Therefore, a line is a relation of points.
A plane is a relation of lines.
A solid is a relation of planes.

A relation is an extrusion. Therefore, a line is the extrusion of a point.
A plane is the extrusion of a line.
And a solid is the extrusion of a plane.

A space is where points, lines, planes, and solids are located.
A time is a line where points are located.
So there are two kinds of points: spatial and temporal.

Spatial points have three coordinates: on the x axis, on the y axis, and on the z axis.
Temporal points have one coordinate: on the w axis.

An axis is a line.

And since the extrusion of a line is a plane, it follows that by having four axes (x, y, z, w), this can be represented in set-theoretical notation. But more importantly, having four axes means that, by extrusion of those four axes, there are four planes: call them a, b, c, and d.

And each plane, extruded, results in a total of four solids in this case: call them 1, 2, 3, and 4.

The common feature to 3D solids and 3D space is that both of them are 3D. But clearly, 3D space is not the same geometric object as a 3D solid in that very same space. In other words, space itself is not a geometric solid, it is instead the place where there are 3D geometric solids.

A place is a location in a space.
And a moment is a location in time.
Therefore, a moment is a geometric point in time, on the w axis.
And a place is a geometric coordinate on the x, y, and z axes.

"Just like a car crash, just like a knife, my favorite weapon is the look in your eyes..."

"Just One Fix". "I could stop if I wanted to".

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And except in areas both obscure and arcane none of this matters - well, sometimes it can matter. — tim wood

*Ahem*...

Empiricism concerns phenomena. Our OP seems to think that is a matter of the perceivable v. the unperceivable. But I shall leave to you a question he so far has ducked: can there be a science of anything that is not perceived, that is not in some way or other a phenomenon observed? — tim wood

Of course there can be such a science. The science of phenomena is called phenomenology. The science of noumena is called noumenology. And the science of Reality Itself is simply called science. It includes the formal sciences (mathematics and logic), as well as the factual sciences (the natural sciences and the social sciences).

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Please — tim wood

Well, since you said the magic word, I guess I have no choice. And by that, I mean that I have to stop being a dick towards everyone, including myself.

tell how a science about unperceivables works — tim wood

I'll try. I can't promise anything in that sense.

keep in mind the qualification that nothing can be observed/perceived. — tim wood

What a strange qualification.

Anyways, here goes. Take the following with a grain of salt.

Kant made a distinction between phenomenon and noumenon. We can speak of phenomena, but it would be somewhat strange to speak of noumena, in the plural, since we don't know anything about them. What we do know, however (this is a famous footnote to the Critique of Pure Reason) is that there is a noumenon, because otherwise there would be appearances (phenomena) without something that appears (noumenon).

For example, it's as if Kant is saying the following:

(1) There are appearances (phenomena).
(2) So, there is something that appears (noumeon).

Kant seems to think that if (1) is true, then (2) must be true a well.

How are we doing so far? Any objections to the preceding?

Science is a method for studying phenomena. If you do not agree, we need to stop here and work this out.

Phenomena are what actually happens, relative to what might otherwise happen. And in a lot of modern science, the phenomena that are studied are on the gauges of machines and the readouts of printers. And that's it, period. Now, an analysis of phenomena can lead to theories, and the theories can be tested, and so on. But in many cases the "thing" studied is never directly observed, never itself a phenomenon. — tim wood

If phenomenon means to be-perceived then no. Science according to the example I have given consists in the study of perceivable or Non-perceivable reality. And I think you agree.

Empiricism concerns phenomena. Our OP seems to think that is a matter of the perceivable v. the unperceivable. But I shall leave to you a question he so far has ducked: can there be a science of anything that is not perceived, that is not in some way or other a phenomenon observed? — tim wood

I believe that in this topic the central criticism has been made of empiricism a la Berkeley, which is empiricism taken to its last true consequences (the criticism of primary qualities). In that sense the critique is absolutely right

I believe that in this topic the central criticism has been made of empiricism a la Berkeley, which is empiricism taken to its last true consequences (the criticism of primary qualities). In that sense the critique is absolutely right — JuanZu

You're right, but you're also far too kind towards me. My critique of bishop Berkeley could be wrong.

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It goes back to establishing some precision in language. Working scientists presuppose willy-nilly what they need to in order to do their work, but we as aspiring metaphysicians, to do our work, have got to try to be as clear as we can about what we presuppose and whether particular presuppositions matter, to see if we're misled or well-led by them. — tim wood

Well, that's why we use logical symbols, like propositional letters, for example, in the context of propositional logic. Symbols such as "p", "q", "r", "s", etc. They don't mean anything, they're just propositional letters.

A more sophisticated logic is first-order predicate logic. Now you have individual constants and individual variables. The latter are of two types: free variables and bound variables. And now you have predicate letters as well, and you also have two quantifiers: the "for-all" sign, and the "for-some" sign, also known as the "universal quantifier" and the "existential quantifier".

So it goes. The next step in complexity is second-order logic. Now you can quantify over predicates, you can use the universal quantifier as well as the existential quantifier to range over predicates. It's just set theory in sheep's clothing, as Quine said. And it's incomplete in a way that first-order predicate logic is not. So, I just don't use second-order logic, I don't like it. If it's set theory in sheep's clothing, then I'd rather use set theory.

But I don't have much use for set theory, to be honest. I just get by with first-order predicate logic and propositional logic, that's all I need for my modest aims. I'm open to the idea that I might be wrong about this, though.

(1) There are appearances (phenomena).
(2) So, there is something that appears (noumeon).
Kant seems to think that if (1) is true, then (2) must be true a well. — Arcane Sandwich


I'm betting sure that Kant never said that any noumenon "appears." But as an education is a valuable thing worth having, I'll gladly pay off.... Now I'll attempt to channel Mww, probably a mistake on my part. But I think he would point out that what appears is the phenomenon, that is, a creation of mind. The noumenon is no creation of mind, and being itself thereby not a phenomenon, never appears. Here, I'll ping Mww and maybe he'll clean up any misstep of mine. — tim wood

Ok, sure, why not?

(some parts have been edited)

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I'm at that level of simplicity. — tim wood

Are there any further levels of simplicity, in that sense? Honest question.

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So what's you point, in that comment, specifically? I don't get it.

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Do you happen to be familiar with the terms "absolute presupposition" aka "hinge propositions" (although not quite the same thing)? — tim wood

I've heard about them, especially the latter, but I don't know much about them. What are they about?

somehow — tim wood

For me there is no somehow except in a very rudimentary stage of science. You perceive something, then you study or analyze it, but you use means to analyze and discover (today more than ever) things that you had not and will not be able to perceive. Even the result of analysis and investigation can totally change what we first thought we perceived.

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Well, if that's the case, then allow me to play the part of the skeptic, please.

What are your APs? What are mine? Which ones would be common to you and me?

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Likely given a taste, you'll read more. — tim wood

I don't know if I want to read it, then. It sounds like a drug.

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How do I know it's not snake oil? I just have to take your word for it?

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Well, if I'm still allowed to play the part of the skeptic here, that just begs the question:

Don't be silly. — tim wood

Is this a request or an order?

The thing is that I already have my metaphysician's hat on and I have never taken it off. And I maintain a position that is in accordance with the metaphysical commitment of the scientist.

So I can say: yes, science as an object of study and as a fact refutes something about empiricism. We are being aware (which differs from perceive) of some things that we do not perceive. And we can study, analyze, investigaste them through technology.