is that John Mill
pretends to refute the Achilles-tortoise fallacy.

The important point to notice here is the intellectualist logic. Both
sides treat it as authoritative, but they do so capriciously: the
absolutists smashing the world of sense by its means, the empiricists
smashing the absolute--for the absolute, they say, is the quintessence
of all logical contradictions. Neither side attains consistency.
The Hegelians have to invoke a higher logic to supersede the purely
destructive efforts of their first logic. The empiricists use their
logic against the absolute, but refuse to use it against finite
experience. Each party uses it or drops it to suit the vision it has
faith in, but neither impugns in principle its general theoretic
authority.

Bergson alone challenges its theoretic authority in principle. He
alone denies that mere conceptual logic can tell us what is impossible
or possible in the world of being or fact; and he does so for reasons
which at the same time that they rule logic out from lordship over the
whole of life, establish a vast and definite sphere of influence where
its sovereignty is indisputable. Bergson's own text, felicitous as
it is, is too intricate for quotation, so I must use my own inferior
words in explaining what I mean by saying this.

In the first place, logic, giving primarily the relations between
concepts as such, and the relations between natural facts only
secondarily or so far as the facts have been already identified with
concepts and defined by them, must of course stand or fall with the
conceptual method. But the conceptual method is a transformation which
the flux of life undergoes at our hands in the interests of practice
essentially and only subordinately in the interests of theory. We
live forward, we understand backward, said a danish writer; and to
understand life by concepts is to arrest its movement, cutting it up
into bits as if with scissors, and immobilizing these in our logical
herbarium where, comparing them as dried specimens, we can ascertain
which of them statically includes or excludes which other. This
treatment supposes life to have already accomplished itself, for the
concepts, being so many views taken after the fact, are retrospective
and post mortem. Nevertheless we can draw conclusions from them and
project them into the future. We cannot learn from them how life made
itself go, or how it will make itself go; but, on the supposition that
its ways o