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Reasoning from Problems not Assumptions

Ron Garret (RG) wrote (CR means Critical Rationalism):

All reasoning has to start from assumptions. Assumptions by definition can't be proven or disproven. So how can we evaluate our core assumptions? If we try to use reason, that reasoning must itself be based on some assumptions like, "Reason is the best way to evaluate assumptions." But since that is an assumption, how can we evaluate it without getting into a infinite regression?

And near the end of the post:

The point is: the apparent infinite regress of rationality bottoms out in its effectiveness

And in comments:

BTW, I very much doubt that CR actually claims that reasoning is possible with no assumptions. If Popper (or Deutsch) ever actually said this, it's news to me. It seems self-evident to me that all reasoning has to start with assumptions. Whatever else a reasoning process consists of, there has to be some point in the process at which you assert for the first time the truth of some proposition. That assertion cannot be based on the truth of any previously asserted proposition because, if it were, it would not be the first time you asserted the truth of some proposition. A proposition that is asserted to be true without any prior assertions to support it is by definition an assumption.

(Note that even this argument makes assumptions, e.g. that reasoning has a beginning, that it involves the assertion of propositions, that words like "assert" and "proposition" have coherent meanings, etc. etc. etc.)

The view described by RG is the standard, non-CR view. It is regarded by CR as incorrectly relying on foundations and justification, and as not having the right paradigm. Example quotes about foundations (partly to explain, partly because of RG’s doubts that the CR thinkers Karl Popper (KP) or David Deutsch (DD) disagree with him):

KP in The Logic of Scientific Discovery:

The empirical basis of objective science has thus nothing 'absolute' about it.[4] Science does not rest upon solid bedrock. The bold structure of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or 'given' base; and if we stop driving the piles deeper, it is not because we have reached firm ground. We simply stop when we are satisfied that the piles are firm enough to carry the structure, at least for the time being.

DD in The Beginning of Infinity:

The whole motivation for seeking a perfectly secure foundation for mathematics was mistaken. It was a form of justificationism. Mathematics is characterized by its use of proofs in the same way that science is characterized by its use of experimental testing; in neither case is that the object of the exercise. The object of mathematics is to understand – to explain – abstract entities. Proof is primarily a means of ruling out false explanations; and sometimes it also provides mathematical truths that need to be explained. But, like all fields in which progress is possible, mathematics seeks not random truths but good explanations.

DD in The Beginning of Infinity:

there can be no such thing as an ultimate explanation: just as ‘the gods did it’ is always a bad explanation, so any other purported foundation of all explanations must be bad too. It must be easily variable because it cannot answer the question: why that foundation and not another? Nothing can be explained only in terms of itself.

KP in Conjectures and Refutations:

The question about the sources of our knowledge can be replaced in a similar way [to replacing the “Who should rule?” question in politics]. It has always been asked in the spirit of: ‘What are the best sources of our knowledge—the most reliable ones, those which will not lead us into error, and those to which we can and must turn, in case of doubt, as the last court of appeal?’ I propose to assume, instead, that no such ideal sources exist—no more than ideal rulers—and that all ‘sources’ are liable to lead us into error at times. And I propose to replace, therefore, the question of the sources of our knowledge by the entirely different question: ‘How can we hope to detect and eliminate error?

The question of the sources of our knowledge, like so many authoritarian questions, is a genetic one. It asks for the origin of our knowledge, in the belief that knowledge may legitimize itself by its pedigree. The nobility of the racially pure knowledge, the untainted knowledge, the knowledge which derives from the highest authority, if possible from God: these are the (often unconscious) metaphysical ideas behind the question. My modified question, ‘How can we hope to detect error?’ may be said to derive from the view that such pure, untainted and certain sources do not exist, and that questions of origin or of purity should not be confounded with questions of validity, or of truth. This view may be said to be as old as Xenophanes. Xenophanes knew that our knowledge is guesswork, opinion—doxa rather than epistēmē—as shown by his verses (DK, B, 18 and 34):

The gods did not reveal, from the beginning,
All things to us; but in the course of time,
Through seeking we may learn, and know things better.

But as for certain truth, no man has known it,
Nor will he know it; neither of the gods,
Nor yet of all the things of which I speak.
And even if by chance he were to utter
The perfect truth, he would himself not know it;
For all is but a woven web of guesses.

Yet the traditional question of the authoritative sources of knowledge is repeated even today—and very often by positivists and by other philosophers who believe themselves to be in revolt against authority.

The proper answer to my question ‘How can we hope to detect and eliminate error?’ is, I believe, ‘By criticizing the theories or guesses of others and—if we can train ourselves to do so—by criticizing our own theories or guesses.’ (The latter point is highly desirable, but not indispensable; for if we fail to criticize our own theories, there may be others to do it for us.) This answer sums up a position which I propose to call ‘critical rationalism’.


