Book Review of "Journey to the Edge of Reason: The Life of Kurt Gödel"

What I liked about this book is the historical detail it allows itself to slip into. I bought it for a friend studying IT/Informatik in Vienna, thinking it would be very fitting. I, myself, listened to the entirety of it on Audible and found the voice actor pretty horrendous, especially in pronouncing German. So I recommend getting a physical copy.

The mathematics in the book are well summarised in an impressive video by the YouTube channel Veritasium: https://youtu.be/HeQX2HjkcNo 

My initial reaction on watching the video: “But what Gödel did for mathematics only, Popper did for the whole of science and the problem-solving of life.” What I meant by that is that Gödel proved via his theorem the necessary incompleteness of all mathematics; the same way Popper proved the a priori creativity of scientific progress, and that without incompleteness science cannot advance, because a theory must always be falsifiable/disprovable/create problems to solve.

Popper would agree with Gödel's statement: “for clear questions posed by reason, reason can also find clear answers.” Both could be classified under what Robert Voegelin calls “Westcoast skeptics”, as mentioned in the book, opposed to Eastcoast skeptics, and finding the fact of our limited knowledge liberating, especially for human creativity.

After a summary comparison of Gödel’s concept of truth, a more in-depth analysis of that of Popper’s is to follow in my review. Gödel’s world view seems to be that we can intuit true (i.e. existing) things that we don’t have a logical justification for and cannot mathematically derive at in any system. Karl Popper, on the other hand, doesn’t believe in that kind of “truth”. Popper subscribes to the correspondence theory of truth: truth is what the facts are. He borrows Alfred Tarski’s definition:

“p” is true if and only if p.

claiming that a HYPOTHESIS is all that “p” is. Our intuitions are only hypotheses and we have no grounds for seeing them as truths in Gödel’s sense. Our brain is analogous to a theory, having tentatively evolved through instruction and selection (Gödel didn’t believe in evolution!), and our conscious experience brings new hypotheses into being, without them having any necessary correspondence with the real world or any existing things in the universe. (Things that we “directly” perceive neither presently, through a process of induction akin to Gödel’s view of how we derive at true mathematical axioms, nor in the past, like Plato’s forms, nor in the future, like the communist society). No idea that we can believe in or grasp is essentially and in its purest form “behind” our factual, corroborating instances of the hypothesis in the “real” world around us; of course ideas aren't literally identical with any physical things and neither are linguistically formulated corroborating statements of fact; this is Popper’s critique of essentialism.

Gödel’s logic applies here: “I don’t see any reason why we should have less confidence in this kind of perception, that is, in mathematical intuition, than in sense perception …” (cited in the last chapter). Here, Gödel correctly puts both areas of inquiry on an equal footing (albeit to make an unwarranted point in favour of idealism).

In describing theories as “closer to the truth”, what Popper means by truth is yet another thing. The sum of our experimental results, if they are positive, corroborating tests, will make a theory acceptable... (= closer to the truth; note that this notion of the truth cannot directly correspond or be identical with the level of true facts and experimental outcomes which are relevant to them, hence “closer to”)

...not, however, worthy of being believed in. The role of science is often to, quote: “overthrow this worthiness”, according to Popper’s own words, never establishing it. (See The Myth of the Framework) We may err in both kinds of perception, mathematical intuition as much as sense perception.

With this last notion of truth (of a scientific theory), Popper is trying to reconcile the vocabulary used for an acceptable theory with that used for a fact. Popper does not deny that there might also be usages for unfalsifiable statements — which may or may not be true, though this can, by definition, not be known — if they can be criticised (though often people do not allow themselves to question or criticise such statements or even elicit implicitly held taboos that can take the form of unfalsifiable statements). My philosophy falls into the category of the unfalsifiable. As does Popper’s, as he readily admits; Popper proposes a sort of pragmatic philosophy for the scientist to adhere to, a program I sympathise with, because I do believe it has had a positive cultural impact. Though no one can ‘disprove’ our problem-solving methods, since what we are talking about aren’t real things, Popper insists that, in science, we attempt to talk about real things. That’s why he uses the words “truth” and “truth-like”. This is a difference between science and philosophy. Yet all philosophy (e.g. epistemology, even political philosophy) and all science, I argue with Popper (and Bacon before him), have in common that they are both about problem-solving.

Thus, down to its bare bones, Popper’s idea of truth, as addressed to his readers, constitutes merely the human claims that potentially attain a certain status as “truth” or acceptability in the eyes of the (scientific) community or in those of a mere individual (rebelling against a community), *rather than explicitly stating that any concept of why a theory is true originates with the believer and, therefore, that this criterion is asserted by a member of the community and is imaginary.* His philosophy denies that there is any criterium that can generally decide on whether something is true or truth-like and he admits that truth-claims are impositions by the individual onto the world (to some extent traceable to Immanuel Kant in Popper's work). Thus, often in his writings, he completely circumnavigates the issue of belief, implicitly and explicitly acknowledging the creativity of human beings. This creates the impression, for me at least, that he ascribes to the statement between asterisks above, without clearly stating it, to provide with a philosophy of science that general readers can come to an agreement on, mentioned in the previous paragraph.

I suppose telling a lie only requires being unaware of the fact of the imposition one is making when asserting a claim; because that is sufficient for a person to appeal to an authority as source of truth. The only source of truth is you.

For Popper the problem of science is a problem in epistemology: “how do I know what I know?”

What distinguishes that from the problem addressed by nihilism is that ours is the problem of belief, asserting: “there is nothing to be believed in”, from which certain questions arise: "why do I believe what I believe to be true?", "why do I desire to believe certain things?", etc. etc. (It is the result of extending Popper’s critique of worthiness for belief in scientific theories, or theories *about knowledge*, mentioned above, to all belief. Note: people usually justify their belief by claiming to know about the existence or “truth” of the things they believe in, otherwise they see themselves and others as acting hypocritically. If someone has no sense of the objective [which can have ontogenetic reasons], or doesn’t value truth [due to contrary motives], that makes them less susceptible to care about the criticisms if put to them.)

While Gödel isn’t alone in talking like this: it is interesting to note that he describes nihilism as “grim”.

The program of nihilism is much more extensive than Popper’s philosophy of science. To my knowledge, Popper never rejected belief systematically in writing. His attitude, like that of many skeptics, nevertheless is indicative of such a rejection and the creativity that comes with it.

The reader may compare what I say here with what I have to say in my video “Against Belief”: https://youtu.be/qjcAaDqkzMY