...you could argue that everything is just an illusion and that there is nothing to explain because nothing can be explained, but that's a boring position, and it doesn't give any motivation for scientific study
I do not know what an illusion is FOR YOU, either; however, I have never claimed that there is nothing to explain. On the contrary, I insist on serious researching by following the three criteria of adequacy proposed by Chomsky in
Aspects, namely:
(1) We should point clearly to the object are we trying to study, debate, etc. (
i.e., we need to be sure to attain the level of
observational adequacy).
(2) Try to describe it in an accurate way or achieve the level of
descriptive adequacy (in here I bring in three further requisites proposed by Marr in his book on
Vision:
2 (a) Describe the
computations that bring about this object and make it work
2 (b) Describe the
representational frame where this object lies.
2 (c) Describe the
implementations that humans have been able to achieve to somehow reinforce that object.
AND, LAST BUT NOT LEAST:
(3) Explain how it came about into the world. Attain the
explanatory adequacy level.
It's anything but boring, you see? But our research does not guarantee that we find out THE TRUTH about this or that. It only guarantees that your model is well constructed and, in the best cases, it will predict likely outcomes and will therefore serve its purpose beautifully.
I am not certain about mathematics (I am an absolute ignorant in these matters, although I remember old Kurt Gödel saying that they cannot be as exact as they claim to be --no idea why, though!) as the only way to describe patterns, but if you can use them and they work for you, be my guest, I have nothing to oppose.
As to the notion of FACT, I think we are typically not observing the same "object" here, you and I.
For me a FACT is a mental representation which is stored directly in the box of representations: "you are reading this now", "your name is Daniel", "you are American and I am Spanish", etc. They are the representations
WITH which we build up our thoughts and reasonings. We don't question them, or doubt them, or explain them. If this would stand for a head (or a box of representations),
[ ], a factual representation would be
[R].
The other represenations, those that are not facts, are embedded into factual representations and we think and reason
ABOUT them, not with them. We could illustrate them like this
[R (R)] where the second R is not a fact. Any fact whatsoever may change its place in the box of representations and so we might be able to debate whether you really are reading this or are imagining it, or whatever, or any other wild discussion.
We normally get factual representations through three sources: (a) perception; (b) communication, and (c) logical thinking. Perceptions are the best means to achieve factual representations.
However, sometimes, we have to admit that communication over-rides perception. We see the sun moving around us, and yet, they have told us that it's we that travel around it. If we attach a strong authority to the communicating source, then we also get factual representations. Finally, we are able to logically imagine that Julius Caesar had never had breakfast with Noam Chomsky; this is normally also a fact for us.
All these notions are MY notions which I have tried to point to as clearly as I am able to do. You may have other notions which point to different objects and so, when we debate we will never be talking about the same thing, although we may call it with the same term, unless we start by pointing clearly to an object/event/relationship and build up from there.
This is what I think is really worth doing!
