Cleric K wrote: ↑Wed Sep 11, 2024 5:03 pm
If we imagine that we have no understanding of space, our visual field will look like an amalgamation of colorful blobs.
This is false. We cannot imagine having no knowledge of space. We already have complete knowledge of the pure forms of intuition, they are a priori and they necessitate us continously. If this were not the case, you would (similar to Locke in his sensualism theory) make the mistake of concluding from a known effect (sensation) to an unknown cause (the body). Furthermore, the sentence "our visual field will look like an amalgamation of colorful blobs" is already a quantitative determination. The term “sensuous manifold” (to which you are referring here) may be conceived neither as order nor as disorder, neither as unity nor as plurality. For that would already be a categorical determination, and it is precisely this categorical determination, however, that makes a space (as an a priori concept) comprehensible to us. Nevertheless, it is already present, as an a priori representation, even if we have not yet formed a concept of it. Their a priori nature is revealed by the
insight that they do not fall victim to the Humean problem of induction like many of the empirical hypotheses do, which are only falsifiable, but not verifiable. The a priori structures are not just thought within the assertoric mode, they are thought as being apodictically, universally true. Similar like the law of causality.
The only conceivable solution of the aforementioned problem (which Locke was trapped into) lies in the Copernican revolution of thought discovered by Kant, namely the reversal of the relation of the previous (incorrect) silent assumption that space and time are independent things in themselves. On the contrary: space and time belong entirely to us, as a priori representations. And they must, otherwise we would not immediately recognize bodies or even have any sensual experience at all. Kant has shown this by the way how they are the necessary conditions for the possibility of (empirical) experience.
I will try to make my train of thought clearer here:
a) The sentence: “Our space is three-dimensional” is wrong.
Three-dimensionality is no more a property of space than the terms “straight” and “curved” are (most people don't know that either, hence they mistake special relativity theory as an actual ontological description of space). Space has innumerable dimensions (eccentric spherical radii) from a point (center) (i.e. in relation to this point). If there is no three-dimensional space, then there is no multi-dimensional space either.
In truth, there is only one axiom on which the determination of size is based, and this is:
“
In one point only three of the innumerable eccentric dimensional lines designated under a) are possible, which are perpendicular to one another"
(e.g. the possibility of constructing a right is also based on the principle of gradualness (category of quality). When the side is turned, it must also pass through the perpendicular line. This follows from the continuity to which the principle of gradualness is applicable)
By virtue of this axiom, the size of a part of space can be determined by three dimensional lines. This axiom, like all the others, is induced by the influence that empty space exerts on the conceptualizing, constructing power of judgment, and with it has also induced the impossibility of constructing more than three perpendicular lines in the same point.
If you dialectically turn this axiom into a property of space in order to arrive at an (apparent) class of spaces with more dimensions, then you are mistaken. The possibility or impossibility of constructing a figure in space never reflects a property of space! Figures can be derived from space, but space can never be derived from figures. You can't construct space from three dimensions, so you can't make a property out of them either (space is, after all, the very prerequisite for the construction of dimensional lines being possible at all, and not the other way around).
Now let us assume that four-dimensional space is a “logical possibility”.
a) But logical possibilities deal exclusively with “mere” concepts, and the study of such concepts, detached from intuition (the necessitating sensuality), is the essence of illusory logic or dialectics (an extremely dangerous cultural troublemaker).
Here, the sensual and individually given space is transformed into a mere concept, which is then made into a (non-inductive) generic concept in contradiction to the individually given sensual structure. With this freely invented generic concept of different spaces, one then associated the property of three- and further four-dimensionality and then pointed out that the latter property **did not logically contradict** this invented generic concept, that consequently the concept of a four-dimensional space was a logical possibility.
**But** where on earth does one get the realization that four-dimensionality does not contradict this generic term, since the object of this generic term is completely unknown?
So it is impossible to say whether a logical contradiction is excluded here! It is problematic/hypothetical even if one allows a space as a generic term. Because we only know one species of space. Our concept of space is based on only one single example. Yes, space is, as I just showed, even the condition for the presentation of individual objects. We can induce generic terms for dogs and cats, but not for the phoenix bird or for dragons. There is no generic term that includes different types of space. It's a fictitious invention.
b) A logical possibility does
NOT belong in physics, or in science at all, but only a real, induced possibility.
The logical possibility, i.e. the absence of contradiction, is never the sufficient reason for the formation of a judgment, i.e. the copulation of two concepts, but only
one of its conditions (conditio sine qua non, coefficient). Rather, according to the law of logic itself, the copula of two terms (as subject and predicate) must have a
sufficient reason (the principle of sufficient reason), which excludes the opposite of the copula (the principle of the excluded middle).
A sufficient logical reason exists when the predicate can be derived from the subject (i.e. in the case of the analytical judgment, so that every logical insight must be analytical, i.e. can only be based on the principle of non-contradiction as the only reason). On the other hand, every synthetic copulation of concepts demands, according to the logic, **
besides** the observance of the principle of non-contradiction, a sufficient reason according to the principle of reason, which lies **
outside** the judgment, i.e. must be induced, i.e. must be a **
real** possibility. The copulation of the synthetic concepts “space” and “three-dimensional” is induced by construction in reality. The copulation of the concepts “space” and “four-dimensional” is not inducible. It is invented a priori (in contradiction even to the empiricist dogma) by the invention of an unknowable subject concept, which is a concept without an object.