Let's define logical psychologism as the view that the correct way to figure out logic and critical reasoning is to think about the mind. Notable defenders of such a view include John Stuart Mill, A System of Logic (1843), Theodor Lipps (1893), Wilhelm Wundt (1880/1883), and Christoph Sigwart (1921). (See Martin Kusch's "Psychologism" entry in the Stanford Encyclopaedia of Philosophy for a great historical overview of the position or his (1995).)
It rarely receives any attention these days, largely because of the withering attacks levelled against it by Edmund Husserl and Gottlob Frege in the early 20C. This is ironic since in his early work the Philosophy of Arithmetic Husserl promoted that all mathematics and logic should be reduced to psychology. He was a proponent of logical psychologism, until Frege set him straight in a now famous review of the work. Let me quote from it liberally:
It is precisely because the boundary between the subjective and objective is blurred, that conversely the subjective also acquires the appearance of the objective. [...] [Husserl has done exactly that with presentation and its object.] In combining under the word 'presentation' both what is subjective and what is objective, one blurs the boundary between the two in such a way that now a presentation in the proper sense of the word is treated like something objective, and now something objective is treated like a presentation (Frege's Review of Edmund Husserl's Philosophy of Arithmetic)
It was Husserl's critique in the Prolegomena of the Logical Investigations and Frege's Foundations of Arithmetic and The Basic Laws of Arithmetic that turned almost everyone working in Analytic philosophy at the time against any form of logical psychologism. In those works, his first principle was "always to separate sharply the psychological from the logical, the subjective from the objective" (Frege 1953, p. x).
The arguments of these two philosophers condemned logical psychologism to the philosophical trash heap. But was that condemnation fully justified? Have we to worry about logical psychologism leading to a logic built on relativism, anthropologism, or subjectivism? Given that idealism seems to be undergoing a virtual renaissance, mostly thanks to work in artificial intelligence and cognitive science, maybe logical psychologism hasn't been dealt a death blow. I want to explore a motivation for logical psychologism that suggests we close a gap between reasoning and our psychology through our pursuit of truth. If this motivation is wrong, then there's no reason to take up psychologism.
Inferences are hard to cash out using only logic. Logic reveals the way that inferences run, and it shows that this-or-that inference is correct. What logic doesn't show is why we ought to accept that inferences must work that way.
Here's a proto-argument against psychologism:
There's no guarantee that when your mind is working the way that it's built to work, it will produce correct (true) conclusions.
So, to find out how to produce correct (true) conclusions, you can't just look at the mind. (from 1)
Thus, you have to do your logic, i.e., to find out what the correct rules of inference are, by looking outside the mind. (from 2)
The trouble is that if logic is outside the mind, then we have to reconcile two claims. First, a rule of logical inference, such as modus ponens, is valid, that is, it's truth-preserving. And, second, you should think using modus ponens. These are two very different claims. They don't say the same thing. One describes the validity of a rule of logical inference, and the other tells us what we ought to do. How do we bridge the gap?
Some might choose to deviate from the inference deemed correct by logic, but still come up with the same conclusion. So, we need not necessarily follow the rules of a priori logic to get something right about inference patterns. If we don't need a priori logic for making correct inferences, then the way the mind works might be able to inform us about logic. Thus, the way the mind works will inform us about logic; psychologism is the correct account.
Here's a second motivational argument that bridges the gap between the descriptive and the normative. Truth is the goal of inference: we want to get true conclusions. You can't get anything out of false premises; the best you can do is to keep and extend the truths you've got. Only valid inferences are guaranteed truth-preserving. Therefore, do your thinking with valid inference rules like modus ponens. On this motivational argument, we bridge the gap between the normative and descriptive by noting that our aim is to preserve truth and valid inferences help us achieve that goal, so logical psychologism oughtn't be rejected out-of-hand.