# What is the name for this "endless definition" problem?

Say I am trying to define "apple", I define it in terms of a specific way by which atoms, molecules, and ions are organized. Then I'd have to define those atoms, molecules and ions, and I do so in terms of elementary physical particles. But then those elementary physical particles, and the way they behave, remain "unexplained", i.e. I accept them as they are without question.

The result of this chain of definition is that, either I end up with an endless chain, or I stop somewhere where I just can't go any further, and I'd have to live with the fact that "it is what it is".

What is the name of this problem? What are the related terms I should look up?

Thanks a lot for any pointers!

• What exactly is the problem that you want to name? A definition of A in terms of B is successful iff either B is understood better than A, or there is some C, different from B, such that C is a successful definition of B. That's what I took from what you said, but I don't see why it's problematic. Sep 4 '13 at 4:32
• Good question - I definitely think this principle deserves a name. Such a name would summarize in a single word the problem with certain mathematical philosophies (e.g. the philosophy of N.J. Wildberger) that claim that mathematics doesn't need axioms, all it needs is definitions. It just doesn't work, because of the problem you describe, wherein there is necessitated infinite regress of undefined terms, resulting in the impossibility of formally specifying any formal systems and therefore the impossibility of doing truly rigorous mathematics. Nov 19 '15 at 3:13
• There is such a thing as knowledge by presence; you know an apple by seeing it, holding it and eating it; definitions don't mean anything unless they refer. Mar 4 '16 at 1:46

The name of the problem is: Münchhausen-Trilemma

It occurs in various fields, and always consists of having 3 options, which all face problems.

Option 1: Infinite Regress - which may be bad, because how does a word gets its meaning, if the chain of defining words is infinite.

Option 2: Fundamentality - which may be bad, because what is fundamental seems to be arbitrary and unjustified.

Option 3: Coherentism - which may be bad, because according to this option you define a word, after some or a lot steps, with itself. Circular reasoning is most often disliked.

I tried to include your problem into the general case, but it should help if you check out the relevant wiki-article

• Also known as the "Agrippan Trilemma". Sep 4 '13 at 17:42

I think there are two related but distinct issues involved in your question.

First, there is the issue of compositionality, i.e. defining something in terms of its constituent parts. Then, there is the issue of semantic holism, by which you cannot define something unless you have defined something else, and thus you can never reach a proper definition of the original concept, since you would need to have a complete understanding of the whole language. This is a strong form of semantic holism, and as far as I know it has been strongly criticised, since sense can be constructed through mechanisms other than mere composition, such as contextual and pragmatic information.

It's called a failure to recognize ostensive definitions.

https://en.wikipedia.org/wiki/Ostensive_definition