Induction and Deduction, and the Induction problem.

Before I go into the post proper I’d also like to recommend a book Hessian came across and that I’ve been flipping through while writing these posts. “Logic A Graphical Guide” by Dan Cryan, Sharron Shatil and Bill Mayblin. It’s a comic book about Logic and is an excellent use of the media. Using pictures, font and careful placement to make many difficult logical concept easily apparent and readily readable. It introduces many key concepts and great thinkers in a quick and useful way. For those who want to get a general over view of Logic quickly I haven’t found a better source. Though I’m not getting paid for this plug so best be moving on. 😉

Deduction and Induction. These two concepts a pivotal to understanding much of what we talk about in logic. Particularly logic in relation to fields outside philosophy. While induction and deduction certainty don’t end the conversation you really can’t escape them. Especially not induction. Now what is Induction and what is deduction?

Deduction is in many ways an extension of the syllogism, but is no longer limited to three sentences and having full command of logical connectives and assumptions. The conclusion (also know in this cases as the deduction, or what is deduced) is drawn directly by the premises, and when done correctly is guaranteed by those those same premises. Like with syllogism.

Induction on the other hand is less certain the premises do not guarantee the conclusion, but rather They support the conclusion.

To explain the difference I’ll build on an example from Logic A graphical Guide.

To inductively prove that ravens are Black you would formulate your argument like this.

P1. This raven is black.

P2. This other raven is black.

P3. All of the other 318 ravens I have seen have been black.

P4. I have never encountered an instance, be it personal written, or otherwise, of a raven that was not black that was also substantiated.

C. Therefore all ravens are black.

 

A Deductive argument on the other hand would look like this.

P1. (Assumption) All Ravens are black.

P2. That is a raven

C. Then that raven must therefore be black.

 

In the inductive argument we have a certain probability that the conclusion is true. We haven’t guaranteed the truth of the conclusion. Because of that Inductive arguments don’t fit under the valid/soundness categories I talked about in my first post. They simply can’t, and deductive arguments can because they, when done properly guarantee the conclusion. This is the problem of induction, inductive arguments can not be valid in the same way deductive arguments can, but this doesn’t mean induction is worse then deduction.

In my first post on the subject of logic I said it is best to ensure that your argument follows from your premises. Ideally that means your conclusion is guaranteed, but as I’ll show you this can’t always be done. When induction and deduction where being discussed in detail by David Hume (1711-1776) but where also discussed by other philosophers of the time is that the use of induction posed a real problem for the still fledgling sciences since induction can not guarantee truth, so  by that metric could not be justified. So science according to hume and similar thinkers should be limited to deduction.

Though fortunately there several answers to this problem I will discuss two. Induction being unavoidable, and the induction bypass. First is the ultimate problem is that all knowledge is ultimately based on some level of induction and assumption. We can not for example guarantee that we exist, and that the reality we perceive exists. We can not, at least not currently, deduce reality and ourselves from anything that actually guarantees its truth. We can make assumptions, and we can make deductions from assumptions about reality. We cannot, however, deductively prove that those assumptions are correct. But we can inductively show those assumption to be highly likely. I talk about that in a bit more detail here, but I may devote a post to this in the future as there is a lot to talk about which does not directly relate to this post.

Which brings me to the induction bypass which I believe was coined by John Stewart Mill but don’t quote me on that It may have been Karl Popper. The Bypass is the notion that induction can be carefully set up so that you make what amount to generalization, which over time, experimentation, and repetition can become more and more precise. That is, over time time and repetition of experiments you become more certain of the truth of your argument and you close off other possibilities as improbable or impossible. What is amount to is that while you can’t 100%  guarantee truth with induction you can, with time and effort, effectively guarantee your conclusion to near by not quite 100%. This is actually a large and necessary competent of what we do in science, and basically all science is founded on the principles of induction, which is in turn pretty damn good evidence for the inductive argument ;).

What this means for induction is that it can compete with deduction, and quite effectively because it allow us to have some uncertainty in our claims and still be justified in making those claims. That doesn’t mean we ought forget about deduction. Deduction is still extremely useful if arguments and when you have sets of facts you think are related like in an investigation, or when looking for consistency is another persons worlds or claims. While science as a whole is probably the best example of induction, deduction is best exemplified by is use in structured arguments. When you formulate a good deductive argument then the conclusion must follow from the premises so you need not worry that your argument itself will come under attack. Rather now you and your opponent must tackle your arguments premises and assumption not it general struture (with out making a fool of themselves that it). And closing off one line of attack always makes arguments much easier to handle. Though more on refuting and defending arguments later.

 

Next time I’ll be doing a video review on a logical argument I quite like, pointing out why I like it what I agree with and how you could hypothetically attack it if you disagree with it. It will function as a practical exercise.

Withteeth