Theory of meaning, and abstract objects.

I take it that there are three views concerning the nature of meaning. They are:

1). Meaning as ideas in the mind. This view is from Berkeley. Concerning this view, there are suppose to be ideas in our mind, and complicated ideas are really conjunctions of many different simply ideas. So, the word "red" corresponds to the idea of red in the mind, and goldmountain is a conjunction of the idea 'gold', and 'mountain'.


2) Meaning as use. This view is from wittgenstein. The thought is that 1 is wrong. Take the word "red". In view 1, we can match the word "red" to the idea of red in our mind. According to W, view 1 is wrong. We can never match the word "red" with anything in the mind. What we can do is to see how certain words like "red" are used in different language games.

3)Meaning as reference. Kripki say it best when he said "the meaning of a name is it` s referent". So, the word "red" is meaningful only to the extend that the word refers to the universal.

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In set theory, for A, B are sets, the following is true:

1. A union B = B union A


The question is: why is 1 true?

Wittgenstain would say: 1 is true by stipulation.

Kripki would say: I is true because there are abstract objects.

mathematical fictionalism would say: There are no abstract objects. What we are doing is pretending that we have abstract objects, and look at the consequences.

If kripki is right, then there ough to be mind-independent sets just like people, and cars. Where are they?

My question is: why do you think 1 is true.