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Great stocking stuffers--Politically Motivated Reasoning Paradigm, parts 1 & 2!

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Reader Comments (32)

link drop "Partisanship, Social Identity, and American Government: Reality and Reflections":
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3090496

December 22, 2017 | Unregistered CommenterJonathan

Dan,

Is The expressive rationality of inaccurate perceptions of fact distinct from The expressive rationality of inaccurate perceptions from 2015, which was your "friendly challenge to Jussim"? Is it an extended version? Is it something you're likely to share with us soon?

December 25, 2017 | Unregistered CommenterJonathan

Dan,

Actually, if you're not into sharing per the above request, could you just give your justification why "expressive rationality" is rational? I see the cite to Anderson's Value in ethics and economics, but don't have a copy of that on hand. Is it similar to as defined in:
http://journals.sagepub.com/doi/abs/10.1177/1043463106066382
?

If so, then it is a very puzzling concept. Seems like one can redefine any type of irrationality as rationality by positing a suitable internal motivation (expressive utility).

I'm trying to understand why people are identity protective in non-social contexts where they are anonymous (much like when voting, as in the above link), and how calling such behavior "rational" is more than just being PC. One way is perhaps that it is behavior triggered by a deontological moral sense (duty). But, some are quite consequentialist - would you expect these people to exhibit lower expressive rationality, hence lower identity protection, in non-social contexts?

December 26, 2017 | Unregistered CommenterJonathan

I'm trying to understand why people are identity protective in non-social contexts where they are anonymous (much like when voting, as in the above link), and how calling such behavior "rational" is more than just being PC.

I sent imagine Dan will see it similarly as I, but I think it is rational to preserve one's sense of self, and that is a (rational) reason to be identity protective.

December 26, 2017 | Unregistered CommenterJoshua

"If so, then it is a very puzzling concept. Seems like one can redefine any type of irrationality as rationality by positing a suitable internal motivation (expressive utility)."

I think "rationality" is being defined as a valid method of reasoning to figure out the best way to achieve a chosen aim. The distinction being made is that some people have a different aim to the one that was assumed. Their aim is fitting in with the group, socially, not truth-seeking. You may recall the social conformity experiments by Asch?

"I'm trying to understand why people are identity protective in non-social contexts where they are anonymous (much like when voting, as in the above link)"

Excellent example! Thank you! And even in social contexts where the person is anonymous (like on the internet). There's no external social cost to non-conformity. I will be interested to see Dan's response.

December 26, 2017 | Unregistered CommenterNiV

@Jonathan -- @NiV describes what I have in mind. But you are still right that if one limits one's self to the conceptual world, one can pretty much redescribe any pattern of reasoning so that it seems to meet the one I am espousing (habits of mind suited for goals of actor). There was a huge debate about this between Kahneman & Giggenrenzer, at one point. In therie Brain &Behavioral Science, Stanovich & West supply a good, empirical test for seeing whether deviations from "rational actor" model in economics (mainly wealth maximization) is irrational or whether is normatively rational or a cognitive bias.

December 26, 2017 | Registered CommenterDan Kahan

@Jonathan -- I'd go w/ @Joshua's point--that expressive rational is connectged to self-understanding & not just undrestanding or how one's self relates to others. But I'd add that R. Frank's account from Passion within Reason is also part of the story: the best way to convey one has values that others expect one to have is to truly *have* them

December 26, 2017 | Registered CommenterDan Kahan

@Jonathan-- there's no more to share as yet. It's the same story, yes, as in in the BBS essay/comment. It is part of likely bkrd section for paper that will be released in not too long a time; it will have pretty cool new stuff in it

December 26, 2017 | Registered CommenterDan Kahan

NiV,

Asch's results don't apply when one is in a non-social anonymous context, as when taking a survey or doing one of Dan's other tests. My point to bringing up voting is to highlight this non-social (nobody sees you) anonymous (the result of your behavior can't be attributed back to you) similarity. In social and/or non-anonymous contexts, I agree this is Asch-like, although not quite (in Asch's experiments, all that was required to induce the right answer from conformists was a single dissenting voice - hence the rationality was probably over the calculus: How will I know giving the non-conformist right answer keep me safe? If there is another dissenter who manages to stay safe, that is evidence. In identity protection, the calculus isn't quite the same, else we'd have grossly different outcomes).

