The limitations of logic

Why I am a heretic(2)

In an earlier post, I suggested that part of why the way I look at things is different from that of traditional philosophy, is because philosophers place so much emphasis on logic to the exclusion of other approaches.  Today, I want to discuss what I see as the limitations imposed by logic.

I’ll begin by reminding the reader that I am a mathematician.  The way that mathematicians use logic is different from the way that it is often used in philosophy.  Some people distinguish between the two by using the expression “philosophic logic” to refer to the use of logic within traditional philosophy.  The reader should be warned that my view of the limitations of logic is colored by my background as a mathematician.

Logic is usually seen as the application of rules of inference to premises.  The Wikipedia page provides a reasonable account of this.  One consequence is that logic itself is solipsistic.  Logic consists of applying rules of inference to mental abstractions, where those mental abstractions are something like idealized versions of natural language statements.

To say that logic is solipsistic is just to say that logic itself has no world.  It can be use in abstract mathematics, and it can be used is solving problems that come from our world.  But the connection with the world does not come from the logic.  It has to come from somewhere else.  For science, the connection with the world comes from its empirical methodologies.  As I have previously posted, I see geometric methods as important here.  However, philosophers mostly like to stay with the logic, and to avoid getting into empirical methods.

Because logic works with assumed premises, the logic cannot begin without inputs.  Philosophers typically take observations as being raw input.  And they see all of the important work as being done by applying logic to observations.  They often take observation for granted, assuming that perception is passive and that everything important happens after perception, presumably as some kind of logical analysis of what is perceived.

We see something similar to this in the field of AI (Artificial Intelligence).  AI proponents assume that the brain is a computer, acting on inputs received and producing outputs.  That suitable inputs are available is simply taken for granted, the assumption being that sensory cells provide those inputs.

Science, by contrast, begins earlier.  It begins before there are observations.  The scientist may have hints that something of interest is happening.  But, at the beginning of a new study, he might have no way of coming up with reliable observations to which logic can be applied.  So the scientist must start by creatively inventing empirical procedures that allow reliable observations to be made.  As an illustration, consider the branch of physics that deals with electricity.  The observations of electrical phenomena include observations of electrical charge, electrical current, voltage (or electromotive force).  None of these observations were possible before the scientific study of electricity began.  Not only were the observations not possible, but they were not even expressible in terms of the concepts that were in use at that time.  Logic alone, applied to observations already being made, could not have been sufficient to investigate electricity.

Our ordinary language statements seem to be about the world.  But, because logic is solipsistic, it cannot account for this connectedness of our linguistic expression with the world.  Philosopher’s use the term “intentionality” to refer to this connectedness.  Some see intentionality as an unexplained mystery.  Others (eliminativists) argue that it doesn’t exist.  I see it as a problem that results from the limitations of logic, and from the emphasis that philosophy places on logic.