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To begin with, consider Chomsky famous construction: "Colorless green ideas sleep furiously". All the words respect a grammatical construction. But "colorless green" seems like a contradiction.

If someone says "beautify the beauty" or "value the value"(the first term as verb, the second as a noun, in the sense of "making value more valueable")

I'd like to know the implications from a logical perspective. The trouble is in the relation between the action and the object of it, as "beautifying" is a verb derived from "beauty" itself, so it seems like an impossible action and maybe not logical. I think "beautify" could only be applied to objects that are not "beauty" itself.

I have the intuition that this constructions do not make sense, but I'd like to know what kind of formalization I could use to demonstrate this. Possibly a categorization.

Being X an abstract noun, and Y a verb derived from X, can Y be applied to X? If yes or no, what is the argument? What I have in mind excludes the sense in which Y means "to make use of X". It would be something in the sense of "making X more X-like".

If someone thinks this question should migrate to linguisticsSE, please comment.

  • If you mean these sentences in the most literal way possible, where the first one means "make the concept of beauty (more) beautiful", then I would think they are more or less meaningless, in that I can't read anything in them that holds meaning for me. They seem to me like sequences of words that do not fit together. – Cerberus Jun 18 '12 at 3:24
  • yes, it feels like a logical problem (or lack of it), I'd like to know what kind of formalization would demonstrate the problem in these sentences – Tames Jun 18 '12 at 3:38
  • I think you would need meaning for formalization to be possible? – Cerberus Jun 18 '12 at 5:14
  • a formalized logic system will indicate which cases are possible and which cases are not, flawed ones that, as consequence, will lack proper meaning. I believe it must be a rather simple thing, the problem is that my knowledge in logic is very primary. I only need to find a reference to do the thinking. – Tames Jun 18 '12 at 13:13
  • Then how are utterances that have a logical meaning distinguished from those that do not? Can logic be applied to, e.g., the cow to the horse and never? – Cerberus Jun 18 '12 at 14:16
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One way to approach this is by Aristotle's metaphysics. According to Aristotle, everything there is can be classified in one of the following ten categories: (1) substance; (2) quantity; (3) quality; (4) relatives; (5) somewhere; (6) sometime; (7) being in a position; (8) having; (9) acting; and (10) being acted upon (1b25-2a4).

According to his definitions, a substance is something that cannot "be said of" nor "be in" another thing. And substances come in degrees: primary substances are individuals, like this particular man or that particular horse. Next on the scale, we find species (e.g. "man", in the sense of human, encompassing the whole class of human beings) and genera (e.g. "animal"). Substance has a primacy over the other nine categories, since all of them exist "in a" substance. A quantity, for example, refers to how many items of a certain substance we are talking about. Similarly for all the other categories, known collectively as accidents.And, among substances, the primacy is reserved to the primary substances. Everything has to ultimately rely upon the existence of individuals. We can only talk about man – as a species – if there are particular men in the world, so we can apply the name "man" to them and say things like "Socrates is a man".

In particular, the category "quality" is important to your question. Although Aristotle does not give us a precise definition of what quality is, we can grasp the concept with little difficulty. When we say that a certain horse is beautiful, it is clear that we are ascribing a quality to the horse. Consequently, we can also beautify a horse, that is, we can increase that quality in the horse.

So, what about "beauty"? Is it also a substance? For linguistic reasons, we are sometimes led to think so. After all, "beauty" is a noun and therefore can be modified by an adjective, like "beautiful". Likewise, it can be the object of a verb, like "beautify". Semantically, of course, the phrases "beautiful beauty" or "beautify the beauty" are problematic (the very heart of your question, after all). But syntactically, they are ok. As in the famous example "Colorless green ideas sleep furiously", which is a perfectly grammatical sentence, but full of self-contradictions. But the fact that "beauty" is a noun doesn't change the fact that it still is quality. Moreover, there are no individual beauties, that exist by themselves, detached from substances and to which we can predicate things.

A bit more formally: "beautify X" means "increase the quality beauty in X", where X is a substance. As we have seen, beauty can only be a quality, not a substance. So we cannot substitute beauty for X, in this case. In other words, "beautify the beauty" makes no sense at all.

