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In logic we can't make any deductions without rules of inference, predicates, and formulas. In probability/statistic we can't make any inferences without assuming some probabilistic model which might include families of distributions connected by joint probabilities together with observed data.

With a model of inference, I mean for example predicate logic together with predicates that represent information in a domain. Or probability theory together with distributions that represent information in a domain. Predicate logic has rules of inference, like modus ponens, probability theory has Bayes rule. However, are these models of inference always needed for reasoning?

Am I correct in thinking that in any form of reasoning a model is needed?

If not, would you be able to give an example of reasoning where a model of inference is not required to make inferences?

(This might be a stupid question, I can't think of any possibility where we can reason without a model. However, it doesn't mean that if I can't possibly conceive a situation that it is actually impossible.)

  • I think in order for this question to be answerable, something approaching a definition of "model" is needed. In particular - and re: your first sentence especially - how is the notion of model different from reasoning itself? – Noah Schweber Jan 21 at 22:10
  • @NoahSchweber I updated my question. – Xochipilli Jan 22 at 7:55
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I'd be tempted to say that logic is not a model that we use to reason. It's a model, a representation, of how we reason (or should reason). People don't need to learn the rules of classical logic to make inferences, but logicians are interested in how people make inferences, this is where the models of logic come from. This might apply to some extent to probabilistic reasoning (people would naturally say that the conjunction of two unlikely events is even more unlikely for instance, even if they haven't learnt any math).

Once the model is in place, we can also use it to make inferences, which is some kind of way of "mimicking" and improving our natural inferential practices. But this second step is optional.

So it's not that a model is needed in any form of reasoning, but rather that any form of reasoning can in principle be modelled.

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    It seems a bit more dialectic to me. "Naive" probabilistic reasoning is plagued with psychological biases that the model "corrects", it is then needed to reason "properly". To a lesser extent, this applies to "naive logic" as well, with its affirming of the consequents and finicky conditionals. The "model" is not really a model of what we do, but a normative "grammar" that answers to other concerns as well, and deliberately alters what we do. The reasoning practice and the grammar both need and feed each other. – Conifold Jan 22 at 8:29
  • I'm reminded of Locke's 'But God has not been so sparing to men to make them barely two-legged creatures, and left it to Aristotle to make them rational'. – Geoffrey Thomas Jan 22 at 11:34
  • @Conifold that's a good point, there's a normative component that is central in logic. I'd say that a model is not necessarily purely descriptive. – Quentin Ruyant Jan 25 at 2:53

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