Rovelli, Klein, and Aristotle’s Definition of Time
Can Aristotle’s definition of time be made non-circular?
Carlo Rovelli has, perhaps unintentionally, allowed Aristotle’s definition of time to become non-circular.
The Reasoning in Four Steps
1. For Aristotle, time is the number of motion according to the before and after.
2. “Number” in the sense of what allows one to count.
3. Carlo Rovelli points out, adopting Aristotle’s perspective, that one can count a motion by using another motion.
4. From there, it is enough to replace “before and after,” which are temporal notions, with “going from one point to another” for a given moving body. Indeed, if one places an obstacle, one can clearly see in which direction the motion goes, without needing to use these temporal notions.
Watch the video
Étienne Klein’s Objection
Étienne Klein, from minute 7:20 to minute 8:20, said:
Il y en a d’autres, plus rares, que l’on appelle les philosophes du concept, qui pensent que le temps ne dépend pas de la conscience.
There are others, more rare, called philosophers of the concept, who think that time does not depend on consciousness.
Aristote, par exemple, qui dit que le temps est le nombre du mouvement selon l’avant et l’après,
(a) Aristotle, for example, who says that time is the number of motion according to the before and after,
Jolie formule qui ne veut rien dire,
(b) A nice formula that means nothing. See point 2
Puisque je vous défie de définir les notions d’avant et d’après sans avoir le concept de temps.
(c) Since I challenge you to define the notions of before and after without having the concept of time. See points 3 and 4
Définir le temps à partir d’un concept qui le présuppose, ce n’est pas le définir, c’est fabriquer ce que l’on appelle une tautologie.
(d) To define time from a concept that presupposes it is not to define it; it is to produce what is called a tautology. TRUE
D’ailleurs, c’est une grande remarque de Blaise Pascal, dont on fête l’anniversaire,
(e) Moreover, this is a great remark by Blaise Pascal, whose anniversary we are celebrating,
Il est impossible de définir le temps,
(f) It is impossible to define time. FALSE
Vous ne pouvez le définir qu’en rapport à lui-même.
(g) You can only define it in relation to itself. FALSE
Alors qu’une vraie définition consiste à montrer comment un concept dérive d’un autre concept qui est plus fondamental que lui.
(h) Whereas a true definition consists in showing how a concept derives from another concept more fundamental than itself. TRUE
Mais pour le temps, c’est impossible.
(i) But for time, that is impossible. FALSE
C’est un concept primitif,
(j) It is a primitive concept. FALSE
Comme on pourrait dire.
(k) As one might say.
Soit on l’accepte sans le définir, soit on le refuse et, à ce moment-là, il n’y a plus besoin de le définir.
(l) Either you accept it without defining it, or you reject it, and then there is no longer any need to define it. FALSE
Central Point
Étienne Klein does not take into account points 3 and 4 in his reasoning—an omission that changes everything.
A Return to Aristotle’s Conception of Time
For Aristotle, time is the number of motion according to the before and after, in the sense of what allows one to count motion. But time itself can be counted by establishing a relationship between two motions, which makes it possible to avoid the parameter t—this idea is presented and defended by Carlo Rovelli.
However, Rovelli, who draws inspiration from Aristotle’s position—if I have understood correctly—thinks that time is discrete, which does not seem to me to be fully in line with the philosopher’s conception.
The Relationship Between Two Motions
It is the same to say that, during a given motion of the clock, there was such-and-such a motion of the body, as to say that, during such-and-such a motion of the body, there was such-and-such a motion of the clock. This makes it possible to dispense with the parameter t.
Just as one cannot deny, from the fact that a body’s existence is continuous, that its motion is continuous, one also cannot deny that time is continuous. For this reason, Carlo Rovelli, while referring to Aristotle, does not, in my view, take the reasoning to its conclusion.
Time, Clocks, and Absolute Simultaneity
The relationship between two motions may vary depending on spatial conditions, but that does not mean there is no present moment for the Universe.
Two “identical” clocks placed in different spatial conditions can very well tick simultaneously at different rates—for example, two “identical” clocks located on two different floors of the same building.
To say that there is absolute simultaneity is to say that there is a present moment for the Universe. The conception of space-time in physics must, in my view, be completely rethought within this framework.
We must also return to an Aristotelian perception of causality, because the perception of causality in special relativity is limited and distorted.
Further development of this conception:
And He Was Hovering over the Waters: Towards a New Vision of the Physical World?Marc Lachièze-Rey’s Interpretive Error
The fact that clocks do not tick at the same rate depending on their spatial position in no way implies that time does not exist. It only means that the rate of physical processes depends on spatial conditions, which is very different from denying time itself.
One cannot arbitrarily rule out the idea that two “identical” clocks, placed in different spatial conditions—for example, on two different floors of the same building—can run simultaneously at different rates. Marc Lachièze-Rey overlooks this point.