A couple of days ago, I wrote about the function of logic.
At the suggestion of my friend robin, I investigated the works of the philosopher Josiah Royce.
Royce wrote an interesting essay on the subject of "Order." In this essay written in 1917, Royce appears to come to conclusions similar to mine:
We may sum up with the observation that, if we had no exact idea of what inference is, we should have no exact idea of what order is, while our very idea of what inference is depends in all cases where an inference relates to classes and to general law, upon our idea of what constitutes the negative of a defined class of objects or cases. Without negation there is no inference. Without inference there is no order, in the strictly logical sense of the word. The fundamentally significant position of the idea of negation in determining and controlling our idea of the orderliness of both the ideal and the real world, of both the natural and the spiritual order, becomes, in the light of all these considerations, as momentous as it is, in our ordinary popular views of this subject, neglected. To the article NEGATION we must, therefore, refer as furnishing some account of the logical basis upon which the idea of order depends. From this point of view, in fact, negation appears as one of the most significant of all the ideas that lie at the base of all the exact sciences. By virtue of the idea of negation we are able to define processes of inference – processes which, in their abstract form, the purely mathematical sciences illustrate, and which, in their natural expression, the laws of the physical world, as known to our inductive science, exemplify. Serial order is the simplest instance of that orderly arraying of facts, inferences, and laws upon which, on the theoretical side of its work, science depends; while, as we have seen, in the practical world, the arraying, the organizing, of individual and social life constantly illustrates, justifies, and renders spiritually precious this type of connexion, which makes our lives consecutive and progressive, instead of incoherent and broken.
As an aside, notice how Royce mixes discussions about propositional logic (the rigorous) with discussions about natural language and religion (the informal). I'm not saying Royce was confused on these issues, I'm just saying that his papers don't seem organized in a logical fashion considering the distinctions involved.
Anyway, I interpret Royce's analysis as consistent with my own: logic is vital for comprehension and perception of structure, and that negation in logic is even more fundamental, negation being necessary for knowledge, even of the most simple facts.
So there you have it. I might just have deduced something that Royce figured out more than 50 years before I was born!
I agree with Royce: without logic there can be no knowledge or structure.
Why was I never taught about the nature of logic in high school or college? Is this conclusion obscure or controversial?
Here's why I think this is an important issue.
Ask your friends this question: "Can we have knowledge without logic?"
I think most people would say yes. However, they are not answering the question literally. They read the question as: "Can a person obtain knowledge without using speech, inner monologue or symbol manipulation?"
Of course, we can know something from intuition or gut feeling without using reason explicitly. Let's look closely at an example. Suppose you work as a security guard at an airport, and a passenger tells you "Yes, I packed my own suitcase." Your gut tells you the person is lying, even though you have little conscious evidence that this is the case. Plausible, right? It is well known that people can subconsciously pick up on small details in a person's body language, speech or facial expressions. However, even this intuitive inference would be impossible if we could not distinguish between one proposition, "The passenger is lying," and its negation, "The passenger is not lying."
This is the one of the pillars of logical positivism: in a domain where logic does not apply, there can be no knowledge or perception. Since causality is itself a form of order (it implies structure in time), there can be no causality without logic.