟨⟨e,t⟩, ⟨e,t⟩⟩) [philosopher]⟨e,t⟩)⟨e,t⟩ [Socrates]⟨e⟩

'Philosopher' & 'is' are applied to give 'is philosopher' of type ⟨e,t⟩, which is then applied to 'Socrates' to yield ⟨t⟩. Next, you consider the following sentence:

(4) Socrates is a man.

You say that Socrates is as an object (type: ⟨e⟩), but you also, for some reason, claim that 'a man' too is an object. By previous reasoning you say that 'man' must be a concept, so how is 'man' both an object and a concept. 'A man', however, is not some particular man, so it's not an object. 'A' is semantically vacuous, and 'man' is an ⟨e,t⟩, which combined with an identity combinator 'is', yields the concept 'is a man' (type: ⟨e,t⟩), which when applied to 'Socrates' gives us a ⟨t⟩. Nothing confusing going on there.

You make some plausible (and familiar) conclusions about how we could go about resolving the concept horse problem. It is, for example, an attractive proposal to say that 'horse' is both an object and a concept, depending on its syntactical role. As Frege says in that excerpt: we could say that horse is a concept (of type ⟨e,t⟩), but when it occurs in object positions, it is automatically converted to an object (of type ⟨e⟩).

An analogous situation happens in programming when you have a floating-point expression like 4.0 and you pass it to sqrt (the square root function), which is defined only for non-negative integers. 4.0 is converted to 4 and then sqrt(4) yields the expected value(s). 4.0 (or horse) stays what it is, but in an expression like sqrt(4) (or 'the concept horse is a concept'), it is automatically converted to an acceptable type so that the expression can have a meaningful value. How plausible a solution this is to the concept horse problem? Who knows? It's a proposal and will no doubt have its pros and cons.


➀ Cumming, S. (2014) λ–Calculus and Type Theory, Lecture Course (Winter), UCLA.
➁ Heim, I., Kratzer, A. (1998) Semantics in Generative Grammar.

  • First I'm not familiar with the gylph (small box) in your first quoted line - (small box)e(small box) - does it stand for something particular or is just for emphasis? Perhaps the question might be marginally less confusing if I said 'Socrates is a horse' rather than introducing 'man'. I'm only familiar with the theory of descriptions from Russell, did he take that from Freges work? May 27 '14 at 17:27
  • (1) Types are used in natural language semantics (look at Heim & Kratzer, for example). To explain what combines with what I've typed them here. You can assign different types to different expressions, as long as you make sure that there are no inconsistencies. (2) Russell's theory of descriptions is different from Frege's. Russell would say that 'the concept horse' is untyped, not that it is an (e,t) or an (e). Russell, as you know, analyzes 'the x if F' as 'some x is an F and every y that is an F is identical to x'. The horse problem isn't a problem for Russell, but for Frege it is. May 27 '14 at 17:35
  • Very interesting! But I think is useful to separate the "interpretative" issue : why Frege's system is in trouble with the (in)famous "concept horse" paradox ? from the "general" explanation. I think that the problem for Frege (see huge literature about it) is that he assumes two "postulates" : every term of the "perfect language" (the Begriffsscrifht) must have meaning (both sense and reference) and there is only one "universal" language with all the "universe" as his domain of discourse. Today, we separate the issues : 1/2 May 28 '14 at 12:38
  • In "perfect languages" like formal lang of math log, we use - following Tarski - the "hierarchy" language/meta-language/meta-meta-...; thus if we use the term "horse" in the language, we do not speak of objects and concepts in the lang, but in the meta-lang. Regarding natural language, following Wittgenstein, we accept the fact that it is not perfect; I dare to say that natural language "works" so well exactly because it is "circular" and "inconsistent". With natural language (pace the Tractatus) we can speak of "all", also about what we cannot say ... 2/2 May 28 '14 at 12:41
  • You have the integer-floating point thing backwards. Basically every language defines sqrt(x) for x in non-negative floating point numbers, and 4 is an integer, so sqrt(4) works but requires a conversion to 4.0 (i.e. floating point).
    – Rex Kerr
    May 28 '14 at 16:23

Well, your questions were among the most basic lessons of a short Logic handbook I have which is based on classical Aristotelian logic as further refined and developed by muslim classical logician-philosophers.