Others as well,

It would be one thing if there was a type of utility (again in non-social anonymous contexts) that was established to exist based on some independent (of this argument) rational reason, and then conclude that expressiveness in line with this utility is rational. It's another to follow the evidence of expressiveness causally backwards and posit that it must have a (previously unknown) backing utility to save it from being irrational.

Dan,

"R. Frank's account from Passion within Reason is also part of the story: the best way to convey one has values that others expect one to have is to truly *have* them".

That still falls a bit short of why one seeks to convey these values when nobody is watching. All the while seating this type of cognition in S2 - hence it isn't some heuristic that is failing to take that aspect of the context into consideration. Substitute talking for this expressiveness - one talks to others when they can hear, and saying things about values one truly has is ample rational motivation. But talking when there is nobody around to hear, even when mentioning such truly held values, is probably not rational (as most would define it).

I'm not arguing against there being some effect here, I am arguing against the rush to judgement that it is rational (or, similarly, irrational). Also, regardless of what it is, its existence suggests cases where you might find some resistance to identity protection - among more consequentialist thinkers/moralizers. Find some people willing to push the fat man off the bridge to block the trolley, and see how well they do in the skin-rash-gun-control test.

December 26, 2017 | Unregistered CommenterJonathan

Jonathan -

But talking when there is nobody around to hear, even when mentioning such truly held values, is probably not rational (as most would define it).

Consider that we talk to ourselves a lot, often (although certainly not always) doing so to preserve our sense of self. (I often think that is an aspect of what drives people to post their opinions anonymously online.) There is never no one around to hear... as we are always hearing ourselves.

. It's another to follow the evidence of expressiveness causally backwards and posit that it must have a (previously unknown) backing utility to save it from being irrational.

That is interesting, but I think somewhat complicated. We often engage in seemingly counterproductive activities. For example, addictive behaviors (or "wasting" time conversing online with people who aren't interested in good faith exchange). But the determination of "utility" is not so straightforward. Just because, from an external perspective, an action isn't productive towards positive goals doesn't mean that it isn't rational, perhaps? Consider a child who develops habitual behaviors to deal with a repeatedly stressful environment (e.g., blames himself for his parents fighting). Are such behaviors, even when carried forth into adulthood when stress is encountered, "irrational?"

Maybe it's flawed to say that there must be a (rational) reason when people engage in counterproductive behaviors..(i.e., that they "must" be getting something out if it - even if that "something" isn't objectively positive). But I'm not sure what criteria you'd propose to determine "rationality."

December 26, 2017 | Unregistered CommenterJoshua

Joshua,

"Consider that we talk to ourselves a lot, often (although certainly not always) doing so to preserve our sense of self."

You do? Oops. I have never done this. I think to myself, and those thoughts don't contain proclamations of identity. I have never been motivated to talk to myself. Well, then, I will withdraw my "is probably not rational (as most would define it)" phrase. I guess I might be in a minority after all (old white guy lib identity aside).

As for the rational/irrational separation: I'm not even sure there is one, in a Sorites-like way. Other than perhaps the evolutionary argument that one wouldn't expect any specific irrational behavior to occur in a majority of the population, assuming irrational implies maladaptive. But there can be irrational spandrels, so long as if they are maladaptive, they haven't (yet) overwhelmed population-wide survival.

Addictive behavior is probably an instance of a maladaptive spandrel. Yet by an argument much like the one used to make expressive rationality rational, it also can be interpreted to be rational by positing a motivation that one is rational in following. This, to me, is worse than leaving the rationality-irrationality divide vague: it makes it completely arbitrary, and so in favor of rationality whenever one wants. It is also anti-scientific in the sense that one is claiming a deductive inference to a cause when in an empirical context, and because it just kicks the can down the road. Rational is usually defined as something like being interactively (as opposed to congenitally) adaptive, with some evidence of why each specific instance is adaptive. If expressive rationality is rational because of expressive utility, then what makes expressive utility rational or adaptive? Expressive turtles all the way down?

