You would think that after the disasters in Afghanistan and Iraq that Republicans would have learned that starting a war in that part of the world is a Really Bad Idea (tm). But no. After utterly failing to bring about regime change in both its eastern and western neighbors, the Trump administration is winding up to try yet again again in Iran. Maybe the third time will be the charm, but I'll give long odds against.
>Maybe the third time will be the charm, but I'll give long odds against.
ReplyDeleteLook at you, using inductive reasoning . . ..
Manifestly not, because if I were I could not even admit the possibility of the outcome being different this time.
Delete[Inductive probability](https://en.wikipedia.org/wiki/Inductive_probability)
DeleteBut the empirical rate of success for the U.S. launching wars in the Middle East is zero, so there is no inductive justification for even considering the possibility that the outcome might be different this time.
DeleteBTW, Blogger comments don't do Markdown. You have to write HTML.
>But the empirical rate of success for the U.S. launching wars in the Middle East is zero
DeleteThis is irrelevant because you wrote:
>Maybe the third time will be the charm, but I'll give long odds against.
Which means you assigned a subjective probability greater than 0.0 for your inductive probability reasoning.
> you assigned a subjective probability greater than 0.0
DeleteYes.
> for your inductive probability reasoning.
No. If I were using induction I would have no possible basis for assigning any probability other than zero for an event of which there are zero past examples. This is one the reasons induction is never valid. Under induction, novelty is impossible.
>No. If I were using induction I would have no possible basis for assigning any probability other than zero for an event of which there are zero past examples.
ReplyDeleteYou're confusing frequency-based induction (where probabilities are tied strictly to observed relative frequencies) with the broader, and far more powerful, Bayesian or subjective framework for inductive reasoning.
When you assign a subjective probability to a future event, you're engaging in inductive reasoning, because you’re projecting expectations about the future based on your background beliefs, prior knowledge, analogies, coherence with past patterns, or even abstract reasoning (all of which are forms of inductive support).
Your assertion that under induction "novelty is impossible" is also incorrect. Bayesian induction, which rests on subjective probabilities, explicitly allows for novelty. That’s precisely why scientists can assign non-zero probabilities to unprecedented events: we often generalize, extrapolate, or hypothesize based on explanatory frameworks, not just raw frequency counts.
You're moving the goalposts -- again. Bayesian inference is not the same thing as inductive reasoning. But my assessment is based neither on induction not Bayesian inference, it's based on an explanatory model: Donald Trump, like George Bush before him, is an idiot who starts wars not because he has carefully thought things through and has a reasonable chance of winning, but because he has an irrational belief in American exceptionalism with its roots going back to the doctrine of manifest destiny. Accordingly, absent some extraordinary circumstances, the U.S. is not likely to prevail in any war started by Trump.
DeleteTo this I will add that I am surprised that the situation in Iran has not spun wildly out of control yet, so maybe I'm wrong. Frankly, few things would make me happier than to be wrong about Donald Trump.
>But my assessment is based neither on induction not Bayesian inference, it's based on an explanatory model:
ReplyDeleteThat model is itself built from past observations, generalizations about behavior, and projected outcomes. That's precisely what inductive reasoning is: forming judgments about the future based on patterns observed in the past, whether informally or through probabilistic frameworks.
If you claim Trump is likely to start irrational wars based on ideological patterns (like manifest destiny), and that such wars are unlikely to succeed because past wars under similar presidents have gone badly — that's inductive generalization. You're using past cases (e.g., George W. Bush) to support a claim about future outcomes (Trump's wars), even if wrapped in narrative or historical explanation.
Your model may not use numerical probabilities, but it's still making probabilistic forecasts. Saying "Trump is not likely to prevail" is a judgment of likelihood based on a pattern. You are implicitly assigning a low probability to success, based on prior examples -- which is what Bayesian inference formalizes. You just aren't quantifying it.
You're reasoning inductively, even if you call it something else.
> You're reasoning inductively, even if you call it something else.
DeleteI call it something else because it has a crucial extra feature that you have left out: *explanation*. That makes all the difference. Calling the scientific method "induction" is kind of like calling nuclear transmutation "alchemy".
> You're reasoning inductively, even if you call it something else.
ReplyDelete>I call it something else because it has a crucial extra feature that you have left out: *explanation*. That makes all the difference.
An explanation you developed using induction.
