2

What logic comes closest to a descriptive model of human thought?

  • It should be a non-monotonic logic. Sometimes a person can be convinced of a proposition by some evidence or argument, and then convinced out of that proposition by further evidence or argument.
  • It should account for uncertainty in some way.
  • It should be applicable to empirical questions and induction.
  • Perhaps it should allow for fuzzy truths as well (propositions that may be partially true).
  • It should be computationally tractable. This is why full Bayesian inference does not qualify. A descriptive model of human thought should not assume a person can immediately deduce all logical consequences of a set of evidence.

Of course, no perfect model of human thought yet exists, but are there good candidates meeting most of these criteria?

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  • Maybe it would be better to a) talk about conceptual thought or, even more specific, human reasoning since human thought does involve thinking in pictures and feelings, and b) specifically include or exclude normativity.
    – Philip Klöcking
    Mar 2 at 13:14
  • I did say I'm looking at a descriptive model, not a normative model. If there is some logic that allows for pictures and feelings as terms, all the better. I don't want to restrict to "reasoning" because that just kicks off a debate over what qualifies as "reasoning." In fact I think much of what we call "reasoning" indeed uses pictures and feelings. However if some logic doesn't account for pictures and feelings, but is true to life in other respects, that's fine too.
    – causative
    Mar 2 at 13:16
  • That's fair, may be a bit fuzzy/broad as it is, therefore the suggestions. And I have to point out that you can easily have a descriptive model of normative statements/reasoning/thinking. Actually, a major part of empirical human sciences does develop exactly that.
    – Philip Klöcking
    Mar 2 at 13:21
  • 1
    None. How humans think is a patchwork of reflexes, biases, habits, analogies and metaphors, etc., with a thin layer of conscious effort on top, that varies from person to person, purpose to purpose, and situation to situation. There is no "best" in multi-critereal optimization, there is only a host of incomparable items each getting "closest" in different contexts for different objectives under different metrics. Classical logic may be "closest" to how mathematicians (ideally) think in (classical) mathematics, for example.
    – Conifold
    Mar 2 at 13:38
  • 1
    Things like defeasible logic and relevance logic approach the ideal you're looking for, but I don't know how close they come. Mar 2 at 17:33
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Like Conifold, I don't think there is a single logic that will do everything you want. The requirement for tractability itself is sufficient to constrain any account to a collection of heuristics that would barely qualify to be called a logic.

There is an ongoing project called 'Progic' (a combination of probability and logic) with participants from several universities, that is exploring the development of a logic of uncertainty that combines elements of Bayesianism with non-monotonic logic. They hold a workshop every other year, and the proceedings are usually published in the Journal of Applied Logic. Some of the main contributors are Niki Pfeifer, University of Regensburg, Jan-Willem Romeijn, University of Groningen, Marta Sznajder, Munich Center for Mathematical Philosophy, Gregory Wheeler, Frankfurt School of Finance and Management, and Jon Williamson, University of Kent.

Saying that you are interested in descriptive rather than normative accounts is a bit different, since that is more in the realm of cognitive psychology than logic itself. Many cognitive psychologists have studied how people reason. Philip Johnson-Laird at Princeton made a career out of it and published several books. Michael Oaksford at Birkbeck College London and David Over of Durham University also come to mind as having done quite a lot of work in understanding how people reason with uncertain information. Oaksford and Chater published a book, "Bayesian rationality: The probabilistic approach to human reasoning" Oxford University Press (2007).

I am not fully versed in this area, but my understanding is that Johnson-Laird favours accounting for human reasoning primarily in terms of mental models, while Oaksford and others believe that people do something that approximates Bayesian reasoning, just not very well. What we do know from experimental studies is that people are mostly pretty bad at logic and quite appalling at reasoning with uncertainties. So I'm not sure what value a descriptive account would have: it would perhaps serve to tell us just how bad we are at reasoning, but we would still need a normative account to tell us how to do it well.