That's why the socially adaptive argument works for me, but this expressive rationality thing doesn't.

Regardless, the rationality aspect of expressive rationality appears central to Dan's thesis, as it is how he explains the prevalence of identity protective behavior as well as how it increases with most other rational cognitive skills. I suspect, when he gets there, it will also be central to any ideas he has for decreasing its impact. Hence, it might be a big deal whether it is rational or irrational in Dan's conception of both. In other words: if it is rational, then one can deduce other aspects from this rationality merely by way of it being rational. If it is irrational, then one loses all such deduction. What I am asking is: if you want license to carry on such deduction, you need to demonstrate that the license is valid. Arbitrary claims don't help.

December 26, 2017 | Unregistered CommenterJonathan

Jonathan -

... I think to myself,...

I was thinking of "talking to myself" as being the same as "thinking to myself".... as in "You dope, when are you going to learn you shouldn't so that," or "Don't forget to pick up that quart of milk."

...and those thoughts don't contain proclamations of identity.

Well, maybe I'm the weird one, but I think that much of my discussion with myself (or thinking to myself in non-spoken words) relates to my sense of identity and my sense of identity differentiation from other people.

But if you think it has nothing particularly to do with exploring a sense of self, what do you think might explain why so many people spend so much time expressing themselves through identity defensive and identity aggressive behaviors in anonymous online comment writing?

Do you think of it as merely utility-less, and irrational behavior? I just have a hard time believing thst such a common behavior would have no utility. I can think of a "utility" in that insulting someone else would have the potential "benefit" of making someone else feel worse about themselves, but I don't get how that would be fully independent of reinforcing one's own sense of identity. One can learn something from such online exchanges, but that learning IMO, is not fully independent of identity-related "utility."

I think I get what you're getting at, and I think it makes sense, but I don't get on what basis you think that identity affirmation isn't a clear (rational) outcome of (anonymous or otherwise) identity-aggressive and identity-defensive, or otherwise identity-expressive behaviors. Why can't I be expressing myself to affirm my sense if self? Not to mention that when people express themselves anonymously, it isn't as if that necessarily means that they aren't seeking and examining responses. I think it is rare that people write anonymous comments and then don't check for responses.

Even when voting, as compared to commenting online where it might be more obvious, I would guess that people are seeking a kind of affirmation by examining the results of an election.

December 26, 2017 | Unregistered CommenterJoshua

Self affirming of one's identity in private is a fine description of what is going on, but it still leaves out why one should consider this rational. It might be common because it has such low cost and is rarely if ever maladaptive - but this is still not necessarily rational. There are many things we consider rational that we do socially that we don't do alone, that if we did them alone, we wouldn't consider rational. Maybe talking isn't the best example. At least, it doesn't follow that every socially rational action is still rational when done alone.

I guess part of my issue here is with the ecological validity of surveys and other similar tests when trying to infer what is done in social contexts. When subjects know that they are anonymous, not being judged, and that the results of their actions will have no consequence (other than perhaps confusing some poor researcher), then I suspect that what is going on isn't always going to be rational.

However, in real world cultural cognition instances, some part of this context is different from the tests. Even in the voting booth - one's vote doesn't matter much in itself, but one does know one is really voting. It could fulfill a duty or be conducive to an ideal of eudamonia (for the deontolocial or virtue-ethic minded, as in Plato's Ring of Gyges). Or be a consequentialist responsibility to the community to help maintain the commons despite one's individualistic interests (a big deal for us communitarians, and arguably quite adaptive). Or it could be an over-firing S1 heuristic, tuned to be socially expressive in all circumstances, that fails to filter out the rare circumstances when one is anonymous. Or it could be a megalomaniacal feeling that one's actions really do have outsized influence. Or it could be cathartic. Or, something else.