>Calling the scientific method "induction" is kind of like calling nuclear transmutation "alchemy".
Where did I call the scientific method "induction"? Scientific methods often use induction.
I don't know why you rail so hard against this. Induction is what makes science special.
Induction is a wholly invalid form of reasoning. There is a reason that the problem of induction is a thing. You need to re-read this and focus on Myth #1.
Delete>Induction is a wholly invalid form of reasoning. There is a reason that the problem of induction is a thing. You need to re-read this and focus on Myth #1:
ReplyDeleteHume demonstrated that induction lacks a purely rational, epistemologically certain foundation. However, Hume also argued that induction is *pragmatically* unavoidable. Even though it cannot be justified by reason alone, it is a natural habit or custom of the human mind to expect regularity in nature, and this expectation practically guides all of our reasoning and action. Without relying on induction, we would be unable to function or make any meaningful predictions about the world.
So, while induction is not epistemologically complete -- it doesn't guarantee truth -- it is an indispensable *pragmatic* tool that underlies everyday reasoning and scientific inquiry. Statistical inference is certainly a *highly successful* application of induction.
Hence Scientists have learned how to tame it. As I've already mentioned, John Norton's Material Theory of Induction argues that inductive inferences are grounded in the background facts of specific domains, not in abstract uniformity assumptions. His follow-up, The Large-Scale Structure of Inductive Inference,explores this further. Other disciplines have developed their own specialized methods, such as the use of Analytic Induction For Social Research. Much of scientific training is, in fact, about recognizing and mitigating the risks of faulty inductive reasoning, not avoiding induction altogether.
Furthermore, you should take a look at When Is Inductive Inference Possible? by Zhou Lu, which provides a necessary and sufficient characterization of when inductive inference is feasible.
Delete> Hume also argued that induction is *pragmatically* unavoidable.
Hume was wrong.
> induction ... is an indispensable *pragmatic* tool that underlies everyday reasoning and scientific inquiry.
No, it isn't. It is a logical fallacy. It is 100% bogus, notwithstanding that it occasionally produces correct results. Epicycles produce correct results too.
> John Norton's Material Theory of Induction argues that inductive inferences are grounded in the background facts of specific domains
Also known as scientific theories.
> a necessary and sufficient characterization of when inductive inference is feasible.
That characterization being:
"the hypothesis class is a countable union of online learnable classes, potentially with an uncountable size, no matter the observations are adaptively chosen or iid [sic] sampled"
So... what is an "online learnable class"? Well, according to the paper, it is "a hypothesis class with finite Littlestone dimension." So.. can you demonstrate that the hypothesis classes of the real world all have finite Littlestone dimensions? Unless you can, this result is vacuous.
Furthermore, despite the fact that I know next to nothing about the subject matter of this paper (I'd never even heard of a Littlestone dimension before) I can *very* confident that you cannot demonstrate that the hypothesis classes of the real world all have finite Littlestone dimensions. I am every bit as confident about this as I am about your inability to build a perpetual motion machine. Why? Because I can easily demonstrate the existence of behavior in the real world that you absolutely cannot predict by induction, and which therefore cannot be explained by any hypothesis with a finite Littlestone dimension. And note that I can know this without knowing what a Littlestone dimension is. It doesn't *matter* what a Littlestone dimension is. If there is *any* property P that is a necessary and sufficient condition for inductive inference to work, then for inductive reasoning to work in the real world one of the following conditions must obtain:
1. All real-world phenomena have property P, which would require that Turing machines have property P (because we can build Turing machines). But we know that some behavior of Turing machines cannot be predicted by any known physical process, let alone by any particular physical process. So no matter what property P is, it cannot possibly be the one that is necessary and sufficient for inductive inference to be valid. Which leads to...
2. Some real-world phenomena have property P and some don't. But this is only useful if you can identify which phenomena have this property. But that is demonstrably impossible because any finite data set can be produced by a Turing machine (indeed, by an infinite number of different Turing machines!) So there is no way to demonstrate that any particular data set was not produced by a Turing machine (let alone which one) and so no way to demonstrate that any physical phenomenon has property P.
Induction may have been defensible in Hume's day because Hume predates Turing by almost 200 years, but it is not defensible today. Today we know about the universality of Turing machines and the uncomputability of the halting problem. Demonstrating the impossibility of valid inductive reasoning is an elementary exercise. Induction is 100% intellectually bankrupt. It is in the same league as flat-earth, lunar-landing denialism, perpetual motion machines, circle-squarers and angle-trisectors. Anyone who advocates for induction deserves to be taken just as seriously as the advocates for any of those theories.