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It's a rhetorical figure known as figura etymologica. Your examples don't qualify as tautologies in my opinion. They are imperatives, not declarative sentences. Apart from that, something like "X lives a life." wouldn't necessarily be true either. ("A life is a life.", however, would be a real tautology.)

  • My examples were actually reductions of sentences I had in mind. The complete idea would be "When X happens, beauty is beautified", for example. Although I see the relation with the rhetorical figure you mentioned, I'd like to know the considerations on this from a logical perspective. There is some difference between "live life" and "beautify beauty", as in my example the action of "beautifying" would modify "beauty" itself, which is not the case of "live life", a homologic example could be "enliven life". – Tames Jun 17 '12 at 11:24
  • I agree that there is a difference in "live life" and "beautify beauty". In your edited question you ask: "Being X an abstract noun, and Y a verb derived from X, can Y be applied to X?", "[...] in the sense of 'making X more X-like'". I don't really see a logical problem here. To me, that's just a nice example of a figura etymologica. In fact, given your formulation, you could substitute the verbal use by something like "amplify"/"reinforce", or even "instantiate", maybe "constitute". So, "beautify beauty" becomes "amplify beauty". Only the rhetoric effect is lost in my opinion. – danlei Jun 17 '12 at 15:40
  • I don't see the same sense in "beautify beauty" and "amplify beauty", for amplifying beauty could be the beauty of a person, a room, etc., i.e. making a person/room more beautiful. In "beautify beauty", it would be like making abstract beauty more beautiful. Do you see my point here? "Amplify beauty" could be "making Z more X-like". – Tames Jun 17 '12 at 15:49
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    "Beautify beauty" can IMO refer to the beauty of a person just as much as "amplify beauty". If I understand you right, you're saying that "the beauty" can't, maybe related to the problem of self-predication of platonic ideals, be made more beautiful. But if we take such ideas as nominalized attributes/predicates, we avoid the problem of self-predication. Also, a sentence like "perfection beautifies beauty" (just an example, not trying to define beauty here) can be read just as a description of what constitutes or defines "the beauty", or what amplifies it when used as an attribute. – danlei Jun 17 '12 at 16:41
  • I agree that considering all possible meanings of "beautify beauty", "increase someone's/something's beauty" is one of them, but only a subset of it. I'm not familiar with the problem of self-predication of platonic ideals. Do you think I'm having a platonic approach to the problem? I understand the statement "perfection beautifies beauty" as "perfection increases beauty", as "perfection is one of the predicates of beauty", therefore "beauty is perfection" would be an analytic judgement. Perfection could make a person more beautiful. But, can we say "beauty is beautiful"? Tautologic, isn't it? – Tames Jun 17 '12 at 17:04
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This is a linguistic question, not a philosophical question. And, like most linguistic questions, the answer depends on context.

Limiting ourselves to English: some sentences of the form you describe are perfectly natural. For example, "I'd like you to dust the dust from the windowsill," or "Please paint the paint more evenly."

Others, such as "Confirm the confirmation to proceed" are very awkward, yet understandable.

Still others, such as "Beautify the beauty, please" seem quite artificial; one would have to imagine an extremely idiosyncratic beautician who would issue that command to his underlings.

I don't think there is any point in trying to create a general rule here; the necessary list of exceptions would render the exercise rather pointless.

  • "Dust the dust" and "paint the paint" do not capture the sense I'm trying to point out here... the verbs "paint" and "dust", have the sense of making use of paint and dust. In these cases, to achieve the sense I'm looking for, would be "paintify the paint", "dustify the dust", something like, "making paint more paint-like". Do you get it? Maybe "confirm the confirmation" is ambiguous in this sense, so I'll take this example out. – Tames Jun 17 '12 at 13:18
  • Removing that example doesn't change the thrust of my answer-- that this "problem" is linguistic and not philosophical in nature, and is tied to particular usage patterns in specific languages. What is it that you are trying to achieve here? What's the problem, really? – Michael Dorfman Jun 17 '12 at 13:26
  • As I see it, a linguistic problem does not exclude logical reasoning, even though they are not the same thing, it is just a matter of where the consequences appear. I'm concerned with Marx's argumentation in "The capital", where he makes use of a construction like this. I sense a problem in it but I'm not enough knowledgeble in logic as to point out exactly what the problem is. It does have deep implications in the theory, if it turns out to be a paradox or something alike. – Tames Jun 17 '12 at 13:36
  • Could you post the example from Marx? The scenario is not reducible to logic, as there is no general rule concerning how verb- and noun-forms of abstract words are created; the sense is going to depend on the specific words in each case. – Michael Dorfman Jun 17 '12 at 14:05
  • I'm posting here my own translation of it, as my text is in portuguese. The idea appears in other parts of the chapter, but the one quoted here is the first one. It is something like "The circulation of money as capital is, on the other hand, a goal in itself, because valorization of value only exists in this movement, always renewed". – Tames Jun 17 '12 at 14:10
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I just wanted to make clearer a tautology in logic. According to wikipedia,