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  • Useful information about Progic, thanks! I don't think one should underestimate the usefulness of thinking like a human. For all that humans are bad at deductive logic and Bayesian probabilities, we navigate the world far more effectively than any system built using the former techniques. Clearly the human mode of thought has something going for it. And I don't think the answer is just "we've got a lot of random heuristics" either - that's part of it but we've tried building systems like Cyc with lots of common sense knowledge as well, and they don't work that well.
    – causative
    Mar 2 at 22:38
  • Perhaps we do something like partial Bayesian inference where instead of the intractable P(A|B) we calculate P(A|B ; R) where R is some specific reasoning, and P(A|B; R) approximates P(A|B) in the limit as the amount of reasoning increases. If a system like this exists I'd be very interested to learn of it.
    – causative
    Mar 2 at 22:40
  • That sounds like it might be related to 'bounded rationality' and 'satisficing', which describe how people find adequate but suboptimal solutions to problems within the constraints of partial information, cognitive limitations and available time. But again, this is mostly expressed as heuristics; I'm not aware of anyone managing to turn it into a logic.
    – Bumble
    Mar 2 at 23:20
1

This is a really difficult topic. If models of cognition like Kahaneman's system1/system2 (aka dual process theories) are correct, then basically there's more than one answer.

It's probably the case that "system2" (i.e. formalized) thinking is not independent of education, so it's unclear if the question is really meaningful for that.

As for what might be a "natural logic" for system1,... there has been a fair bit of experimental research e.g. on quantification, or on conditionals, or on on membership. At least the latter two lines of research generally point to less-than-classical logic. (Related; one experimental paper concludes that no normal modal logic captures how people intuitively think of possibility.)

I don't know if any of these woks can considered definitive as on some level they are related to the semantics of natural language, which in itself is a big topic; see Montague semantics etc. It's actually been a disputed topic in developmental psychology how much logical inference depends on language. Primates for examples exhibit some level of "conjunctive thinking", e.g. they can seemingly infer the order of any pairs in a sequence from exposure just to adjacent pairs pairs (aka "transitive inference"). On other hand it's been (even) more debated whether "disjunctive thinking", i.e. from knowing that a or b is true, and that a is false, then b must be true (which is related[*] to modus tollens) is related to language or not. In human infants, ability to reason along the latter lines develops simultaneously with language. Some monkeys are apparently capable of solving tasks like that too, but only a minority of them (2-3 out 10), and even those that manage it only succeed with some 60%-70% probability (the higher end with training). (For what's that worth, there's one 1980's paper that found that nearly half of the scientists in that sample failed to recognize/apply modus tollens.)

[*] some authors (e.g. Granstom pp. 37-39) call the "common" modus tollens "A implies B, [fusion] not B, therefore not A" modus tollendo tollens and "A or B, [fusion] not A, therefore B" modus tollendo ponens.)

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What logic comes closest to how humans think is the logic we conceive! Through rational inquiry we've been able to observe and control some of the fundamental laws of nature, and these discoveries have been made by using imagination, ingenuity, invention and mathematics.

The universe contains perceivable and predictable order, and the human brain can detect, observe and quantify patterns in both nature (external world) and intrapersonally (contemplation).

The logic we have invented is a reflection of the capability of the human mind and intellect - it is an expression of our attempt to explain natural phenomena and invent systems for computation.

The universe can be described as occurring in an ordered fashion, and contains symmetry, and mathematics being described as “the language in which God has written the universe” - and given we humans are a product (existence) of the universe, it is reasonable to see that human beings have inherited some of the qualities of the universe (nature).

The ability for the human mind to construct logical thought processes have evolutionary benefits, such as by using rational inquiry to control the forces of nature, and all for the sake of survival.

If the human mind is capable of inventing Boolean Logic, then this is one of the closest to how humans think. Like wise for multiplication...