Oh, and by the way, this will no doubt come as a shock to you given your general lack of contact with reality, but Kamala Harris was attorney general of California from 2011 to 2017. At the risk of stating the painfully obvious, that makes her a former prosecutor.
>> induction ... is an indispensable *pragmatic* tool that underlies everyday reasoning and scientific inquiry.
ReplyDelete>No, it isn't. It is a logical fallacy. It is 100% bogus, notwithstanding that it occasionally produces correct results. Epicycles produce correct results too.
Induction is not a fallacy; it's a distinct form of reasoning. A fallacy involves invalid structure in *deductive* reasoning. Induction doesn't pretend to offer certainty -- it offers probabilistic or plausible inference based on evidence. Calling it a "fallacy" misunderstands its domain entirely.
>I can *very* confident that you cannot demonstrate that the hypothesis classes of the real world all have finite Littlestone dimensions. I am every bit as confident about this as I am about your inability to build a perpetual motion machine.
... and of course you're wrong. While you've successfully discovered adversarial examples, these are artificial. Artificial adversarial systems can force infinite Littlstone dimensions. However, the natural world is not adversarial to our learning about it. Real-world physical processes are not arbitrarily programmed like Turing machines. They are governed by physical constraints -- symmetries, conservation laws, causal structures -- that limit the observed complexity. Therefore, finite Littlestone dimensions for physical systems are not only plausible, they're expected, because nature imposes limits on complexity and variability.
>Demonstrating the impossibility of valid inductive reasoning is an elementary exercise.
Demonstrating the success of inductive reasoning is even more elementary. Every scientific field -- whether physics, chemistry, biology, or economics -- relies on inductive generalization from observed data to unobserved cases. Marie Curie's determination of the crystal structure of radium chloride, or Darwin's inference of natural selection, are classic examples. So unless you want to discard all empirical science, you cannot seriously call induction "invalid."
>Oh, and by the way, this will no doubt come as a shock to you given your general lack of contact with reality,
You might want to examine your own grip on reality. Two things are overwhelmingly obvious:
1. Scientists use more than one method; there is no "one scientific method."
2. Scientists use induction in their work -- routinely.
> Induction is not a fallacy; it's a distinct form of reasoning.
DeleteIt is an *invalid* form of reasoning.
> A fallacy involves invalid structure in *deductive* reasoning. Induction doesn't pretend to offer certainty
Calling it a fallacy is just another way of saying it is invalid, i.e. the conclusions do not follow from the premises, which you just explicitly acknowledged.
> it offers probabilistic or plausible inference based on evidence.
So do all logical fallacies. That is the reason they persist.
> Calling it a "fallacy" misunderstands its domain entirely.
Denying it is a fallacy misunderstands what a fallacy is.
> the natural world is not adversarial to our learning about it. Real-world physical processes are not arbitrarily programmed like Turing machines. They are governed by physical constraints -- symmetries, conservation laws, causal structures -- that limit the observed complexity. Therefore, finite Littlestone dimensions for physical systems are not only plausible, they're expected, because nature imposes limits on complexity and variability.
And how can you possibly know that? Not by induction.
> Demonstrating the success of inductive reasoning is even more elementary.
Demonstrating *success* and demonstrating *validity* are two completely different things. Many inductive inferences are correct. That doesn't mean induction is valid.
> Every scientific field -- whether physics, chemistry, biology, or economics -- relies on inductive generalization from observed data to unobserved cases.
No, it relies on *explanations*. Explanations are not inductive generalization.
> Marie Curie's determination of the crystal structure of radium chloride, or Darwin's inference of natural selection, are classic examples.
I don't know anything about Curie's work, but Darwin is absolutely not an example of induction. It's an example of *explanation*.
Do you think Lamarck used induction? How do we know that Darwin was right and Lamarck was wrong? How can you tell the difference between a correct inductive conclusion and an incorrect one?
> 1. Scientists use more than one method; there is no "one scientific method."
There is only one that actually works.
> 2. Scientists use induction in their work -- routinely.
Maybe. Scientists are human. They make mistakes like everyone else. That doesn't mean induction is valid. It isn't.