The definition of induction will be generalised
Popper's epistemology rejects the viability of induction, yet many scientists, professionals and, indeed, the public at large operate in the world with indifference. With Popper and Deutsch as my inspiration, I offer the conjecture that we can broaden the definition of induction and use it to categorise knowledge, systems and ideas as being viable versus illusory.
What is induction you say? Induction is when we blindly use empiricism and call it an explanation: it is the attempt to take a small sample of observations, extrapolate out, cobble together a prediction and palm it off as understanding. But it doesn't work, it can't work (and any practitioner of risk must develop an instinctual understanding of this if they are to survive).
The opposite, deduction, has its limitations, but it is logically consistent. Deduction is when we take general principles and use those principles to make predictions that can be judged by observations. The problem: how do we know we have the correct general principles? We don't. All deductive inferences rest on the supposition that our general principles be the correct ones.
Many have tried to try to fix induction (first dubbed by Hume as "the problem of induction") as it provides the illusion that one can somehow ground one's knowledge with a foundation. The logic works something along the lines of - the observations themselves are real, so all we need to do is somehow solve the problem that inductive inferences are illusory. For example, Bayesianism and verificationism conjecture that more and more confirmatory predictions somehow increase our confidence in an inductive inference; they are ham-fisted attempts to solve "the problem of induction."
Popper outright rejects that "the problem of induction" is even a problem. How does he do this? He offers the logic that the source of any of our knowledge is never, and can never be, the data or observations themselves; all knowledge is derived from conjectures that are the product of human creativity. Appealing to fallibilism, Popper concedes that we cannot have a foundation for the certainty of our knowledge, however we can dichotomise between scientific knowledge and all other knowledge via his criterion of demarcation: scientific knowledge is that which is falsifiable. Thus, scientific knowledge starts out as conjecture and is (temporarily) confirmed, refined or disregarded through a process of criticism and refutation. Deutsch elaborates by postulating science as the quest for good explanations: a good explanation is difficult to vary, a better explanation has reach (explains more than the original problem it was designed for); and explanations that are also falsifiable are deemed scientific.
I like to try to visualise abstract ideas as simple pictures and diagrams. This helps me to understand what I read and place new ideas in the context of my existing ideas such that I don't have to memorise or remember everything that I read. The prime benefit of operating in this manner is that it can help you to think about something complicated until it gets simple; then you may actually understand something new. I will be using this technique to generalise a definition of induction that can help us to identify its prolific (and illusory) use in modern society.
First, I start by defining something I call the problem-space (I suspect it is similar, if not the same, as Popper's problem-situation though I have not found a definition that nails down exactly what he means by it). A problem is a phenomenon that requires an explanation. The problem-space for a problem encapsulates all possible data that the problem could produce. The problem-space is a landscape of possibilities; it can be abstract or physical. For our purposes, I will represent the problem-space as a 2-dimensional plane (figure 1).
Now, lets consider the problem-space as a representation of the earth's surface and imagine a pirate sailing on the ocean. One day our pirate decides to sail in one direction and finds himself arriving back at his starting point. He makes several more observations by sailing off in different directions and always finding himself back at his starting point (lets of course assume that he avoids land). From these observations, the pirate concludes that he will always return to his starting point if he travels in one direction for long enough, he cannot fall off an edge. Notice that our pirate has not provided an explanation of the problem-space, he has simply induced from his observations (figure 2).
If our pirate wants an actual explanation of the problem-space, what is he to do? An explanation requires that he make a creative leap. In this instance, our pirate could conjecture that the problem-space, earth, is situated on the surface of a spherical object. Notice that the explanation resides in another dimension. Our pirate’s problem-space is 2-dimensional and its explanation resides in the 3rd dimension (figure 3). I suspect that this is no mistake, and it forms the basis of my first conjecture.
Conjecture 1
We can generalise the definition of induction - An inductive inference is when we attempt to explain a problem using the problem's very own problem-space. It follows that - all explanations must reside in another dimension to the problem-space of a given problem (whether or not that problem is physical or abstract).
Trading and epistemology | Blog | No more posts
DISCLOSURE
PAST PERFORMANCE IS NOT NECESSARILY INDICATIVE OF FUTURE RESULTS. THE RISK OF LOSS IN TRADING COMMODITY FUTURES AND OPTIONS CAN BE SUBSTANTIAL.
THIS COMMUNICATION IS FOR INFORMATION PURPOSES ONLY AND SHOULD NOT BE REGARDED AS AN OFFER TO SELL OR AS A SOLICITATION OF AN OFFER TO BUY ANY FINANCIAL PRODUCT, AN OFFICIAL CONFIRMATION OF ANY TRANSACTION, OR AS AN OFFICIAL STATEMENT OF TOMAS TECHNOLOGY PTY LTD OR RELATED ENTITIES.
