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All People in Canada are the Same Age (1997)

math.toronto.edu

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Re: All People in Canada are the Same Age (1997)

#51
post #13

In 2003, I remember studying fallacies in English class. I literally had an outbreak of laughter during an exercise where the prompt was: “vote for me or admit you’re racist”. It seemed so ridiculous to teenage me that such a thing could be said. In 2020 it has been said. I’m no longer falling out of my seat laughing.

I'm not clear how your anecdote is germane to the topic.

Re: All People in Canada are the Same Age (1997)

#52
post #35
post #30

Earlier quoted context omitted.

Not exactly, it was saying that you assumed S(2) implicitly which is wrong.

Why can’t you asume S(2)? Is it not included in the inductive hypothesis S(k)?

The page gives a better explanation than I could :-)

Re: All People in Canada are the Same Age (1997)

#53
post #46

Earlier quoted context omitted.

Right, it proves S(2)->S(3), but induction asks you to prove S(n)->S(n+1) for n in general, and not just for some n. The inductive proof doesn't work for S(1)->S(2), so it clearly can't work for the more general n->n+1.

The inductive step is fine, but it only works for n >= 2. The issue is a disconnect with the base case n = 1. However, if it were possible to prove the case n = 2, we would have a valid inductive proof for n >= 2.

> it only works for n >= 2

Right, so it doesn't work -- either it's a correct proof of a non-sequitur ("true for n implies true for n+1, provided n meets some criteria"), or an incorrect proof of an inductive step ("true for n implies true for n+1").

Because it's claimed to be proof by induction, it's meant to be the latter -- the person doing the proving claimed to have proven the inductive step, and their proof of it was incorrect.

Re: All People in Canada are the Same Age (1997)

#54
post #46

Earlier quoted context omitted.

The inductive step is fine, but it only works for n >= 2. The issue is a disconnect with the base case n = 1. However, if it were possible to prove the case n = 2, we would have a valid inductive proof for n >= 2.

> it only works for n >= 2 Right, so it doesn't work -- either it's a correct proof of a non-sequitur ("true for n implies true for n+1, provided n meets some criteria"), or an incorrect proof of an inductive step ("true for n implies true for n+1"). Because it's claimed to be proof by induction, it's meant to be the latter -- the person doing the proving claimed to have proven the inductive step, and their proof of…

“True for n implies true for n+1, provided n >= 2” is a perfectly good inductive step.

However, it must be coupled with a base case >= 2, which isn’t the case here. The only base case proven is 1.

See also “Induction basis other than 0 or 1” [0].

[0] https://en.wikipedia.org/wiki/Mathematical_induction#Inducti...

Re: All People in Canada are the Same Age (1997)

#55
post #29

Earlier quoted context omitted.

One part of mathematics that I rather like is figuring out how to phrase a statement as precisely as possible. (For me, this is also what differentiates good philosophy from bad philosophy.) I've been struggling with the best way to interpret the 2016 election results, especially with the 2020 election coming up. The most precise way to phrase it is as follows: For each person who voted for Trump in 2016, at least on…

The primary fallacy is that racism is a Boolean value of some sort.

I agree that racism is a spectrum, spanning anywhere from microagressions that contribute to systemic racism, to overt dismissals of human rights. Generally, the term "racist" is used to mean "exists further than X on the scale of racism". Whether or not somebody is racist by virtue solely of voting for a blatantly racist candidate is a matter of discussion for where that line of X is, and is covered under my comment about option (C).

This also gets into the point where racism will continue to exist so long as "not racist" is seen as one end of the spectrum. Rather, in order to be appropriately egalitarian, one must be anti-racist wherever society is racist.

Re: All People in Canada are the Same Age (1997)

#57
post #13

In 2003, I remember studying fallacies in English class. I literally had an outbreak of laughter during an exercise where the prompt was: “vote for me or admit you’re racist”. It seemed so ridiculous to teenage me that such a thing could be said. In 2020 it has been said. I’m no longer falling out of my seat laughing.

One part of mathematics that I rather like is figuring out how to phrase a statement as precisely as possible. (For me, this is also what differentiates good philosophy from bad philosophy.) I've been struggling with the best way to interpret the 2016 election results, especially with the 2020 election coming up. The most precise way to phrase it is as follows: For each person who voted for Trump in 2016, at least on…

And perhaps a slightly more liberal approach would be that racism applies to ideas/worldviews/modes of communication rather than baked into people.