The logic which comes closest to how human think is the logic (of both past and present time) we are able to conceive, i.e. we do not receive logic from some unknown external system - but logic is formed within the mind through learning, imagination, rational inquiry and intelligence.

0

That's a question for a discussion, as there does not exist any one particular logic that meets all of your requirements.

First, I'd try to comment your postulates:

ad.1 I am not aware of any axiomatic system that's not monotonic (if someone is, please comment), that'd be againts the core idea: "for the same input, you should always get the same output". And it doesn't matter whether it's a deductive or inductive one. That's just one of our civilazation's basic principles of thought (again, I'd love to get to know the arguments against).

ad.2 Dealing with uncertainty (namely: "probability") is actually quite common. All of the inductive logics are based on the notion of probability. But if by "uncertainty" you mean uncertainty of the logical values, you have Zadeh's fuzzy logic (actually Lukasiewicz's many-valued logic).

ad.3 I don't exactly get the requirement here, as most commonly-used logics are. Dealing with empirical data is culturaly one of the main demands for "logic".

ad.4 What you ask for here is, among the fuzzy logic, which I assume you're well aware of, because of the usage of the term "fuzzy"; the whole group of paraconsistent logics.

ad.5 I think you're mixing here two distinct concepts: logic theory and logic model. What you asked for in [1 - 4] is a logic theory, but what you ask in [5] is logic model (we can easily imagine applying a propositional calculus theory to a model, which applies its laws with a time delay).

As a software developer, working with AI, I think it's a really good question, and would like to see other answers, maybe presenting some examples.

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"What logic..."

(Modus Ponendo): This expression assumes the existence of multiple forms of logic which would imply that they are incoherent between them (only in such case they can be different, in order to be multiple).

Such argument is evidently false. All forms of logic are coherent.

(Modus Tollendo): If they are coherent between them, there's only one logic. There is no "X logic" which correspond to human thinking. All forms of logic correspond to human thinking, and therefore, human thinking follows logical rules (evidently, when logic is applied properly).

The problem addressed by the question is not which are the rules humans follow to think, but which is the goal that human thinking aims to.

In simple words, you can follow different methods to solve a logical or mathematical problem, but all results will be the same, following the same inputs.

Any expected difference, in general, will come from the inputs. That is, it is the goal that human thinking is applied for that will provide different results.

Regarding such discussion, there are multiple arguments about what is the final human goal. Some say it's happiness, others say it's pleasure, etc. My preferred argument is survival. So, two human beings can find opposite solutions to the same problem, simply because they have different inputs (previous knowledge) (e.g. John might say that vaccines risk survival, because he saw someone dying after a vaccine, and Mary could think that vaccines help survival, because she knows the statistics).

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This is field of psychology, one I've taken at least one class on.

https://en.wikipedia.org/wiki/Psychology_of_reasoning

I remember being impressed by how poor people were are deduction

The responses given to the selection tasks showed the usual facilitation of deontic over indicative problems, with 64% correct (i.e.,p + not-q responses) on deontic tasks and 8% correct on indicative tasks.

http://www.reading.ac.uk/AcaDepts/sx/ARL/uor-department/people/clare/ClareHarley_plymouth%20paper.pdf

an indicative conditional is a conditional sentence such as "If Leona is at home, she isn't in Paris", whose grammatical form restricts it to discussing what could be true.

8% of students (at one uni) are able to solve these sorts of problems. This seems amazing, especially if it can be taught, uses few cognitive resources.

The Monty Hall Problem is quite famous, and can be described as a "cognitive illusion". Perhaps many failures of reasoning can be. Interestingly, many very clever people failed to understand even the solution to the MHP.

