Yet our brains assume that we hear about all those disasters [we read about in the newspaper] because we've personally witnessed them, and that the distribution of disasters in the newspapers therefore reflects the distribution of disasters in the real world.

Even if we had personally witnessed them, that wouldn't, in itself, be any reason to assume that they are representative of things in general. The representativeness of any data is always something that can be critically assessed.

This seems to be a common response - Tyrrell_McAllister said something similar:

I think that your distinction is really just the distinction between physics and mathematics.

I take that distinction as meaning that a precise maths statement isn't necessarily reflecting reality like physics does. That is not really my point.

For one thing, my point is about any applied maths, regardless of domain. That maths could be used in physics, biology, economics, engineering, computer science, or even the humanities.

But more importantly, my point concerns what you think the equations are about, and how you can be mistaken about that, even in physics.

The following might help clarify.

A successful test of a mathematical theory against reality means that it accurately describes some aspect of reality. But a successful test doesn't necessarily mean it accurately describes what you think it does.

People successfully tested the epicycles theory's predictions about the movement of the planets and the stars. They tended to think that this showed that the planets and stars were carried around on the specified configuration of rotating circles, but all it actually showed was that the points of light in the sky followed the paths the theory predicted.

They were committing a mind projection 'fallacy' - their eyes were looking at points of light but they were 'seeing' planets and stars embedded in spheres.

The way people interpreted those successful predictions made it very hard to criticise the epicycles theory.

I fully agree, and this is completely in line with the points I was trying to make.

It is theoretically possible to accurately describe the motions of celestial bodies using epicycles, though one might need infinite epicycles, and epicycles would themselves need to be on epicycles. If you think there's something wrong with the math, it won't be in its inability to describe the motion of celestial bodies.

But I don't think there's anything "wrong with the math" - I even said precisely that:

A believer in epicycles would likely have thought that it must have been correct because it gave mathematically correct answers. And it actually did . Epicycles actually did precisely calculate the positions of the stars and planets (not absolutely perfectly, but in principle the theory could have been adjusted to give perfectly precise results). If the mathematics was right, how could it be wrong?

.

While 'accurate' and 'precise' are used as synonyms in ordinary language, please never use them that way when talking technically about the meanings of words.

I was trying to talk about how people actually use them, and one of the things I was suggesting is that people do actually tend to treat them as synonymous.

Similarly, please never use 'begs the question' or any form of it when not referring to the logical fallacy.

Isn't this a little picky? The way I used 'begs the question', in the sense of 'raises the question', is fairly common usage. Language is constantly evolving and if you wanted to claim that people only should use terms and phrases in line with their original meanings you'd have throw away most language.

As far as I can see, that's just an acknowledgement that we can't know anything for certain -- so we can't be certain of any 'laws', and any claim of certainty is invalid.

I was arguing that any applied maths term has two types of meanings -- one 'internal to' the equations and an 'external' ontological one, concerning what it represents -- and that a precise 'internal' meaning does not imply a precise 'external' meaning, even though 'precision' is often only thought of in terms of the first type of meaning.

I don't see how that relates in any way to the question of absolute certainty. Is there some relationship I'm missing here?

I'm not trying to be a jerk. Let me try to explain things, as I don't think I communicated my point very clearly.

Just to start off, the quoted text is something you said.

But perhaps you are saying that the sentence I've embedded it in does not reflect what any thing you said? If so, it's not mean to - it's describing the point I was making, and to which your response included that quoted text.

Essentially, my last comment was trying to point out what I'd originally said had been misinterpreted in the Just-So Story bit, even though I didn't do a great job of making this clear. Of course you may argue that you didn't misinterpret me, but I certainly wasn't trying to put words into anyones mouth.

An intuition is correct if it matches reality.

Indeed, and that is why it's wrong to say that attempts to rationally justify statements about reality are "almost certainly going to produce an ad hoc Just-So Story".

science is basically a means to determine whether initial intuitions are true.

No, science is a methodology to determine whether an assertion about reality should be discarded. If it merely dealt with initial intuitions, it's usefulness would be exhausted once the supply of initial intuitions had been run through.

I'm not sure what the second sentence there is taking "initial intuitions" to mean, but I don't think there's any substantial disagreement between our statements.

I doubt those kings can be killed. I think victory against them comes more from inserting layers of suppression between them and action, to modulate and reduce their power. You might be able to think of those layers as governmental machinery.

“If a nation expects to be both ignorant and free in a state of civilization, it expects what never was and never will be” -- Thomas Jefferson