Q&A: On the Concept of Intuition
On the Concept of Intuition
Question
Hello
Regarding the concept of intuition that recurs in your books (I apologize if the questions stem from not having studied them carefully):
– Different people use this concept in very different ways. For example: as mathematics students, my friends and I use it mainly to indicate an understanding of a general concept based on a clear picture of a representative case, rather than on formal logical analysis—a picture for which the distance from the formal analysis is sometimes minimal. By contrast, New Age people sometimes use this concept as a symbol for knowledge that comes in a mystical way, without relying on sensory information. In what sense do you use the concept?
In particular—can intuition, like other aspects of human functioning, be described as an algorithm?
– In light of the answer to the previous question, what is the mechanism that makes intuition effective in the diverse contexts in which you suggest giving it weight?
I do not mean an a priori logical justification for using intuition, but rather an a posteriori explanation of its effectiveness—analogous to the psychophysical explanations of how the senses work, the evolutionary explanations for the existence of a fairly effective innate perception of space-time, and the probabilistic models that try to explain the effectiveness of the scientific method.
Thank you in advance, and also for what you have already contributed to my worldview
Answer
Hello Bnaya.
I use "intuition" to describe how we acquire our basic assumptions. They do not arise from logical analysis (by their very nature as first principles), and usually not from observation either (since observation does not yield general concepts, and really not concepts at all. Observation is of objects). Within this framework, the definition of concepts and our understanding of them is also its product.
The question whether this is mysticism—my view is no. Science is based on this, as is all rational thinking. Not everything that is not logic is mysticism. After all, even a logical argument is based on assumptions that do not come out of logic.
Understanding a general concept through a representative case is a kind of generalization (like scientific generalization), as Wittgenstein discussed it. This is a clear example of the use of intuition (making the generalization correctly).
The question whether our intuition can be algorithmized is the subject of the Church-Turing hypothesis, and today it is considered an open question. I am hardly qualified to answer it (though I suspect not. For example, proving Gödel's theorem, and perhaps even more so interpreting the meaning of that proof—it is hard to accept that an algorithmic machine does that). It is quite clear that in practice we do not do this algorithmically, but perhaps there is an algorithmic model that models it. Something like this is the visual recognition of a Torah scholar in the laws of returning a lost object. The Talmud assumes that a person (any person, not only a Torah scholar, contrary to what people commonly say) has the ability to grasp whether this object is his object even without resorting to concrete identifying marks. And still there is room to discuss whether this is a non-algorithmic ability, or whether it is a perception of many small signs that combine into ordinary sensory recognition. In that case, it is basically a kind of algorithm (not essentially different from identification by signs).
As for the mechanism or explanation, what is wrong with evolution or divine design? As you wish. In my opinion, both.