Each such possibility is prone to different inferences. For example, if it is a misfiring S1 heuristic, then MS2R isn't entirely in S2 - which is a possibility I mentioned in the lengthy skin-rash-gun-control test discussion: it could be a failure of an S1 alarm to trigger S2 skills, where the failure is entirely in S1. Although some of Dan's other tests suggest probably not.

The difference in potential inferences makes the difference matter. I'm prone to assume (without further evidence) that it's irrational precisely because that discourages assuming the tool of deduction from rationality is available. For those that have taken econ 101: please don't assume a ladder or can opener. Things get weird after that.

December 26, 2017 | Unregistered CommenterJonathan

Surely there is an easier way of figuring out what's going through people's minds when they do this - examine by introspection what goes through *your* mind when you do this.

Its not a question I can answer, because my own introspection tells me that I don't - it's the main reason why I think Dan's hypothesised mechanism is not how it works. But presumably it applies to Dan, or he'd not have proposed the explanation, and maybe it applies to you too. When you come to your judgement on a culturally contended issue like global warming, and you do so in order to align yourself with your cultural group, what rationalisation do you use to justify it?

It should be an easy enough question for you guys to answer.

December 27, 2017 | Unregistered CommenterNiV

"Surely there is an easier way of figuring out what's going through people's minds when they do this - examine by introspection what goes through *your* mind when you do this."

This is a point that Dan attacks in The Cognitively Illiberal State - whether doing such introspection tells one something valid.

Also, regardless of one's anecdotal introspective result and its (in)validity, it appears that Dan needs some universal rational justification. This is because Dan's thesis seems to say:

- It is more rational for most people, due to their powerlessness and the importance of social standing in their lives, to care about their social concerns more than about objective truth.

- This causes them to express attitudes aligned with their social concerns in social contexts.

- Because it is both easier and more rhetorically effective to express attitudes that one believes in, this rationally produces beliefs teleologically from the desire for these expressions to be efficacious.

However:

- The tests Dan has done contain explicitly non-social (private) contexts. Also, voting is a very important explicitly private context in which we are interested. We'd like a justification for why the measurements Dan takes in such contexts should be expected to be ecologically valid despite the absence in private contexts of the hypothesized primary motivator of rational social concerns.

- If we had such a justification, why wouldn't it undercut the hypothesis of rational social concerns in social contexts as well as motivating in private ones? If it somehow motivates only in private contexts, how do we know its impact is highly correlated to the rational social concerns in social contexts? And what drives that correlation?

December 27, 2017 | Unregistered CommenterJonathan

Oh - further pressure on Dan: voting is after all an explicitly private context because of our belief that this frees the voter from social pressures so as to vote as their true self. If whatever justification we get for the above exposes this belief as a fallacy (either because privacy doesn't prevent social pressures, or because the true self is that which is socially pressured), then what to do about voting?

December 27, 2017 | Unregistered CommenterJonathan

"This is a point that Dan attacks in The Cognitively Illiberal State - whether doing such introspection tells one something valid."

Introspection gives you an observation, not a conclusion. It has to be treated with caution. The fact that it can sometimes be misleading doesn't thereby allow one to dismiss it entirely. If introspection tells you that it's not how it happens, then you need a *damn* good reason for thinking otherwise.

And I'm interested anyway. Dan came up with the hypothesis, so is that what he experiences when he makes such a judgement? I obviously can't tell without asking him, and I don't dismiss the possibility. When other Democrats come to the same judgement on global warming - something I find baffling - is this what they're actually doing? Do they consciously decide to go with belief not because they think it's the truth, but to fit in with what they know fellow Democrats believe, and indeed, insist on *everyone* believing?

I'm dubious, because I don't, and nobody I've talked to in this debate has ever stated, or even alluded to this being their reason. Every single one of them said they believed what they believed because they thought it was the truth. I'm guessing from you're reaction that it's not your experience either. You didn't choose to 'believe' in global warming because you knew other Democrats did, and you were afraid of being socially ostracised if you admitted to climate scepticism. I'm also guessing from the fact he hasn't answered the question so far that Dan didn't either - although the likelihood ratio is close to 1 on that; Dan often doesn't answer questions. (That's not a criticism or complaint, by the way.) In fact, I suspect this is another application of the Deficit model - the hypothesis is actually that only Republicans are doing so, but nobody is admitting that's what they're doing.