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  • The correct answer to the Monty Hall Problem is dependent on how the question is formulated. Many people who comment on the Monty Hall Problem do not realise that as formulated in the Wikipedia article, there is no reason to switch the initial choice. Thus, most of the allegedly wrong answers are in fact perfectly correct. This observation may not apply to other formulations of the problem. Mar 6 at 11:07
  • the assumptions are simple and easily stated. i've never read the original question, so i can't comment on their ambiguity @Speakpigeon
    – anon
    Mar 6 at 22:07
  • i don't see any ambiguity in the question, the 'say' is clearly parenthesised "Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?"
    – anon
    Mar 6 at 22:32
  • for me, the assumptions are contained in the original wording, without ambiguity, only a relative lack of clarity / emphasis on what those are @Speakpigeon it could well be that adds to the confusion about the MHP, but i suspect that is out of proportion when compared to other similarly clear puzzles
    – anon
    Mar 7 at 0:29
  • Statements in natural language can be very easily misunderstood. The Monty Hall Problem is not badly worded or phrased, Rather the situation described is just complicated enough that many people will miss a crucial detail. And in this case, it appears that most pundits miss it, although I don't don't why. Mar 7 at 16:30
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Logic is one of those things about which most people have more misconceptions than correct ideas. Take the word "reasoning". The relevant definitions are as follows:

Reasoning 1. the act or process of drawing conclusions from facts, evidence, etc.

Reason 2. a. The capacity for logical, rational, and analytic thought;

Reason is the capacity of consciously making sense of things, applying logic, and adapting or justifying practices, institutions, and beliefs based on new or existing information — https://en.wikipedia.org/wiki/Reason

Given these definitions, we may get the impression that typical reasoning consists in a conscious process of drawing conclusions using our capacity for logical, rational, analytic thought. Yet, it turns out that we really suck at doing this. We all have opinions on things, but when we are challenged to justify our claims, we invariably fail to provide anything like a proper reasoning as defined and indeed as usually understood. All we can usually do is exhibit a few paltry reasons, reasons that we usually are again incapable of justifying properly. And this is not just "ordinary folks". Lawyers may be considered as professionally motivated to be good at it, and yet, they too fail. They certainly can string together a large number of reasons, often reasonable enough, but in the end nothing that would constitute any actual logical reasoning. We can verify this also with philosophers, in particular with analytic philosophers, the ones who actually tried really hard to do it. And who also failed. Perhaps the best evidence of our inability to produce reasonings as we usually understand the term is the failure of mathematical logic to formalise the mathematical reasoning supposedly justifying mathematical proofs. The best that mathematicians have been able to achieve in this respect is to adopt the material implication as the most accurate model of the logical implication at the heart of any logical reasoning. Yet, it is apparent, and philosophers and mathematicians who know the history of logic recognise this, the material implication is not any accurate model of the logical implication. And thus, mathematical logic does not provide any formal description of any mathematical reasoning. This does not stop mathematicians doing mathematics and producing proofs, just not anything like formal proofs of their theorems. More explicitly, whatever mathematical logic proposes in lieu of formal proof has in fact little relation to the logical reasoning of mathematicians themselves.

It is the failure of mathematicians to describe logical reasoning which has come to provide the rationale and the motivation now for many philosophers to reconsider the fundamentals of our view of human reasoning. Essentially, most philosophers now seem to have resigned themselves to the idea that there is in fact no such a thing as logical reasoning. It is of course easy to exhibit all sorts of examples of actual human reasoning that seem to confirm this relatively new perspective. And so the conclusion is now that human reasoning is so riddled with cognitive biases and quirks that the search for the logic of human deductive reasoning can only be a goose chase.

Yet, it is easy to falsify this view. For example, it is a fact that Aristotle's syllogisms all seem perfectly logical to us. Similarly, all logical truths discovered by traditional logicians since Aristotle also all seem perfectly logical to us. Mathematicians themselves discovered some logical truths, such as for example De Morgan's Laws. And nobody has any doubt that they are correct (Pierce's Law apart, but this is a special case). The few arguments philosophers have proposed purporting to show that the modus ponens or the modus tollens are not quite true or don't apply to all cases are gross logical fallacies and mostly recognised as such.

