Subject: Speed of light finite or infinite?

I am asking a question on the Fizeau’s experiment for measuring the speed of 
light. The diagram of this experiment can be found at the following webpage: 
http://en.wikipedia.org/wiki/Speed_of_light
Please look at it before answering my question.

Assume that the speed of light is infinity. Fizeau’s experiment proves that it 
is finite. I am saying, no, his experiment does not prove that. Here are my 
arguments:

When the light hits the eye or the detector, we see from the figure that an 
open slot is in front of the detector. But at the same time an open slot is 
also in front of the light source. So I can say that the speed of light is 
infinity and what you see is the source light, reflected through the mirror 
instantly.

What Fizeau is calming, apparently is the following: The light you are seeing 
is the light that passed through the previous open slot in front of the source 
and it came back after reflection when that open slot came in from of the 
detector. He is saying this has happened because the light was blocked by a 
tooth at one time.

I am saying when light was blocked no light passed. The one that went through 
the previous slot vanished because it has infinite speed. What you are seeing 
is the one that is passing now through both open slots. This is because the 
speed is infinity.

My argument seems to be correct. Where is the fallacy?

Re: Speed of light finite or infinite?