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//************** Mill and Induction - September 10th, 2019 ******************//
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- Alright; no quiz today, hip-hip hooray!
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- "I said the Aristotle reading was the most confusing we'd have all semester; today's reading, from John Stuart Mill, will be the longest"
- Most of the class made it through around half of the paper
- When you're dealing with a longer paper like this, it's often helpful to:
- Read a summary of it from a 3rd party
- Take notes
- Pay attention to the structure and read actively! If you recognize what argument the paper is making, and what it's trying to say, you can figure out which pieces you can skim and which are major points you need to pay attention to
- Mill, for example, tends to give multiple, extended examples after proving his point, and you can generally get the gist and then skip over it
- Most professors don't read research papers in their entirety; they just identify the main arguments and skip the details they're not interested in
- After today, most of the readings will become shorter and stylistically easier, since they'll be from 20th century sources
- So, today you had to read some stuff by Mill!
- John Stuart Mill (1806 - 1873) was an extremely influential British philosopher, and wrote extensively on politics, economics, and social reform
- In his life, he was especially well known for his defense of free speech and support for women's rights
- Today, he's best known for arguing for utilitarianism in books like "On Liberty"
- So, what's Mill's version of induction, and how is it different from Whewell's?
- So, at the start of Chapter 2, Mill's definition is that induction involves making an inference that goes BEYOND the data you have; it's going from particular examples to a general rule
- This differs from Whewell because Mill thinks that just collecting facts into a general rule isn't enough; you can't just "represent a summary of the observed facts," or even think about the data you have in a different way; you need to make the leap from some particular instances to a rule for ALL instances
- So, given that, what's the difference between inductive and deducive arguments?
- For deductive arguments, the conclusions MUST be true if the premises are true
- For inductive arguments, that's NOT necessarily true; your induction might only hold for a subset of things you have
- From Chapter 8, then, what're Mill's methods of experimental inquiry?
- Well, there are 5 of them!
- The METHOD OF AGREEMENT is where if 2+ instances of something ONLY have 1 thing in common, then that thing is probably the thing's cause
- As an example, suppose you go out to dinner with Bacon, Hume, and Whewell - if all of you got sick, and all of you also ate the seafood but had different meals besides that, the seafood must've gotten you sick!
- This does NOT prove that it had to be the seafood, though, since we would need to know about everything else in the situation to make sure that was the only thing in common - but, alas, we never have perfect knowledge
- The METHOD OF DIFFERENCE, where the phenomenon occurs in a certain situation, but doesn't occur in a slightly different one
- So, if Bacon and Hume and Whewell all get hallucinations, but we didn't, and the only different thing about our menu was that we didn't eat the chicken, we can conclude the chicken is to blame!
- The JOINT METHOD of agreement/difference, where if the thing occurs but only have 1 thing in common,
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- The METHOD OF RESIDUES, which relies on previous inductions
- So, if Popeye goes to this restaurant and gets super-strength, we know the beef, chicken, and seafood are all bad, so the super-strength must've come from the salad
- The METHOD OF CONCOMITANT VARIATIONS relates how much strongly occurs to some specific quantity
- So, if You and Mill and Hume feel sicker depending on how many brownies you've eaten, and the more brownies someone ate, the sicker they feel, that's an example
- Unfortunately, we rarely have these clean-cut, discrete differences in the real world, so these are more general rules for thinking about causation than the be-all end-all of how science gets done
- Where are these rules more/less applicable?
- There definitely are cases; if we have complete datasets for these kind of situations, and these clear, discrete differences, we can use these well! In areas like medicine, though (where it's difficult to tell how people's bodies differ without being invasive), it's much harder
- Alright, that's what Mill has to say about induction - but what about deduction, in Chapter 11?
- He breaks it down into a 3-part process:
- Inducing the general rules that should apply
- So, in Mill's view, the premises we use to do deduction are actually based on induction!
- "Ratiocination," or using deductive logic to reach a conclusion via syllogisms, etc. from the general rules
- Verification, to make sure we didn't make any mistakes and that our inductions hold up
- And what is verification, in his mind, based on Chapter 14?
- To start off from last time, Whewell's idea of verification was mostly based on prediction: if we can correctly predict things in nature with our theory - especially unexpected things - than Whewell says that's strong proof that it's true!
- Mill, though, says something different
- As Mill points out, prediction as proof doesn't pass the logical test of a valid inference; it's a one-way connection!
- "If hypothesis X is true, then Y will happen" is NOT "If and ONLY if X is true..."
- There could be any number of hypotheses that conform to known data and make correct predictions!
- So, we need to somehow get to this "If and only if..." form of the hypothesis to prove the hypothesis as true
- According to Mill, Newton's gravitation theory passed this test, since he showed that if you had ANY other relationship than inverse-square, our data would be different
- ...the problem, of course, is that Mill is WRONG here. Newton didn't prove that conclusively!
- Bringing back Hume here, we have to show that the regularities between different situations always hold for an inference to be valid - but Newton didn't show this, and neither did Mill!
- So, Mill was right to point out we need a bidirectional truth relationship to "prove" a hypothesis...but he was wrong that we have this. Perhaps you'll disagree with me, but I don't think this can obviously be shown.
- So, we'll start to read some more modern authors like Karl Popper and Wesley for Thursday, and they'll be covering some of this same stuff (i.e. it's okay if you're still confused about some things!)
- So, do those readings for Thursday, and I'll see you then