There is no doubt that there is such a thing as the logic of human deductive reasoning. It is by definition very limited. The logic of something is by definition the few basic principles that underpin the way something works. Thus, we shouldn't ask formal logic to provide a model of the psychology of human reasoning. Logic is by definition limited to the fundamental principles of deductive reasoning, principles we can easily recognise when we see them. What reasonings people actually do is something else entirely. We are all free to reason illogically and we do it all the time. I don't believe for a moment that we can think illogically, but we can without the shadow of a doubt articulate illogical reasonings. Indeed, it is probably easier to do that than to bother articulate a properly logical reasoning. Even mathematicians themselves never bother to articulate formal proofs of their theorems. They think it is good enough to simply provide the minimal explanation which will be sufficient to satisfy their peers that the proof is good. A sort of very sensible gentlemen's agreement.

So it is indeed apparent that a model of actual human reasoning is beyond our current means of investigation, but this shouldn't lead us to throw the logical baby with the bath water. Logic is here to stay and once you put in perspective the historical failure of mathematical logic, it is easy to see that humans do have a logical capacity which can only be native, and to see that Aristotle provided a very good portraiture of it. Nothing like a formal model yet, but good enough that we can all recognise the thing when we see it: If A and B is true, then A is true, but A and B is true, so A is true.

So I don't believe we are close to producing any good description of the way humans think, but producing such a model will inevitably require that we first produce a formal logic which will be an exact model of the logic of human deductive reasoning. The debate currently is muddled by the failed attempt at mathematical logic, but there is little doubt that we will move beyond this problem at some point. Philosophers have also displayed the limitation of their discursive methodology. Most of the discussions philosophers have on the subject is either a Scholastic exegesis of mathematical logic, which cannot possibly provide any clue about the actual logic of human deductive reasoning, or an effort to find another direction. Yet, the subject is well known and it is properly identified. All we need to do now is to develop a properly empirical science of logic, as opposed to the mathematical science of logic, which was doomed to fail from the start simply because mathematicians are not empirical scientists and so don't have the methodology adapted to the task.

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  • Most of this answer seems a red herring to me: it's accusing mathematical logic of failing to provide an account for how people think in everyday reasoning. As far as I know that was never a goal of mathematical logic. (The question asker also doesn't seem to be holding such an idea.) The rest of the answer seems to argue that only if we could conduct the "proper" experiments, we could find out. But plenty of experimental work in the psychology of logic was conducted. It's not clear if this answer is just unaware or dismissive of that (for some unstated reason).
    – Fizz
    Apr 13 at 3:07
  • FYI: "Frege, Whitehead, and Russell established first-order predicate calculus, which is now usually referred to as classical logic. [...] it is a “mathematical logic” – not only is its form mathematical, but also its subject matter, as it was designed primarily to provide a logical foundation for mathematics (Haack 1978; Kneale and Kneale 1962). The most important form of reasoning in mathematics is theorem proving, and in this process theorems are derived from axioms and definitions, following well-defined inference rules." [continues]
    – Fizz
    Apr 13 at 3:46
  • "To serve this purpose, Frege took a very strong “anti-psychologism” position, and argued that logic should study “the laws of truth” rather than “the laws of thought”."
    – Fizz
    Apr 13 at 3:46
  • @Fizz "As far as I know that was never a goal of mathematical logic." Of course it was. Read Boole's first book. He is very explicit that this is what he has just done. And his other book, i.e., "the Laws of Thought" says it in the title itself. Further, mathematicians are human beings and they don't do any logical reasoning that other human beings would somehow be incapable of. Apr 13 at 11:17
  • @Fizz "but also its subject matter" No; The subject matter of mathematical logic is the logic of human deductive reasoning. You are confusing the fact that mathematicians needed specific methods of proofs, such as the truth table or natural deduction systems. The French and the British have come to use different languages, but the logic is the same, as can be demonstrated by the fact that mathematicians can be French or British, or indeed both. Apr 13 at 11:22

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