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If something cannot be defined using outside references, does that mean that such a thing does not exist?

For example, Totality (supposed to mean absolutely everything including this statement) cannot be defined without self-reference since there is no "outside" references available to create a definition. Does that mean that the concept of "Totality" is flawed?

How does philosophy treat situations like this? - "I am because I am"-situations.

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Idea: another approach to this question could be ontological, e.g. Is there a situation where a concept does not fit some category? and what does that imply about its existence?

  • Related: Limitations of definition. I haven't quite read it, but I see a lot of philosophers' names there. – user3164 Jun 5 '13 at 15:00
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    The point of a definition is to explain the term being defined. If you know a term used, then you can get away with not knowing what it means (in terms of a more primitive notion). In the case of "Totality" as you describe it, the answer to the question "But does that also include X?" is always "Yes". In fact, you could say that the set of a term's usages provide a sort of extensional definition of the term. – David H Jun 8 '13 at 12:53
  • Nice question. In philosophy beyond the Academy the problem is solved by conceding that the Unity that is All cannot be positively described. To award it positive or partial properties would be to deny its Unity. One subtlety would be that the All cannot be a concept, it would be inconceivable. This implies that we cannot state it exists or exists-not, and we see just this claim in mysticism. For more check out 'non-dualism' or Kant's 'thing-in-itself'. . – PeterJ Sep 21 '17 at 10:16
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You can argue that existence is not a property of things, but of descriptions. If it were really a property of things, then nonexistence would also be a property of things, but you would never be able to apply whatever test you wanted to apply to see whether the nonexistent thing really was nonexistent. I cannot take my purple unicorn and feed it to the nonexistence-detector to find out that there is no purple unicorn.

What we really evaluate with the apparent property of existence is the description of the thing that may or may not exist. That makes really determining the existence of something with no description awkward. But a description is not necessarily a definition. Jon Jay Obermark, the author of this post, the owner of Elke and Hank Molsbee (my dogs), the person who answers my phone number, etc. are all descriptions of me, and any of them should be able to determine that I exist. Still, do any of them really define me? Things can be referenced and described, and their existence implied, without knowing any actual definition.

And some of those things may or may not have definitions. We can discuss the boundary of France. But we know that the length of this boundary is vastly different at many different scales, and a some scale, France is made up of relatively isolated individual particles and really has no boundary at all. Still, we would like to think the boundary exists, as a complex network of all these interrelated descriptions, none of which can be a complete definition. We have fought enough wars over it that if it didn't exist we would be very sad.

On that basis, it would not be fair to link existence to definability.

Totality is a predicate that just says yes whatever you apply it to. That is a pretty reasonable predicate to put into our existence checker. But I do agree that if you feel like you have defined totality, you should be able to do things like apply 'comprehension' to it and get a real answer to Russell's paradox. I don't think that has to mean it doesn't exist, only that it cannot be combined with other concepts in specific ways -- the same way that it might be highly unwise to attach the notion of the boundary of France to the idea one should measure it.

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"Outside definitions" are neither necessary nor available. Everything you know and can speak about belongs to your domain of experience or can be reached by combining elements of this domain.

When you start your life, you have not many words except lala and mama or so. Every object you have to learn is shown you as an original or as a picture or a gesture by your teacher, mostly your mother, and you are told its name. Later more abstract notions and their names are added.

Leopold Kronecker, a very great German mathematicians said: "Often it has been said that mathematics should start with definitions. The mathematical theorems should be deduced from the definitions and the postulated principles. But definitions themselves are an impossibility, as Kirchhoff used to say, because every definition needs notions which have to be defined themselves, and so on." [Leopold Kronecker: "About the notion of number in mathematics", Public lecture in summer semester 1891 at Berlin – Kronecker's last lecture. "Sur le concept de nombre en mathematique" Retranscrit et commenté par Jacqueline Boniface et Norbert Schappacher: Revue d'histoire des mathématiques 7 (2001)]

So everthing is defined exclusively from inside. And of course all particles of the universe exist and all thoughts that ever will be thought and all sets and Russell's male barber who shaves all men who don't shave themselves. Only logic is not fit for all conceivable cases.

  • "Russell's barber" is a concept that has no instantiation. Namely, there is no such situation (village plus barber). It is not in any way a paradox except if one makes inconsistent (worse than unsound) assumptions such as naive set theory. Note that it is perfectly possible to have a set theory with a universal set (NFU) or a type theory with a universal type (the first-order theory of Turing machines where each TM is also the type of all TMs that it accepts). The latter is concrete and shows clearly that a universal type is not inherently problematic. – user21820 Sep 10 '17 at 9:30
  • Russell's Barber has the instantiation "Russell's Barber". Because we all know what is meant by this definition, like we know the pink elephant and the smallest real number and other definitions which have no realization. There are definitions that define possible or realizable objects and such which define non-realizable objects like the fraction the square of which is 2. – Heinrich Sep 10 '17 at 11:22
  • No. By instantiation I mean the same thing as realization. There is absolutely no realization of "Russell's barber". And if you're not familiar with set/type theories that have a univeral type, I don't think you're qualified to judge whether "logic is not fit for all conceivable cases". – user21820 Sep 10 '17 at 11:29
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    The text "Heinrich" is not the same entity as the Heinrich I'm now talking to. "Heinrich" is something that I can put on a piece of paper. Heinrich is someone I can't physically touch, much less put anywhere. The two do not have the same properties. Similarly the mere phrase "Russell's barber" is just a phrase and is not a barber of any sort. Concerning set theory: it's not self-contradictory even if it is nonsense, but you're not qualified to judge that. – user21820 Sep 10 '17 at 12:10
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    @Heinrich: I will cease discussion if you insist that you are correct about the standard set theory in mathematics today (ZFC), because you are totally wrong. – user21820 Sep 10 '17 at 16:36
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Your question basically: "If something cannot be defined using outside references, does that mean that such a thing does not exist? For example, Totality (supposed to mean absolutely everything including this statement)"

Thinking about your question and Totality:

A good definition for Totality is "everything". "Thing" is an accepted outside reference and "every" is an accepted concept, therefore Totality is acceptably defined.

Thinking about the first part of your question with regard to existence and definitions using outside references. The question was: "If something cannot be defined using outside references, does that mean that such a thing does not exist?

The answer is no, because "If something cannot be defined" means something exists.

The answer relates to materialism and idealism. Where do things originate from? Do material things originate from ideas or do ideas originate from matter? I do not really know whether ideas or matter existed first. Did ideas exist before humans or did humans exist before ideas? It is not advisable to prioritize idealism or materialism, because the two philosophies are interrelated. Matter influence ideas and ideas influence matter, without a doubt. Let's say ideas and matter have always existed and they are both "outside references".

I could, i.e. say intequities, the new idea exist. Another person could ask, what intequity is. If no defining follows, it will affect the existence of the new idea intequity. The word intequity (capital of ideas) was first used for research about Accounting of ideas, by combining the words 'integrity' and 'equity'. After that, "intequity" was used in business names. Using the word as names, did not define the idea, but without a doubt the businesses exist. Using references to matter and ideas thus seems to ease the defining of something new.

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