So my answer to the questions ‘How do you know? What is the source or the basis of your assertion? What observations have led you to it?’ would be: ‘I do not know: my assertion was merely a guess. Never mind the source, or the sources, from which it may spring—there are many possible sources, and I may not be aware of half of them; and origins or pedigrees have in any case little bearing upon truth. But if you are interested in the problem which I tried to solve by my tentative assertion, you may help me by criticizing it as severely as you can; and if you can design some experimental test which you think might refute my assertion, I shall gladly, and to the best of my powers, help you to refute it.’

The standard, non-CR view involves problems like a regress because it tries to do things like argue for ideas "based on the truth of any previously asserted proposition” (RG’s words above). RG acknowledges some of the problems with arbitrary foundations or, in the alternative, an infinite regress. He tries to solve them by suggesting an effectiveness criterion for judging ideas. This doesn’t solve the problem: it is an arbitrary foundation or leads to a regressing debate about the effectiveness of the effectiveness criterion, and the effectiveness of whatever arguments are used in that debate, and so on.

The CR view is that we start our reasoning with problems, not assumptions. We proceed to brainstorm guesses about solutions. We do not assert that our guesses are true; we expect our guesses to one day be discarded as obsolete falsehoods because progress is infinite. And then we criticize the guesses. This leads to fixing the errors in some guesses and rejecting other guesses, and generally to progress.

The CR paradigm is not about establishing things on the basis of assumptions or on any other basis or foundation, nor is it about choosing a criterion for what types of theories are best (e.g. effective ones or simple ones). The CR paradigm is about error correction. CR says we learn not by making foundational assumptions and building from them to other ideas, but by making unjustified guesses to try to solve our problems, which we then expose to error correction.

Both CR and the standard view try to deal with the problem of differentiating good and bad ideas. The standard view seeks to find a good starting point, and good methods of thinking, so that bad ideas can never be introduced (or at least are hard to introduce). The CR view accepts there is no way to avoid error or even to make it uncommon, and instead focuses its primary effort on error correction. We can’t make error uncommon because we’re all alike in our infinite ignorance (as KP said) and we’re always at the beginning of infinity (as DD said) with infinite stuff left to learn. (There are also other arguments about fallibilism.)

The CR view on assumptions and foundations is that we can start anywhere. We can start with high level ideas or low level ideas. We can start in the middle. Anything goes because we aren’t trying to solve the problem of avoiding error by limiting where we begin our reasoning. What’s important is that all ideas be held open to error correction. Nothing is beyond question or criticism. There are no limits beyond which we can’t delve further and learn more. No matter where we start, we can always work in any direction. We can flesh out prior or lower level ideas more. We can flesh out later or higher level ideas more. We can go sideways. And things don’t organize neatly into levels anyway, for all is a woven, tangled, chaotic, web of guesses, not a pyramid hierarchy.

What stops the regress of asking “Why?” and “How do you know?” infinitely? Nothing formal. CR isn’t about proving we’re right. A CRist will say, “I’ve explained why I think this, and how I know, in what I think is an adequate level of detail to solve the problem I’m trying to solve. Do you see an error I’ve made?” CR is about searching for and fixing errors, not establishing that our answers are correct. We expect our answers will be improved in the future. We follow our interests in our attempts to live our lives, solve problems, and learn. There are infinite places we may direct our attention and we make judgments about which to prioritize. These interests and judgments, like everything else, are themselves open to criticism.

There is no way to provide infinite detail about one’s reasoning. This is not actually a problem unique to foundations. It applies just as well to the consequences of one’s reasoning (the further implications). But we don’t need infinite detail if we aren’t after a guarantee of correctness. If instead we know we may well be wrong, but we’re doing our best to find and correct errors, then the finite detail is adequate for that purpose. And there are no bounds on where we can go into more detail. Any part that people think could use more questioning can be critically considered more. We never have to stop, we just stop when we think our attention is better used elsewhere (and we don’t know of an error with that).

A criticism is an explanation of why an idea does not solve the problem it’s claiming to solve. The reason we shouldn’t accept (or act on) criticized ideas, even tentatively, is because we have an explanation of why they won’t work. And all criticisms are themselves open to criticism. (What do you do if people keep throw infinitely many dumb criticisms at an idea? In short, criticize infinite categories of idea all at once. Criticize patterns of error. Don’t criticize all the criticisms individually. In general, good will and good faith are helpful and make things better. But if someone wants to throw infinitely many criticisms at an idea, they may try it. It’s easy to do that if you generate the criticisms according to a pattern, but then they can also be criticized as a group because they fit that pattern. To defend against this, we’ll only need one counter-argument for each pattern the critic thinks of to form an infinite set of criticisms from. So we don’t have a greater burden than he does. And actually it’s better than that if we can identify a meta-pattern – a pattern to his patterns – and criticize that. If we use powerful criticisms with high “reach” (DD’s term meaning broad/wide applicability), which deal with the right issues, it becomes harder and harder for a critic to think of anything new to say which isn’t already addressed by our criticisms. And we can write them down and reuse them with all future critics. That is one of the main projects intellectuals should be engaged in.)