There is research to indicate people respond to visual cues as an indicator of in-group/out-group tribalism, but that mental software can be overrun by observing the individual as opposed to categorizing the individual into a group. https://greatergood.berkeley.edu/article/item/look_twice This would be connected to one's communication that can be overcome.

As well as this, G. Loury describes racial stigma, which is to observe existing race gaps as a combination of past racist policies, exacerbated by present egalitarian/meritocratic policies, where the inequality is incorrectly ascribed to innate, immutable characteristics of race, rather than a consequence of an individual/hobbled community starting 50 meters behind everyone else in a 100m sprint. https://www.irp.wisc.edu/publications/focus/pdfs/foc241a.pdf This would be connected with one's worldview which can be overcome by understanding racism within history, as well as global weather distributions, and geographical resource distribution (Guns, Germs and Steel by Jared Diamond).

And I don't think I need to cite anything about racist ideas not covered by the above can be overcome by using enlightenment values and unifying messages.

I'd say trump has proclaimed some very racist ideas which run against enlightenment values and consequently are repulsive. There are obviously some percentage of followers of trump that hold worldviews that I'd find repulsive due to my alignment with enlightenment values. That doesn't mean the ideas these people hold are immutable.

Whilst my main political priority is minimising inequality at large, which in this context will disproportionately assist populations currently in poverty and resolve a lot of racial tension and racial stigma, policies that DON'T assist communities suffering from poverty should not be assumed to be racist, but rather are exacerbating gaps generated from previous racist(read discriminating by skin colour) policies. Whilst it might be unpalatable, I believe it is more realistic when you consider a large part of the American dream is about pulling yourself up from your bootstraps.

Also, Trump holds positions on economics that resonate large swathes of the American populous in communities that have been decimated by both automation, and job exportation, as pointed out by Andrew Yang. And as scarcity replaces abundance, individual's sphere of compassion shrinks. As a general example, consider who you would be considerate to if you were in an unescapable location undergoing famine.

Whilst I appreciate the desire to simplify the world around you which all humans try to do, I think to try to compress an individual's political worldview into 3 binary dimensions is dropping the majority of an individual's motivation.

I'd say that the main cause of racial gaps is historical institutional racism, that are exacerbated by today's egalitarian/meritocracy policies practices. And since the 1970s, corporate America began it's ascendance to decimate the middle class, rural America, collective bargaining, profit over economic equality, and almost completely corrupt the political system. This means to me that the biggest problem in America is political corruption and corporate power/corruption which results in increased inequality. Solve that and I think America's other problems of racial stigma, various important gaps across populations, lack of national pride, strength of democracy locally and globally, and the decreasing ability to pursue happiness in America would be much easier to solve.

This is just one Australian's opinion though. I might be wrong about the whole thing.

Re: All People in Canada are the Same Age (1997)

#58
post #32

I heard this in the “All horses have the same color” version.

The version I had come across was "all billiard balls have the same color" in Liu's Discrete Mathematics [1]. It is an exercise problem in one of the chapters.

[1] https://www.amazon.com/Elements-Discrete-Mathematics-C-Liu/d...

Re: All People in Canada are the Same Age (1997)

#59
post #54

Earlier quoted context omitted.

> it only works for n >= 2 Right, so it doesn't work -- either it's a correct proof of a non-sequitur ("true for n implies true for n+1, provided n meets some criteria"), or an incorrect proof of an inductive step ("true for n implies true for n+1"). Because it's claimed to be proof by induction, it's meant to be the latter -- the person doing the proving claimed to have proven the inductive step, and their proof of…

“True for n implies true for n+1, provided n >= 2” is a perfectly good inductive step. However, it must be coupled with a base case >= 2, which isn’t the case here. The only base case proven is 1. See also “Induction basis other than 0 or 1” [0]. [0] https://en.wikipedia.org/wiki/Mathematical_induction#Inducti...

Sure, their mistaken proof of the n->n+1 implication could be taken for what it does prove, and such a theorem could be used in other circumstances to prove different things, but that doesn't really bear on any of the claims in the original context.

Nobody was trying or claiming to be doing any other kind of induction. They said they had the base case and the inductive step, and they were clear about the base case and the inductive step. Their proof of the base case was correct, and their proof of the inductive step did not prove what they said it did. It doesn't matter what it did prove.

Re: All People in Canada are the Same Age (1997)

#60
post #5

Fun stuff, there's a few more on this page: https://www.math.toronto.edu/mathnet/falseProofs/fallacies.h... The last one in particular I thought was interesting

The ladder problem is one that I seem to remember was in our first-year classical mechanics text back when I was in grad school, and caused a lot of debate... it's a good one.
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