Whether that's true or not, I do still think it would be an interesting datum in any case. On the topic of global warming, you have all selected the conclusion aligned with your cultural group. By introspection, how did your cultural group figure in making that decision? Were you not aware of it doing so? And if we're coming up with "just so stories" about when cognitive methods are adaptive, what do we think are the evolutionary advantages in hiding your own true motivations from *oneself*?

December 28, 2017 | Unregistered CommenterNiV

NiV,

I am aware of one very major issue in which I am not aligned with almost all libs, and this non-alignment has caused social friction with libs, including family members. However, the meaningfulness of that is in question, as Dan has pointed out that PMR is very issue dependent - so maybe I'm immune there but susceptible everywhere else. But it is a bit of evidence perhaps that my other beliefs may not be impacted by political motivation. Also, I probably qualify as science curious according to Dan's definition.

So, I probably cannot speak for other Dems. However, I have observed both libs and cons displaying what I had previously interpreted as knee-jerk behaviors - they seem to fly to the flame of their group's platform without much rational consideration.

I suspect that Dan is wrong about the S2 rationality of PMR. I think it is S1 and adaptive, and operates by interfering with the triggering of S2 behavior (on the theory that all S2 causal chains must lead back to S1 at some point to provide them with motivational triggering). I think that this is an adaptive S1 heuristic sensitive to long-term social maintenance and insensitive to transient public/private distinctions. I think there is a distinct S2 rational cognition sensitive to transient safety vs. opportunity assessment that shows up in the Asch tests. I hypothesize that if one measured timing of Asch test responses vs. Dan's test responses that are identity-protective, one would find that the Asch test responses take longer, and future fMRI results might even show that Asch subjects experience internal conflict while Dan's subjects don't.

December 28, 2017 | Unregistered CommenterJonathan

"I am aware of one very major issue in which I am not aligned with almost all libs, and this non-alignment has caused social friction with libs, including family members."

That's another very good point. I've found that my views on a lot of subjects are at odds with everyone around me, and cause social friction. Many minority belief systems maintain their beliefs even in the face of widespread persecution, ridicule, or contempt. I've often had to hide my beliefs to avoid arguments and problems - I've never felt any inclination to change my mind about them as a result.

So how does this theory explain people maintaining their beliefs even when isolated from their community and in the face of heavy social costs?

Also, I've observed that climate sceptics most active in the community spent a huge amount of time arguing with one another, disagreeing on particular points with some or all of their fellows in the most vehement and intransigent terms, frequently at a considerable social cost. It seems inconsistent with the idea that they're only being climate sceptics to fit in with their community; although as Joshua frequently points out to me, the people most active in the debate are not necessarily representative of the community in general.

"However, the meaningfulness of that is in question, as Dan has pointed out that PMR is very issue dependent"

Why would that be? I thought the issue dependence was mediated by whether it was culturally entangled. What else distinguishes issues - such that people will oppose their own community on one culturally entangled issue, but not most of the others?

"But it is a bit of evidence perhaps that my other beliefs may not be impacted by political motivation."

Which is precisely the problem. Everyone believes their own beliefs are not impacted by political motivation, but we're using political motivation to explain the divide. So presumably the implication is that only the *other* side is politically motivated, while *our* side is guided only by the clear-eyed search for truth?!

People are symmetric in their belief in asymmetry. Unless people are able to acknowledge that their *own* beliefs are politically motivated too, then it's inconsistent to simultaneously claim that political motivation explains the divide and that the two sides are symmetric. You can't have it both ways.

And I think everyone knows by introspection that on these particular contested issues they're not themselves simply conforming to fit in with their community. At best, people will hide their heretical opinions, or lie about them. But you can't control what you believe to be the truth, and not even fear of social ostracism can make you believe otherwise than you do.

You don't, and I don't, and I bet Dan doesn't. Do we have any direct evidence of anyone else who does?

