Inductive reasoning is reasoning from what happened in the past to predict the future. Whenever the X we've seen Y. All men before Socrates eventually died, so he probably will too.
Deduction yields a purer type of knowledge than induction. Deduction from true premises yields truths. Induction can only yield probabilities: likelihoods or odds.
The problem with deduction and it's privileged position in teaching reasoning is that true, readily agreed upon premises are rare. I think that we should think more about induction.
Thinking about induction in law and science
Law
In both science and law, there are agreed-upon ways to express the likelihood that something is true based on a set of evidence or set of observations.
In law, there is standard of scrutiny. In a civil trial, the standard of scrutiny of evidence for the jurors is a preponderance of it: they have to determine whether there was a greater than .5 probability that the that the defendant is liable. (.5 probability = 50% chance). In a criminal trial, the jury must believe that based on the evidence the defendant was guilty beyond a reasonable doubt. While not quantifiable, this is a stricter standard than "the preponderance of the evidence." Laws before the Supreme Court face different levels of scrutiny - standard, heightened, strict - depending on the Constitutional issues at hand.
Only one of the legal standards of evidence is somehow quantifiable, the "preponderance of the evidence." It's basically saying "is what you're saying more likely true than not based on the evidence."
Science
Scientific scrutiny is similarly probability-based: how likely is what you're saying to be true based on the evidence? The phraseology in science is, more particularly: "what is the probability that what you have observed is due to random chance." The most common answer is "less than 5% chance" but it differs based on scientific field. In science, there are systematic and objective ways of answering this question by using statistical methods.
We can't use statistics too often in our day-to-day life to test the likelihood that what we think about the world is due to random chance. But we can think about truth in the more inductive – the more scientific – way. A scientific truth is never a certainty, only a probability: one, as far as we know, that's never quite one.
The practical consequences of the properties of induction
Induction is how we reason about the world: how we find truths. We've seen the sun rise every day so we believe the sun will rise tomorrow. The limitation of induction is that it doesn't give us a truth that we're certain is true. We could reason deductively, based on the laws of planetary motion, that the sun will rise tomorrow. Even the laws of planetary motion, just about as true as anything we know, are still based on the scientific method, which is a fundamentally inductive method that removes a lot of the subjectivity associated with day to day reasoning.
Does this leave us in some postmodernist situation where there aren't facts and that the notion of "truth" deserves little respect? Absolutely not. The facts - truths - we perceive are the basis of how we deal with reality, whether we think about it or not. Facts are real.
However, many of the facts we deal with are not as reliable as we might expect. Harry Frankfurt points to how lies distort our world and make us feel as a result: "When we encounter a lie, we are disturbed primarily by what is done to ourselves. A lie (which we believed) has distorted our reality. A liar has, in a sense, “made us crazy”. We feel that we have been injured by it in a very profound manner." . . . “The most irreducibly bad thing about lies is that they contrive to interfere with, and to impair, our natural effort to apprehend the real state of affairs.”
One of Frankfurt's examples allows me to explain, at least in its context, my approach to truth. In arguing the absurdity of the postmodern "factless" world, Frankfurt points out how nobody in their right mind would go see a surgeon "who doesn't care about the truth." This is true, but a surgeon who can't appreciate the limitations of their factual knowledge when making judgments is not a good surgeon to visit either. In anatomy, variation is the rule, and a better surgeon will have the ways that anatomical structures tend to vary on their intuitive radar.
Conclusion:
Why do I think that cultivating an "intuitive radar" for the limitations of facts is a good thing? From theoretical to practical: I think that it gives us a better understanding of the nature of truth as it's available to us, I think that it helps us identify the weaknesses in our interpersonal arguments and communications, and I think that it can actually just help us deal with the world more effectively.
If you think that I'm bothering to write about "intuitive radar for factual limitation" as an approach to combating dogmatism in our mindsets and discourse then you're not wrong; it's a big part of why I think about these things. But there's a very practical aspect of what I'm talking about. Great surgeons don't stop saving lives and limbs just because they're not certain how a particular artery courses; on the contrary, they actually do a better job of it. As do drivers who still look both ways when red turns to green, lest someone be barreling through the intersection once they proceed.
