How does indefinability affect existence?

Question

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?

Answer 1

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.

Answer 2

"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.

Answer 3

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.