Our guesses can be arbitrary non sequiturs. They need not be based on anything – the source or basis is not the important thing. However, it’s hard to make them survive criticism if they don’t use any existing knowledge. It’s hard to start over, without the benefit of any existing knowledge (which has had a bunch of error-correction effort already put into it) and make something good. So we often build on, e.g., the English language. However, just because I use the English language to help me formulate my idea does not mean my idea depends on the English language in some kind of chain of logical implication. The English language is not necessarily assumed or an important basis. My idea may well be approximately autonomous. Maybe we’ll one day find huge flaws in English, and find that Japanese is much better, and then notice that my idea can be easily translated to Japanese because it was never actually tightly coupled to English in the first place. It’s like how the C programming language isn’t based on any particular CPU architecture and code can be recompiled for other architectures (so while my code needs a CPU to run, it’s not based on whatever CPU I’m currently using).

The CR paradigm lacks the solidity sought by the standard view. It doesn’t justify its ideas. It doesn’t provide justified, true belief. It doesn’t offer ways to demonstrate that an idea is true so that we need never worry about it having an error again. It doesn’t offer ways to positively establish ideas. It differentiates good and bad ideas by criticism of the bad ones, not by anything to bestow a good, positive status on the good ideas (which CR views as merely ideas which are not currently known to be wrong). CR is all we can have due to logical problems that the standard view has been unable to deal with century after century. And CR is enough for science to work, among other things.

I suggest rereading the DD and KP quotes (that I gave above) at this point. I think they’ll make more sense after reading the rest (both what they mean and how they are relevant), and they’ll also help clarify my text. See e.g. how KP talks about the sources of our ideas not mattering.

This is all a lot to understand. As far as I’ve been able to determine, DD and probably Feynman are the only people who ever understood CR by reading Popper’s books, without the help of a bunch of discussion with people who already knew CR (like Popper, Popper's students, or DD). We’ve never found a single person who has understood CR well from DD’s books without discussing with DD or DD’s students. I had many large confusions after reading FoR, which took years of discussion, study and DD help to resolve. CR is deeply counterintuitive because it goes against ~2300 years of philosophical tradition, and those ideas have major influence throughout our culture. Supporting people’s CR learning processes, if they’re interested, is one of the important purposes of this forum. Questions are welcome and you shouldn’t expect to fully understand this already or soon.

Note that CR theory explains this (the previous paragraph). Errors are inevitable and common, including when understanding even one sentence[1]. Trying your best to correct your own errors is a good start, but critical discussion has big advantages. People have different strengths and weaknesses, knowledge and ignorance, biases and irrationalities, etc. People differ. External criticism is valuable because other people will catch errors you miss (including errors they made in the past and already fixed). Because error correction is such a big deal, critical discussion is approximately necessary for ambitious people (the alternative plan is to be one of the best thinkers ever who is so much better than ~everyone at ~everything that external criticism doesn’t add much). Critical discussion also lets people share explanations, problems, and other knowledge which isn’t criticism, which is also helpful.

[1] DD in The Beginning of Infinity:

SOCRATES: But wait! What about when knowledge does not come from guesswork – as when a god sends me a dream? What about when I simply hear ideas from other people? They may have guessed them, but I then obtain them merely by listening.
HERMES: You do not. In all those cases, you still have to guess in order to acquire the knowledge.
HERMES: Of course. Have you yourself not often been misunderstood, even by people trying hard to understand you?
HERMES: Have you, in turn, not often misunderstood what someone means, even when he is trying to tell you as clearly as he can?
SOCRATES: Indeed I have. Not least during this conversation!
HERMES: Well, this is not an attribute of philosophical ideas only, but of all ideas. Remember when you all got lost on your way here from the ship? And why?
SOCRATES: It was because – as we realized with hindsight – we completely misunderstood the directions given to us by the captain.
HERMES: So, when you got the wrong idea of what he meant, despite having listened attentively to every word he said, where did that wrong idea come from? Not from him, presumably . . .
SOCRATES: I see. It must come from within ourselves. It must be a guess. Though, until this moment, it had never even remotely occurred to me that I had been guessing.
HERMES: So why would you expect that anything different happens when you do understand someone correctly?
SOCRATES: I see. When we hear something being said, we guess what it means, without realizing what we are doing. That is beginning to make sense to me.

When you read books, you guess. Many guesses are wrong. You fix many of them yourself. Critical discussion helps fix more errors. People routinely overestimate how well they understood moderately difficult books that they read, and it becomes a huge problem with very hard material like CR books. Understanding of books should be tested, and one of the best methods of doing that is to write down your understanding and then share it with people who already understand the book and see if they agree that you have their position right. (You can do this test of understanding whether you agree or disagree with the material).

Summary: According to CR, making assumptions is not the way one solves problems. One solves problems by brainstorming solutions and doing error correction on the solutions. And while doing that, CR holds that it’s important to recognize the fallibility of all of our ideas. We should hold our ideas open to critical questioning and improvement, and expect that they can be improved, not take them to be true. (Here I'm contradicting "All reasoning has to start from assumptions." An "assumption" means a proposition taken to be true). CR holds things like: Don’t assume your ideas are true; keep looking for errors.

I originally wrote this in 2019 and I've made minor edits.

Elliot Temple on June 16, 2021


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