Infinite & Bound (Part I)

Socrates: Let us attend to this matter prudently and endeavour to make firm the beginning of self.

Protarchus: We must examine this matter in depth.

Socrates:  Let us divide into two, or if you prefer three, all things that exist [being] now and everywhere.

Protarchus: Tell us how you would do this.

Socrates: By considering some of the things we have already reasoned.

Protarchus: Which ones?

Socrates: We believe that the God revealed the unlimited/infinite and the limited/bound in living beings.

Protarchus: This is so.

Socrates: Let us take these two ideas and, from this mixture, produce a third one. The components of this third one are the two ideas mixed together. However, as a human, I deserve to be laughed at for knowing this division and counting out the numerous in this way.

Protarchus: Why is this my good friend?

Socrates:  It appears that there is a need for a fourth idea.

Protarchus: Say why.

Socrates: By seeing the cause of the former two ideas mixing together. And now in addition to the three ideas, cause shall be the fourth.

Protarchus: Will there be a need for a fifth that can be separated?

Socrates: Perhaps, but not at this present moment in time. But if there is a need for a fifth, let me go ahead and pursue it.

Protarchus: Yes, certainly.

Socrates: Then, of these four, divide three and observe two of these. When one is divided, it becomes separated, and there are many. Next, gather together the many into one again and let us attempt to understand how each one self is both one and many.

Protarchus: I could understand your words if you talked more clearly about these selves.

Socrates: The two I am referring to now are the same ones I mentioned first, the infinite and the bound. I will attempt to show that the infinite, in a way, is many, and the bound can continue to exist as one.

Protarchus: It can.

Socrates: What I ask you to examine is difficult and may cause hesitation. Examine it anyway. First, take hotter and colder and see if you can think of any limit/bound. Or, would not the more or the less that dwell in these kinds of self, whilever they are present, prevent an end. For if they are brought to an end, then these kinds of selves would also be brought to an end. 

Protarchus: This is true.

Socrates: When we talk of the hotter or colder, we always assign the more or the less to them.

Protarchus: Yes, very much so.

Socrates: Reason tells us that the hotter and the colder will never have an end. Being without an end, they are altogether unlimited/infinite.

Protarchus: I strongly agree with you on this matter.

Socrates: You have understood well, O friend Protarchus, and it reminded me that the strongly you have said, and indeed softly, possess selves that have the same power as the more and the less. Whenever they are present, they do not allow for a precise amount to exist, and instead, their presence allows for the stronger or softer. Thus, they always produce more or less without the precise amount being seen. In what we have just seen, if the precise amount did exist, and self allowed this, then measure would be introduced to rule directly the more and the less, and the stronger or the softer. These very selves would be removed from their position because, by the presence of measure, the hotter and the colder would not exist. For in a like manner, the hotter and the colder are constantly in motion, and they never abide in the same place. But, measure always abides in the same place, and the motion is ended. Our reasoning suggests that both the hotter and the colder must be unlimited/infinite.

Protarchus: This appears to be so, Socrates, but as you said, these things are difficult to understand. Perhaps hearing these things repeatedly, the one asking the questions will reach an agreement in their mind with the one being questioned.

Socrates: You speak well, and indeed we should try to do so. Now, to avoid stretching out our argument by putting forward every unlimted/infinite, we may consider accepting our present position as the way of assigning the nature of the unlimted/infinite.

Plato, The Philebus