December 29, 2017 | Unregistered CommenterNiV

NiV,

There probably is a distinction between intra-group conflict issues that may increase one's standing within a group relative to others within the same group, vs. inter-group conflict issues that get one ostracized from a group. Considering the evolutionary advantage of being able to tell the difference, as well as play well on either side of that difference, it doesn't seem much of a stretch to suggest humans probably do this well.

As for introspection: There are cases where I know my introspection is wrong based on reason, but can't shake the feeling that introspection is truth conducive. Perhaps the most egregious such case is the introspective belief in free will. I can't shake it. I'm not even sure what shaking it would involve. But, rationally, I see no reason to even suspect the variety of free will I feel exists (in which agency is not merely a mix of deterministic and indeterministic causes). There are other biggies - such as the fear of being dead (distinct from fear of the process of dying). I seem to fear death introspectively as though I anticipate that, once dead, I'll dislike the experience for various reasons. But, my reason says that this makes no sense.

So, my reason has reason to doubt the ability of my introspection, but, interestingly, not vice versa. My introspection of my reason says it is to be trusted. Which, perhaps, is yet another good reason to doubt introspection, or both reason and introspection (although, then, what is this doubt based on?). Another advantage that reason has over introspection is its ability to be externally validated. Of course, I could just view that as an advantage because of my communitarianism.

December 29, 2017 | Unregistered CommenterJonathan

NiV,

There's also this effect:
http://journals.sagepub.com/doi/abs/10.1177/0956797617723377

non-paywall version

December 29, 2017 | Unregistered CommenterJonathan

"There probably is a distinction between intra-group conflict issues that may increase one's standing within a group relative to others within the same group, vs. inter-group conflict issues that get one ostracized from a group."

Good point.

Although I've seen plenty pursue an argument even if it makes them unpopular. The problem I have with this is that the distinction seems post-hoc. Any exceptions to the list of inter-group conflict issues are simply moved to the intra-group conflict list, and the problem goes away. It's unfalsifiable.

"As for introspection: There are cases where I know my introspection is wrong based on reason, but can't shake the feeling that introspection is truth conducive. Perhaps the most egregious such case is the introspective belief in free will. I can't shake it. I'm not even sure what shaking it would involve. But, rationally, I see no reason to even suspect the variety of free will I feel exists (in which agency is not merely a mix of deterministic and indeterministic causes)."

Your introspection isn't wrong. What's wrong is your reasoning telling you that your introspective perception is inconsistent with it being a mix of deterministic and indeterministic causes. (It's the same sort of issue as writing and sounds having a *"meaning"* - but there are only atoms jiggling about, so what sort of atoms is "meaning" made out of? Nevertheless, meanings clearly exist, as we perceive. Jiggling atoms can have other properties associated with their behaviour, without adding anything extra to the physics.) But the "Compatibilist" philosophy of free will (as well as that of semantic meaning) is complicated, and I don't have the time to go into it now.

However, I'm not making any claim that introspection constitutes *valid* reasoning - only that it constitutes a direct perception of the reasoning mechanism at work. If I was to claim that everyone knows that free will is invalid and untrue, but many choose to 'believe' it only because they would be ostracised from their religion (in which free will is a dogma) if they said so, then your introspection would tell you this is not true. You know that people believe in free will because that's what it really feels like, not because their religion tells them to. Whether their feelings are right or wrong is irrelevant to that.

Another example of what you're talking about is paradox - when people come to inconsistent conclusions by seemingly valid lines of reasoning. They know they've made a mistake somewhere, but cannot see it. However, I think if you asked them, they would recognise that state as the truth. Even though you have a *feeling* your reasoning is valid, the paradox tells you you've made a mistake, and you will say so. Even though you have a *feeling* that you have free will, you would still say you haven't based on what you see as the rational argument. The truth is you've made an error, and admit it, but it's also *true* that you have a feeling you haven't.

"I seem to fear death introspectively as though I anticipate that, once dead, I'll dislike the experience for various reasons. But, my reason says that this makes no sense."

Again, the problem isn't with the fear of death, but with the reasoning process that says the only reason for fear is the desire to avoid an unpleasant experience. Your introspective perception is fine. That's just how your genes have programmed you.

