In this book, A.J. Ayer cites Gilbert Ryle, who says that the act of seeing a tree, much like the action of Achilles racing the tortoise, does not designate something that is 'in process' but something that is accomplished and as such is now at a state of completion. Ayer sees Zeno's paradox as belonging to a different conception of time, one situation as being of differentiated instants, while the other representing a continuous whole. Therefore, he concludes, anyone who tries to draw ultimate definitions to experience or define existence in terms of a predicate action is making an error in logic. However, Ayer contends that Ryle is incorrect when he says that the impressions that philosophers cite as evidence of the data coming in from our senses do not really exist. The supposed validity of this view, which was popular around the turn of the 20th century, he says, was strengthened by the fact that there was a mistake in the then-current thinking of the day: the mistaken belief was that something must mediate between external objects and the mind. Accordingly, Ayer does not feel this state of affairs poses a major objection to the sense-datum theory of reality.
Like the uncovering of the language-game inherent in Zeno's paradoxes, Ryle's comments on the everyday transactions between sensation, perception and materiality does not comprise a vocabulary of real life in the sense that it is rendered inadequate for the ordinary purposes of communication. To further refute Zeno and the other philosophers who, he says, were confused between the logic of reality and the logic of language, Ayer says that it is a mistake to consider statements about physical objects as being translatable into statements about sense-data. This is yet another false assumption that has hampered logical thinking for millennia.
The third advance on the faulty logic of the great philosophers of the past, and perhaps the most incomprehensible one Ayer advocates, is the proposition that later events are in fact responsible for earlier effects. Ayer seems to feel that the truth of this statement is augmented by the common and supposedly consensual notion that the world, and the universe surrounding it, is growing ever more uniform through the progression of time. This argument, which fails to be fully convincing to my mind, is not only contrary to the Aristotelian conception of the order of time-logic, but it springs from what Ayer speculates is the mistaken assumptions made from the fact that our notions of causality is derived from the experience of human action; such a mistake potentially arises, Ayer says, when we consider the fact that our actions are directed towards the future and not the past.
At the end of the book Ayer takes up David Hume's skeptical position that suggests that human life and consciousness is extinguished with the loss of the body and, as he puts it, he is not convinced that the alternative proposition, i.e. that a person's existence is tied to the existence of the body, is necessarily true. This to me is a very revealing passage in that it shows Ayer's ideological motives behind all of his indubitably demonstrable intent of sweeping up the logical problems and paradoxes of philosophy. In my opinion, this is a line of thinking to be used only when discriminating between various philosophers at the highest critical level. This style of thinking is brought to bear on the fact that, Ayer suggests, Hume was misled by his own philosophical assumptions. To state it as clearly as I can, Ayer implies that Hume may have been mistaken in saying that, because he said he could not conceive of God's existence due to the radical bent of his positivist worldview, which did not accept the alternative logic of a bodiless soul, i.e. that there is not God, it should not be the case that the only accessible models of reality are the physical facts of existence itself. Is this true or should the concept of divinity stand opposed to the vacancy of continuous bodies and cardinal integers that the logical positivists claim are the ne plus ultra of physical existence? On this note Ayer concludes his book here, saying, "Further than this we cannot go."