Example is that the word unknown is not unknown so it doesn't define itself. Similarly French is not French, it's in English, and "long" is not long and only 4 letters short. That's by example my understanding of heterological and no real definition besides "true about itself".

English is autological since the English is in English and therefore "suits itself" but how does the law of excluded middle apply to these cases about themselves? Using the law of excluded middle, can we therefore apply the law of excluded middle to itself, assuming it is autological and follows its own rule so that either the law of excluded middle holds or we have derived a contradiction? It seems so and therefore the law of excluded middle is autological.

Like having a binary state of either /or is true about itself or false? Clearly a thesis of yes or no should have a binary state but having three or more states (yes / no / maybe / undecided) is also acceptable but does not "suit itself" since you either have at least 3 states or less, so having a number of states or a number is heterological.

Can these problems be formalized more how besides inspection we can tell whether an entity, system or person is autological (being like its name) or heterological (not being like its name for instance a person named Rock may not be a physical rock.)

How can we mean that something is no automatic without referring to automatics and there making it automatically (according to law of excluded middle) and therefore being automatic is automatically false and therefore it's true that there can be something automatic since it is automatically false.

Can you elaborate, develop, comment or answer I'll be very glad to know.

Can you number a property such as "not having a number" since if you can number the property of not having a number then nothing can exist that doesn't have a number so setting a boolean value for having a boolean value also contradict itself. If we introduce a boolean value that says that a formal language or method can't have a boolean variable then it contradicts itself since a boolean for whether a boolean is part of the language can't have the value false since then it must have the value true.

Here is a reference to the paradox http://en.wikipedia.org/wiki/Grelling%E2%80%93Nelson_paradox

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    Any chance I could persuade you to clarify this a bit? In particular can you specify context -- provide details on the actual problem you are facing, and what you have found out so far? – Joseph Weissman Aug 17 '11 at 17:54
  • Dear Joseph, the problem is applying a statement to itself i.e. "Is heterological heterological?" If it is heterological, then it isn't heterological since then it describes other meanings than heterological which results in a contradiction. "Is autological autological?" is not a problematic statement since it's not defined as a remainder while heterological is defined as the statements other than autological. Also for example there is computer program language design where there are no boolean values allowed. This is a boolean value saying boolean is forbidden so the rule breaks itself. – Niklas Aug 17 '11 at 18:03
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    This seems to boil down to quoting. See the use-mention distinction. – Mitch Aug 17 '11 at 19:35

You seem to be playing with a variant of Russell's paradox.

If this sort of thing interests you, there are plenty of examples to be found-- second order logic is full of these types of problems, and attempts and formalizing them.

Personally, I don't find these paradoxes to be very interesting, unless they lead us to something more profound.


You need to be careful with the use of quotation marks here. A word in quotation marks is being mentioned, not used. The sentence "'French' is not French" is true. Because there I am mentioning the name of a language, and noting correctly that that is not the name of the french language in the french language. But the sentence, "French is not French" is a falsehood, since it asserts that the French language is not the French language. In other words, in the second sentence the word "French" is being used as the name of the French language. When a noun or adjective is being used it stands as the name for an object which the predicate describes as having some property. When a noun is being mentioned, the subject of the predicate of the sentence is just the word itself.

There are a bunch of great examples of fun autological sentences: my favorite is from Hofstadter.

"'Is meaningless unless preceded by its own quotation,' is meaningless unless preceded by its own quotation."

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