What, precisely, are space and time, according to Kant?

Task: What, precisely, are space and time, according to Kant? Reproduce and explain at least two of his arguments from the Transcendental Aesthetic.

N.B: Clearly define your terms and present arguments, not mere opinions or assertions, to defend your point of view. Utilize the text and point to specific examples and passages when appropriate.

Helpful resources:

1. https://www.proquest.com/docview/614177836/B9E68B388ED74C9FPQ/5?accountid=8289&sourcetype=Books

2.

https://myclassroom.apus.edu/d2l/le/enhancedSequenceViewer/162788?url=https%3A%2F%2Ff54cbe36-23a9-4505-85fe-e251f80ec34d.sequences.api.brightspace.com%2F162788%2Factivity%2F13332123%3FfilterOnDatesAndDepth%3D1

To demonstrate that time and space must be finite, Kant first assumes the opposite, namely that time and space are each infinite, and then proceeds by way of indirect proof. If he can prove that time and space cannot be infinite, then by logical disjunction, each must be finite. He then proceeds to argue in the same way for the other side.

Select each item to learn more.

To see why time must be finite, suppose the opposite, that time is infinite.

“For if one assumes that the world has no beginning in time, then up to every given point in time an eternity has elapsed, and hence an infinite series of states of things in the world, each following another, has passed away. But now the infinity of a series consists precisely in the fact that it can never be completed through a successive synthesis. Therefore an infinitely elapsed world-series is impossible, so a beginning of the world is a necessary condition of its existence.” (A426/B454)

Time cannot be infinite, for an infinite succession can never be completed in any amount of time. Yet, at each individual moment, an infinity of states of affairs in the world would have come into being and passed away, i.e., elapsed. However, since an infinite series can never elapse, and temporal series do elapse, time must be finite.

“[If space were infinite] then the world would be an infinite given whole of simultaneously existing things. Now we can think of the magnitude of a quantum that is not given as within certain boundaries of every intuition in no other way than through the synthesis of its parts, and we can think of the totality of such a quantum only through the completed synthesis, or through the repeated addition of units to each other. Accordingly, in order to think the world that fills all space as a whole, the successive synthesis of the parts of an infinite world would have to be regarded as completed, i.e., in the enumeration of all coexisting things, an infinite time would have to be regarded as having elapsed, which is impossible.” (A429/B457)

Space cannot be infinite, because there is no way that we could represent space as a quantum (a single, discrete thing), save through a synthesis of all of its parts. We see something as a quantum in one of two ways:

Through a glance that takes the whole in (as happens when I see a pencil, or a person, etc.; I see them as a single thing, bound within a determinate spatial region)

Through a successive synthesis of all of the parts of the quantum (as happens when I sail around the world, charting the landmasses and geographical features that I see).

Since the entire spatial extent of the universe obviously cannot be taken in “at a glance,” we can only think of space as a unified thing through a successive synthesis of all of its parts. However, if space were infinite, then the synthesis of its parts could never be completed in any amount of time, hence it could not stand before us as a quantum, or ‘thing,’ to be grasped or discussed.

But What about the opposite?

Kant now turns to the “Antithesis,” in which he will prove the opposite, namely that space and time must be infinite.

To see why time must be infinite, suppose the opposite, that time is finite, hence, has a beginning.

“Since the beginning is an existence preceded by a time in which the thing is not, there must be a preceding time in which the world was not, i.e., an empty time. But now no arising of any sort of thing is possible in an empty time, because no part of such a time has, in itself, prior to any other part, any distinguishing condition of its existence rather than its non-existence.” (A428/B456)

Time cannot be finite, because that would mean that time “began.” It makes no sense, however, to speak of time “beginning,” inasmuch as ‘to begin’ means ‘to come into being out of a time in which it previously did not exist.’ In other words, to say that something “begins” is already an intrinsically temporal notion. Things begin within time; for time to “begin,” time would already have to exist, for to say that something begins is to reference a temporal framework that must pre-exist the thing that is beginning. Therefore, time cannot ‘begin,’ and hence, must be infinite.

To see why, suppose the opposite, that the spatial world is finite and thus bounded in space.

“Then it (space) exists in an empty space, which is not bounded…Now since the world is an absolute whole, besides which there is encountered no object of intuition, and hence no correlate of the world to which the world could stand in a relation, the relation o the world to empty space would be a relation of the world to no object. Such a relation, however, and hence also the boundedness of the world by empty space, is nothing; therefore the world is not bounded at all in space, i.e., in its extension it is infinite.” (A427/B455)

Space cannot be finite, because the only thing that can serve as a boundary to space, is more space (whether filled with things, or empty). If we were to board a spaceship and fly to the edge of the universe, what would happen when we reached ‘the end’ of the universe? Would we find a brick wall with a sign saying “closed past this point?” Even if we did find such a wall, the wall would exist in space, and hence space would not be bounded by something that could limit it, for the only thing that can serve as a boundary to space is more space, meaning that space must be infinite.

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