Part I, Question 1, Article 1:
Whether the finite contains the infinite, and vice versa?
Obj. 1: The finite does not contain the infinite, since the terms are incommunicable.
Obj. 2: Definitions of finity and those of infinity cannot be interchanged, as for example, what a thing is cannot subsist contrary to its nature. For example, an untrustworthy person (if they are always — namely, infinitely — untrustworthy) cannot subsist (i.e., today, with this amount of responsibility, to deposit these number of dollars, into this treasury, at this time, etc. — i.e., in the finite) as trusted.
Obj. 3: That which is distinguished in thought cannot be united except in thought. Therefore, just as the finite is distinguished by the infinite in thought, so it is said to be contained within the infinite, though only in thought.
Ad contra.: “I contain multitudes,” Walt Whitman.
Respondeo: Consider a single plane whereon lie two points. It is necessary that there exist one line between these two points; namely, a straight line of length y. There can exist a non-straight line of length not-y, since a line can be drawn that begins at pointA and terminates at pointB and contains arcC. And consider that the arc of this line, which we call arcC, can be of any amplitude. And consider that arcC can be of infinite amplitude. And consider that the line of not-y length between points A and B can have any number of arcs of any amplitudes. Therefore, line not-y has infinite arcs of infinite amplitudes, and this line begins at pointA and terminates at pointB.
If there exist two coplanar points, then there exists a straight line that terminates at each point. If there exists a straight line between two coplanar points, then there can exist a non-straight line of infinite length, which terminates at each point.
The finite distance y between two coplanar points is a line. There can be any distance between these same points, and the line measuring this distance will have an arc. Now, this arc can be extended indefinitely. Furthermore, this arc can have other arcs within it, which likewise can be extended indefinitely. The line joining two coplanar points is both finite and infinite — the plane on which two points lie, after all, was never determined in extent.
Res. obj. 1: Terms are manners of speaking, whereby thought can be manipulated for expression and comprehension. Although terms cannot be communicable between one another, this is only to express what is signified by each term, since if by house I could also refer to bedroom — and thereby use house and bedroom in communion, that is, as one and the same — then my language would be ineffective. So, the communion between finity and infinity, as terms, is repulsive, but the communion between finity and infinity, as ideas, is ensured.
Res. obj. 2: This is the same argument as objection 1: the terms are not the objects of thought but the process by which thoughts operate. There is a distinction between speech and thought, since what I say can always adhere more or less closely with what I think. Thus, terms can be exchanged one with another more or less adroitly not because of themselves but because of what they reveal — namely, thoughts.
Furthermore, To be given no-responsibility is the untrusted person’s responsibility; sc., the untrustworthy person is worth trust, and the trust is of no measure. The responsibility commensurate with this person’s measure of trust is none. For example, the number of dollars entrusted to this person are no dollars. But, no dollars given is equivalent to some trust given. The measurement, however, is null.
Res. obj. 3: Community between terms finity and infinity is said to obtain in thought only, neither in speech nor in observation. Yet, if in thought, then in both speech and in observation, since what is spoken is a consequence of what is thought, and what is observed is a consequence of what is given (to thought).
Part I, Question 1, Article 1: