Thursday, January 27, 2011

The First Way in Syllogistic Form


Share/Bookmark

I. The Text (ST I.2.3c):

"The first and more manifest way is the argument from motion.  It is certain, and evident to our senses, that in the world some things are in motion.  Now whatever is in motion is put in motion by another, for nothing can be in motion except it is in potentiality to that towards which it is in motion; whereas a thing moves inasmuch as it is in act. For motion is nothing else than the reduction of something from potentiality to actuality. But nothing can be reduced from potentiality to actuality, except by something in a state of actuality. Thus that which is actually hot, as fire, makes wood, which is potentially hot, to be actually hot, and thereby moves and changes it. Now it is not possible that the same thing should be at once in actuality and potentiality in the same respect, but only in different respects. For what is actually hot cannot simultaneously be potentially hot; but it is simultaneously potentially cold. It is therefore impossible that in the same respect and in the same way a thing should be both mover and moved, i.e. that it should move itself. Therefore, whatever is in motion must be put in motion by another. If that by which it is put in motion be itself put in motion, then this also must needs be put in motion by another, and that by another again. But this cannot go on to infinity, because then there would be no first mover, and, consequently, no other mover; seeing that subsequent movers move only inasmuch as they are put in motion by the first mover; as the staff moves only because it is put in motion by the hand. Therefore it is necessary to arrive at a first mover, put in motion by no other; and this everyone understands to be God."



II. The Argument in Syllogistic Format:

P1-A: Some things are in motion (m).
P2-A: If some things are in motion (m), then they are put in motion by another (a).
C-A: Therefore, they are put in motion by another (a).

[P1-B: If they are put in motion by another (a), then either this goes on to infinity (i) or it is necessary to arrive at a first mover, put in motion by no other (f).]
P2-B: They are put in motion by another (a).
C-B: Therefore, either this goes on to infinity (i) or it is necessary to arrive at a first mover, put in motion by no other (f)

P1-C: Either this goes on to infinity (i) or it is necessary to arrive at a first mover, put in motion by no other (f)
P2-C: But this cannot go on to infinity (~ i).
C-C: Therefore it is necessary to arrive at a first mover, put in motion by no other (f).


III. The Argument in Symbolic Format:

P1-A: m
P2-A: m ® a
C-A: a

[P1-Ba ® (i V f)]*
P2-B: a
C-B: i V f

P1-C: i V f
P4-C: ~ i
C-C\ f.

* This premise is implicit and necessitated by the text (which means the argument is an enthymeme).




IV. Legend:


V = either... or... (but not both)
~ = it is false that
\ =  therefore
m, a, i, f = variables representing propositions 
P1-A, P2-A, etc. = numbers assigned to premises 1 and 2 of arguments A and B, etc.
C-A, C-B, etc. = the conclusions of arguments A, B, etc.



V. Proofs of Selected Premises:

Proof of P1-A: It is certain, and evident to our senses.

Proof of P2-A: For nothing can be in motion except it is in potentiality to that towards which it is in motion (cf. definition of motion: "the act of something in potency insofar as it is in potency"); whereas a thing moves [another] inasmuch as it [i.e., the mover] is in act.  For motion is nothing else than the reduction of something from potentiality to actuality. But nothing can be reduced from potentiality to actuality, except by something in a state of actuality. Thus that which is actually hot, as fire, makes wood, which is potentially hot, to be actually hot, and thereby moves and changes it.  Now it is not possible that the same thing should be at once in actuality and potentiality in the same respect, but only in different respects. For what is actually hot cannot simultaneously be potentially hot; but it is simultaneously potentially cold. It is therefore impossible that in the same respect and in the same way a thing should be both mover and moved, i.e. that it should move itself. Therefore, whatever is in motion must be put in motion by another.

Proof of P2-C: Because then there would be no first mover, and, consequently, no other mover; seeing that subsequent movers move only inasmuch as they are put in motion by the first mover; as the staff moves only because it is put in motion by the hand.


Post a Comment