- Once upon a time there was a ... who ... .
- Imagine a ... such that ... .
- Let P, Q, and R be the vertices of a triangle in which all sides have the same length.
- Consider a country which ... .
- Let us say that person A and person B are one an the same person.
- Let us say the person we are talking about is me and that room we are talking about is the room we are in right now.
- Let us say that the radius of circle C is actually 3m.
- When I say "forward" I mean the direction in which I am now pointing.
Similarly, we can do what may be considered the opposite of identifying things: We can "make a distinction". For example, we may say: "Let us distinguish between 'The person who performs role A' and 'The person who performs role B'. In what we have said so far we have assumed these to be the same, but let us imagine situations where they are not."
Actually, the things just listed need not happen through language at all. Nature itself may "introduce new things", "make two things become one", "make an object disappear", or "split an object into two". And in a fairy tale, things can be "introduced" and made to "disappear" though magic. With computers one also "creates" ("introduces") and "deletes" ("forgets about") objects: For example, I am right now creating a blog post.
What I am getting at is: The operations I have described are very fundamental. Arguably, you find them in any computation, wherever you have cause and effect. They are certainly central to the contents of this blog. Whenever you see questions about what words mean/refer to (as used by some particular speaker in some particular situation), think to yourself that this is really about introducing things (words/concepts as well as things they refer to) and making identifications.
One type of identification deserves special attention: We may identify something we have "introduced" with something with which we can interact. This is very relevant to the questions about "how language is connected to the world". To deal with problems of this kind, imagine "a human-like being B in an environment E". You can then discuss how B interacts causally with E and how words that B uses are linked through causal chains to things in the environment E, but then you can either:
- Identify E with your own environment (and, optionally, B with yourself). This makes what you said about B and E "become real". It takes you from "mere ideas" to "actual things".
- Make assumptions on E that means it cannot be "our world" (for example, you can assume it has a number of dimensions that differs from what we are used to). The possibility of doing this means that noone can tell you that B and E must be in a certain way. You are free to see them as your own fictive inventions which you are free to shape in your own way. Make appropriate choices, though, and it will be undeniable that what you say is relevant to "reality".