1. Materialism holds that thinking consists of nothing more than the transition from one material process in the brain to another in accordance with causal laws (whether these transitions are conceived of in terms of the processing of symbols according to the rules of an algorithm à la computationalism, or on some other model).
2. Material processes have their causal efficacy, including their ability to generate other material processes, only by virtue of their physical properties (i.e. those described by physical science), and not by virtue of any meaning or semantic content that might be associated with them. (For example, punching the symbols “1,” “+,” “1,” and “=” into a calculator will generate the further symbol “2” whether or not we associate the standard arithmetical meanings with these symbols or instead assign to them some eccentric meanings, because the electronic properties of the calculator alone are what determine what symbols get displayed. Similarly, neural processes that are in fact associated with the thought that all men are mortal and the thoughtthat Socrates is a man would still generate the neural process that is in fact associated with the thought that Socrates is mortal even if these neural processes had all been associated with some other meanings instead, because the neurophysiological properties of the processes alone are what determine which further processes get generated.)
3. But one thought can serve as a rational justification of another thought only by virtue of the meaning or semantic content of the thoughts. (For example, it is only because we associate the symbols “1,” “+,” “1,” “=,” and “2” with the standard meanings that “1 + 1 = 2” expresses an arithmetical truth. Similarly, it is only because “All men are mortal,” “Socrates is a man,” and “Socrates is mortal” have the meanings they do that the first two sentences logically entail the third, and only when the neural processes in question are associated with the corresponding thoughts that the first two provide a rational justification for believing the third.)
4. So if materialism is true, then there is nothing about our thought processes that can make one thought a rational justification of another; for their physical and causal relations alone, and not their semantic and logical relations, determine which thought follows which.
5. So if materialism is true, none of our thoughts ever is rationally justified.
6. But this includes the thoughts of materialists themselves.
7. So if materialism is true, then it cannot be rationally justified; the theory undermines itself.
The upshot of this argument is that instantiating causal relations, of whatever sort, does not by itself amount to instantiating logicalrelations; and this is precisely what Popper is getting at in the passage above when he says that “brain mechanisms” or “computer mechanisms” may “differ physically as little as you may specify, yet this difference may be so amplified that the one may operate according to the standards of logic, but not the other.” Hence even if we concede that certain causal processes are necessary conditions for our reasoning logically (which Popper allows insofar as he says that our ability to follow standards of logic is “in some sense connected with, or based upon, physical properties”), they are not sufficientconditions – in which case there can be no (purely) causal explanation of our ability to reason logically.
Step 2 of the argument seems to follow from the standard materialist assumption that whatever happens in the natural world supervenes on what happens at the microphysical level of nature – the level of the basic particles described by physics and the laws governing them – together with the further materialist assumption that meaning or semantic content is not a microphysical property, whatever else the materialist wants to say about it. That this appears to make the meanings of our thoughts “epiphenomenal” or causally irrelevant to what happens in the world is known as “the problem of mental causation.” Of course, the meanings of our thoughts seem to have an effect on what we say and do; in particular, it certainly seems to us that we judge an inference like All men are mortal and Socrates is a man, therefore Socrates is mortal to be rational because of the meanings associated with these words, and would not judge it to be rational if they had some different content. But Popper’s point is that, if materialism is true, then we can have no grounds for believing that what seems to be the case really is the case. Perhaps the inference in question is in fact irrational, while an inference that seems irrational to us, like All men are mortal, and Grandma drives a Buick, therefore robots are stealing my luggage is a paradigm of rational thinking. Perhaps we don’t see this for the same reason the calculator would spit back “2” in response to the sequence “1 +1 =” even if the latter set of symbols expressed the question Does Grandma drive a Buick? and the former expressed the bizarre answer No, robots are stealing my luggage – namely for the reason that only the physical properties of events occurring in both calculators and brains, and not any semantic or logical properties associated with them, determine what effects they will generate.
For this reason Popper claims that materialism tends to reduce the argumentative function of language no less than the descriptive function to the sub-rational expressive and signaling functions, and thereby tends also to “make us blind to the difference between propaganda, verbal intimidation, and rational argument” (The Self and Its Brain, p. 59).