Centrifugal force is defined as a force that would cause an object to travel directly out from the center of rotation when released from circular motion. No other direction is possible due to centrifugal force. Therefore, if an object cannot travel directly out from the center of rotation when released from circular motion, then the direction an object travels after being released from circular motion is not explained by centrifugal force.
If an object always travels tangent to the circular motion after being released, then an object cannot travel directly out from the center of rotation when released from circular motion. If an object cannot travel directly out from the center of rotation when released from circular motion, then the direction that object travels after being released from circular motion is not explained by centrifugal force. Therefore, If an object always travels tangent to the circular motion after being released, then the direction that object travels after being released from circular motion is not explained by centrifugal force.
When you jump off of a merry-go-round you always land at a point tangent to the motion of the merry-go-round. Hammer throwers release the hammer at a tangent to the rotation of their body. Every careful observation suggests that when an object is released from a circular motion it will travel in a line that is tangent to the rotation. This is consistent with Newton's first law which is commonly accepted. There has never been any counter-example to contradict this view of the world. Due to the preponderance of observational and theoretical evidence we can be reasonably sure that objects do always travel tangent to the circular motion after being released.
The following argument has been supported: If an object always travels tangent to the circular motion after being released, then the direction an object travels after being released from circular motion is not explained by centrifugal force. Objects do always travel tangent to the circular motion after being released. The direction an object travels after being released from circular motion is not explained by centrifugal force.
The first paragraph states the main argument:
P1 - If an object always travels tangent to the circular motion after being released, then the direction an object travels after being released from circular motion is not explained by centrifugal force.
P2 - Objects do always travel tangent to the circular motion after being released.
C - The direction an object travels after being released from circular motion is not explained by centrifugal force.
The second and third paragraphs combine to make a complex argument that concludes with the first premise (P1):
P1a - Centrifugal force is defined as a force that would cause an object to travel directly out from the center of rotation when released from circular motion. No other direction is possible due to centrifugal force.
IC/NBP(1) - If an object cannot travel directly out from the center of rotation when released from circular motion, then the direction an object travels after being released from circular motion is not explained by centrifugal force.P1b - If an object always travels tangent to the circular motion after being released, then an object cannot travel directly out from the center of rotation when released from circular motion.
P1c [IC/NBP(1)] - If an object cannot travel directly out from the center of rotation when released from circular motion, then the direction an object travels after being released from circular motion is not explained by centrifugal force.
IC/NBP(2) [P1] - If an object always travels tangent to the circular motion after being released, then the direction an object travels after being released from circular motion is not explained by centrifugal force.
The fourth paragraph supports P2. Notice that this support is not a deductive argument. Also note that the statement that no counter-examples have been found is only meant to suggest that many people have tried to find counter-examples and that the statement, by itself, doesn't provide support for P2.
The last paragraph summarizes what has been done, repeating the argument of the first paragraph and culminating in the overall conclusion of the essay.