According to my textbook, a proper noun such as "Socrates" is categorized as a particular concept which will necessarily have only one particular external referent (one "object" to borrow from your terminology), whereas "philosopher" is a general or universal concept that can (or does) refer to multiple individual referents or instances of the concept; and so does "horse".

So, it's really simple. I think you are heedless of the fact that every object once reflected in our mind becomes an image, and once that image is associated with a word, a concept emerges. Concepts forged as such are known as particular non-abstract concepts.

But human mind can also forge another type of concepts (such as "philosopher") and this takes place through the process of abstraction. That is by taking perceived similarities among a particular species of objects and arriving at as such universals as philosopher, man, rock, tree, etc.

It is noteworthy, that these examples are only one category of abstract concepts as they come in other types as well. Concepts such as "cause", "length", "universal", "heavy" are examples of other varieties of abstract concepts which are not abstracted from species of concrete reality, though, but from what we perceive as laws, relations, dimensions among or within concrete objects.

  • 1
    Intriguing, but I'd say heedless is a little strong: "every object once reflected...a concept emerges", sounds similar to Kants notion of a concept, except these are forged with reference to categories which are a priori. Do the muslim classical logician-philosophers include Ibn Rushd (Avveroes)? May 27 '14 at 17:17
  • @MoziburUllah I apologize for "heedless"; I couldn't think of a more suitable word. But I thought you might have missed the very simple difference between the concept and the referent, and the common confusion rising from their application: "horse" can be regarded both as a concept (when in mind) or as a referent (the actual horse). And the problem is solved as simply as that. In application we should be wary of confusing the two.
    – infatuated
    May 27 '14 at 18:23
  • And I'm not closely familiar with Kantian epistemology, but muslim philosophers deny the existence of pre-existing categories in human mind, if that's what you meant by a prior categories. And as for logician-philosophers, yes, Ibn Rushd is one. More prominent examples are al-Farabi, Avicenna (both predating Ibn Rushd) and Khaje Nasir. These are a succession of polymath thinkers who drew upon each others' work. And they rose to much higher prominence among muslim thinkers than Ibn Rushd.
    – infatuated
    May 27 '14 at 18:27
  • And as for the confusion I should add that it can occur with every concept including the particulars, e.g. Socrates.
    – infatuated
    May 27 '14 at 18:45
  • (1) Sure, its a useful distinction; I think Frege is aware of this (his Sinn & Bedeuting) but this question isn't concerned with that distinction, but in a sense a grammatical one. Having said that, the distinction is a useful clarifying one which would have helped in giving more shape to the question. (2) Presumably from the same sense as the mind being a tabula rasa; (3) What would you recommend as texts for these polymath thinkers? I'm only vaguely acquainted with them - in the sense of encyclopedia entries like wiki or the SEP. May 27 '14 at 18:53

I think the problem comes from our natural overloading the word "is." Consider instead it's two possible meanings:

  • "IS A" - something is an instance of a concept
  • "EQUALS" - the two things are one-and-the-same

Then you can say that a "Socrates IS A philosopher" - he is of that species, but is not the general concept of philosopher. You can also say that "Socrates EQUALS that philosopher," i.e., that man Socrates over there and that philosopher who taught certain things are the same person.

  • 1
    If you want to be precise, you have to add also "inclusion"; in "all men are mortal" the verb "to be" means set inclusion ... May 27 '14 at 14:33

Concepts are whereby (quo) we know, not what (quod) we know. Confusing the two is known as the "quo/quod fallacy."

See this article for more information: "The Quo/Quod Fallacy in the Discussion of Realism" by the semiotician John Deely, which discusses how it is really a trichotomy: quo / quod / in quo.

See also this book, which is about what "concept" is.

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