December 29, 2017 | Unregistered CommenterNiV

. We provide the first clear empirical support for acquiescence: People can 1) have a faulty intuitive belief about the world, 2) acknowledge the belief is irrational, but 3) follow their intuition nonetheless

Like when I turn off the TV because by I sense that by watching I'll jinx my team and cause them to lose.

... – even when doing so is costly.

Well, not sure I'd go that far.

December 29, 2017 | Unregistered CommenterJoshua

NiV,

Our argument played out here:
https://aeon.co/essays/do-thought-experiments-really-uncover-new-scientific-truths


Joshua,

Some crazy endings you wouldn't want to miss.

December 30, 2017 | Unregistered CommenterJonathan

"Our argument played out here"

An entertaining essay, thanks!

But as Brown sees it, the best evidence for empiricism’s failure – or perhaps ‘incompleteness’ – doesn’t come from science anyway; it comes from mathematics and from ethics. Empiricism can’t explain why the square root of two is an irrational number, or why it is morally wrong to hurt someone for no reason.

Those are both empirically founded. The particular axioms of mathematics we select to start with are based on physics - the properties of things we can count, of lengths and other quantities we can compare against one another. Our mathematical axioms constitute an (imperfect) model of those observed physical properties. And then thought experiments manipulate those models to derive their implications or contradictions. It's new knowledge in a sense, even though it is logically implied by knowledge that we already have. But it's all based on physics. The axioms are selected to model reality, and computation/proof are physical processes carried out by physical computers (brains or Turing machines or whatever).

And morals are like languages - a set of rules that we instinctively collectively negotiate in order that we can live in close social groups without stepping on one another's toes. Asking why it is morally wrong to hurt someone for no reason is like asking why all properly formed sentences must contain a verb. Some rules are derived from the function of morality - to enable us to live together without harming one another, there are obviously going to be a lot of rules talking about when you can and cannot harm. Other rules are the result of the arbitrary historical accident of those mutual negotiations, like why the list of letters "cat" is the word for that furry creature sat over there. But morality and language are human instincts, and we learn what we know about it by making empirical observations of how humans behave.

Plato's realm may well exist, but we can only ever see the shadows cast on the cave wall.
:-)

December 30, 2017 | Unregistered CommenterNiV

Jonathan -

Some crazy endings you wouldn't want to miss.

Actually, good point. That risk is a part of the equation.

December 30, 2017 | Unregistered CommenterJoshua

NiV,

If mathematics were based on physics, we should discard infinity and continuum. Constructivists would also have us throw out the law of the excluded middle.

"...like why the list of letters "cat" is the word for that furry creature sat over there." I prefer WPDDS (weaponized pet-dander distribution system).

December 30, 2017 | Unregistered CommenterJonathan

"If mathematics were based on physics, we should discard infinity and continuum."

There are several varieties of infinity that have perfectly valid uses in physics (projective and conformal geometry, in particular), and the detailed mathematics of the continuum (where it gets particularly weird) was specifically invented to enable calculus to be done rigorously (to exorcise Bishop Berkeley's "ghosts of departed quantities"), and calculus was invented to do physics.

"Constructivists would also have us throw out the law of the excluded middle."

Under certain circumstances, you have to! A system of mathematics based on a particular set of independent, consistent axioms gives rise to a class of true statements. If you take one axiom away and replace it with its negation, the result is also consistent, and has a different set of true statements. So if you simply take it away, the axiom you took away can be either true or false - the system doesn't say.

There are statements that can be either true or false. There are other statements that can be neither true nor false (the liar paradox, for example). It can be dangerous in mathematics assuming the law of the excluded middle for general statements!

Physics is even worse! People used to say that the 'weaponized pet-dander distribution system' must be either dead or alive (not dead). It can't be both at the same time, can it?

January 2, 2018 | Unregistered CommenterNiV

NiV,

...and calculus was invented to do physics. A slightly wrong variety of physics. Now we have Planck length, dSR and such. One wonders what mathematics we would have if the apparent lack of infinitesimal in nature was known back in Newton/Leibniz days.