In logic, a tautology is a formula which is true in every possible interpretation.

Let's look at this closely:

A (well-formed) formula is a (finite) string of symbols built up by formula-building operations.

For example, let our symbols be (, ), ¬ (negation), → (implication), and sentence letters α, β. And let our formula-building operations be Σ¬ and Σ such that, for sentence letters α, β, Σ¬(α) = (¬α) and Σ(α, β) = (αβ). Let's stipulate that for our formal language, any formula that is not built up by our formula-building operations is not a well-formed formula, e.g. ¬→β) is not a well-formed formula.

An interpretation, according to wiki, is

an assignment of meaning to the symbols of a formal language.

The meaning assigned to the logical connectives such as ¬ and → are simply their truth conditions:

α) is true iff α is false.
(αβ) is false iff α is true and β is false; otherwise, true.

Now, for some examples of tautologies:

  1. ¬(α → ¬α)
  2. (αα)
  3. (α → (βα))
  4. (α → ¬¬α)

The first thing to note is that these are all well-formed formulas. The second thing to note is that no matter what you assign to α or β (true or false) -- this is, how ever you interpret α or β -- these will always come out true. Take a look at (3): If α is false, then the whole formula is true. If α is true, then (βα) is true, and the whole formula is true.

If we translate the example daniel gave ("A life is a life") using our symbols, we could get something like ((x is a life) → (x is a life)) which is an instance of (2) above -- and is thus a tautology.

However, this is assuming that "life" has uniform meaning in daniel's example, and I'm not convinced it does. For example, we could imagine the following statement being made: "I am against the death penalty. After all, a life is a life." Here, "life" does not have uniform meaning -- the second "life" we could interpret as "something that is sacred and cannot justifiably be taken away under any circumstances."

Here then, we'd get the following (informal) symbolization: ((x is a life) → (x is something that cannot be taken)). This is hardly a tautology or something true simply based on its formal presentation. After all this would be an instance of (αβ) which is certainly not a tautology as noted in defining the meaning of "→".

A tautology in logic is something purely formal: it is something that is true under every interpretation. "A life is a life" or "Money is money" certainly seems tautological and could be symbolized as such, but isn't necessarily tautological.

Hope that is clarifying. It should at least be clear that the examples you gave are not tautologies.


Russel's Paradox is certainly a logical problem. Let S = {x | xx}. We can ask whether or not S is a member of itself.

Assume that S is a member of itself. Remember that if any set is in S that set cannot be a member of itself. So, if S is in S, then S is not in S. Contradiction.

Now, assume that S is not a member of itself. Remember that S is the set of all sets that are not members of themselves. So, if a set is not a member of itself, then it is a member of S. Since we are assuming that S is not a member of itself, then S must be a member of S. Contradiction.

Thus, {x | xx} cannot be a set.

When people were first thinking about set theory, e.g. Georg Cantor, they defined a set as any definable collection. Russell's Paradox is the counter example to this naive conception of set. There have been other attempts at defining what a set is that avoids such a paradox; notably, G Boolos' paper on the iterative notion of set: a set is "built-up" from previous stages that way you could never get a set that was a member of itself which sidesteps Russell's Paradox.

  • I'm aware that Godel deals with differences between Cantor's and Russell's conception, so that, if I understood it right, Russell's formalization has it's owns flaws, or if it is flawless, cannot be demonstrated within it's own system, same thing with Cantor. I do not know the work of Boolos though. I'll look for it. Anyway I'd like to know if you think the problem I proposed is related to this. – Tames Jun 17 '12 at 13:29

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