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I noticed that every logical theory seems to have a meta logic or language.

For instance, we say "x is so and so, it is different from so and so, therefore, x is y, etc."

We have not defined 'x' or 'so' or 'and' or 'it' or 'is' or 'different' or 'therefore'. And of course the meta language which allows us to even examine this as well is like so as well.

It seems that they clearly have meanings and yet the very framework of me writing what I'm writing now is itself under the assumption of a framework of things having meanings.

To even ask this question requires concepts. And even the concept of a concept is itself like so.

Can we define them all, including even the word define. Can we actually have it be so that all theories are defined and we have certain primitives? But then again, even the concept of primitives and non primitives and things and theories and these theories requiring this particular explanation is also a thing as well.

These are all frameworks. And yet the very question I asked right now is distinct from a question of which is not like it. Very curious, how difficult it is to truly have no idea.

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  • We cannot define everything. Dec 16, 2023 at 8:50
  • @MauroA so then are there undefined terms? But doesn't "undefined term" itself have a meaning? As well the concepts used to even say this now? Dec 16, 2023 at 9:02
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    We use natural language. How we learnt it? Reading a vocabolari? Dec 16, 2023 at 9:21
  • Fair enough. But I can't help but feel a bit stuck at the notion of unproven terms being used to ground our knowledge. Hmm Dec 16, 2023 at 9:29
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    You don't need to use symbols in all your definitions; you can just point at the sky and say "sky". People will figure it out.
    – g s
    Dec 16, 2023 at 9:37

2 Answers 2

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If you peruse a dictionary, it should be apparent to you at once that definitions in language are inherently circular. Any given word in the dictionary is defined in terms of other words which are themselves defined in the dictionary by other words, and so it goes on. What you have in your mind are various primitive conceptual building blocks associated with words, and as you master language you figure out how they fit together, rather in the way that you might figure out how the parts of a child's construction set inter-relate- this part goes with that one but not with this one, and so on. In everyday speech words have meanings that are attributed to them by speakers and listeners based on their experiences of having seen or heard the words used before. Few of us gain the majority of our vocabulary from a dictionary. Take the word 'despicable' for example- I have never looked up its definition in a dictionary, but having on several occasions heard the word spat from the mouth of an incensed nun at my infant school, I have a very visceral sense of what it means.

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  • Wonderful answer very enlightening. But I wonder, what are these primitive blocks and can we not question even the ideas "primitive" and "blocks"? Dec 16, 2023 at 19:10
  • for instance, how would you define NOT? it seems to be completely primitive Dec 22, 2023 at 20:34
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Can we define everything?

We can define everything that we understand, but this requires more than just words. Our natural ability to make sense of our environment is tantamount to an implicit definition of things in terms of each other. Words just come on top of that, as a sort of additional linguistic layer.

Perhaps the misconception is to think that you can for example define all mathematical concepts just using words.

Abstract words have to be defined using other words while concrete words have to be defined using ostensive definition, by pointing one way or the other at the objects.

Fortunately, children seem to have an awful lot of cognitive capacities allowing them to pick up what words are used to mean from repeated exposure to usage in context, which has the same effect as ostensive definition.

Verbal definitions come after the real battle, once humans already have an understanding of the things to define. You cannot make anyone understand what the word "sun" is used to mean if they don't already understand what sort of thing is the sun. Using just words to define each word couldn't possibly work.

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  • I suppose I meant concepts in general. For instance, the concept of a concept is a concept, and yet the words used to communicate that they are in fact a concept is still a concept. So we have a thing before it's definition. "concept" does not mean "apple", but yet they are both concepts. Dec 16, 2023 at 23:03
  • @GeraldRobertson "the concept of a concept is a concept." Trivially true. 2. "the words used to communicate that they are in fact a concept is still a concept." The word we use to say that a concept is a concept is a word, not a concept. A word is a word. A concept is a concept. No problem. 3. "So we have a thing before it's definition." Things presumably exist before we come up with any definition. No problem. 4. ""concept" does not mean "apple", but yet they are both concepts." No. The word "concept" and the word "apple" are not concepts. They are words. No problem. Jan 19 at 16:38

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