It can't be both at the same time, can it?

As long as it stays in the box such that it's reality doesn't become entangled with mine, I'm willing to forgo my need for closure on that one.

January 2, 2018 | Unregistered CommenterJonathan

"A slightly wrong variety of physics. Now we have Planck length, dSR and such."

:-)

The operative word there being "slightly". All of physics is models of reality, and we know what George Box said about models...

[Although I'd note in passing that the Planck length doesn't really mean the universe has a minimum length scale. It means that the deeper you go, the more curvature you get, so below the Planck scale you get more and more space crinkled up like a fractal foam. It's still mostly continuous (bar any singularities that might form), and makes the continuum look normal!. :-) Both general relativity and quantum mechanics, which predict this effect, are defined on manifolds over the Real numbers.]

The continuum was invented to model physics, as was geometry, and the natural numbers. They're all approximate models of reality, but it was the physics of our universe that they were approximating.

January 2, 2018 | Unregistered CommenterNiV

NiV,

And what is your view about renormalization? I think these things all indicate that our intuition about a natural continuum is not quite right, and we'd have a better approximation (with possibly less fugly math) if we could abandon it. Even continuum math itself independent of its use a a model of physics has issues, like the Banach-Tarski paradox.

So, my intuition is that these things are telling me there's something wrong with my intuition about the continuum. My intuition is thus wrong at least once. I'm sure you'd agree with that!

January 2, 2018 | Unregistered CommenterJonathan

"And what is your view about renormalization?"

It's an artifact of having to use perturbative methods. We start with an exact solution for a simplified case we know how to solve, and then consider the effect of small deviations from it. The problem is that the coordinate system we use to represent the solution can't represent the actual form of the true solution, but diverges. Because of the way it's constructed, the diverging representation acts in some ways like the real thing, but not all.

Take the series 1/(1-x) = 1 + x + x^2 + x^3 + x^4 + ... For some purposes the series on the right acts like the function on the left. If we multiply the series by (1-x), we get 1 + 0x + 0x^2 + 0x^3 + 0x^4 + ... and so on forever, which is just 1. And for values of x close to zero, the calculation even works. But what if we set x = 2? Then we get -1 = 1 + 2 + 4 + 8 + 16 + 32 + ... which looks really weird. (Although if you've ever had a lot to do with programming computers, you might recognise the "two's complement" representation of negative numbers!) The function on the left works fine everywhere (except the point x = 1), but the series on the right is trying to represent it using coordinates (the coefficients of the power series are just coordinates of a vector space where the powers of x are the basis vectors) that don't work here. If you pick a different coordinate system, you can find coordinates that do work.

Physical reality is some well-behaved function that works everywhere, like the function on the left. The perturbation methods we're forced to use in all but the most trivial cases gives us something like the series on the right. Formally, it diverges. But like two's complement numbers, it still "works" if you ignore the divergence and carry on manipulating it formally.

"So, my intuition is that these things are telling me there's something wrong with my intuition about the continuum. My intuition is thus wrong at least once. I'm sure you'd agree with that!"

Oh, agreed. As I said before I'm not saying that intuition is always valid reasoning, or true. I'm saying it's a generally accurate observation of our reasoning processes.

For example, we can certainly agree that the average man-in-the-street when thinking intuitively about objects moving about in continuous spaces *isn't* doing so with delta-epsilon methods or Dedekind cuts! His intuitive methods are wrong, and can give wrong answers, but his introspective observation of *how* his intuition works (or doesn't work in this case) is accurate! He's truly not secretly using Dedekind cuts internally and is simply unaware of it.

Introspection about intuition isn't always right. For example, it's very common for people to think there's *no* reasoning involved in some of the processing the brain does - it's just "obvious" - when actually there's a huge amount going on under the surface. And there may be some cases where we think we're doing one thing when we're actually doing another - I expect a psychologist could offer examples. Nevertheless, introspection is still an observation that needs explanation if it conflicts with our favoured hypothesis.

January 2, 2018 | Unregistered CommenterNiV

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