Critical thinking
Quoting John Sweller
"We need to teach kids how to think critically!" - a common call.
One result is perhaps the number of threads here that tell us how physics or mathematics has it wrong, while demonstrating a lack of knowledge of either physics or mathematics.
Critical thinking without context is dangerous.
Cognitive load theory assumes that, for example, critical thinking is biologically primary and so unteachable. We all are able to think critically if we have sufficient knowledge stored in long-term memory in the area of interest.
A car mechanic can think critically about repairing a car. I, and I dare say most of you reading cannot. Teaching us critical thinking strategies instead of car mechanics is likely to be useless.
"We need to teach kids how to think critically!" - a common call.
One result is perhaps the number of threads here that tell us how physics or mathematics has it wrong, while demonstrating a lack of knowledge of either physics or mathematics.
Critical thinking without context is dangerous.
Comments (214)
A sizeable portion of what science and mathematics 'know' today will turn out - in the fullness of time - to be wrong. See, for example, Phlogiston theory and various other intellectual car wrecks from the past:
https://en.wikipedia.org/wiki/Superseded_theories_in_science
There is already enough group think in the world. What we need is people thinking out of the box and challenging the received 'wisdom'.
So true. How do you convince someone who wants more knowledge that they need more knowledge?
As far as today's science and math being "phlogistons." Come on. Not everything gets superseded. Most fields are stable up to a certain level of complexity. Most changes are refinements. If there really is a paradigm shift, it is going to evolve out of existing theories, not "around" them. Systems Philosophy is far and away the leading paradigm shift candidate that I have seen.
You think we have it all perfect and that list of superseded theories will not grow? You are mistaken - science is a history of 2 steps forward, 1 step back, why should the future not follow the pattern of the past?
- We have huge problems with Cosmology and maths relating to the assumption that actual infinity exists.
- QM and GR are incompatible so one or the other will have to give way.
- There are no sound interpretations of QM.
- We have no real clue how the brain works.
Criticism is over-rated.
That's clearly not what was said. Take QM - and contemplate just how much discussion and agreement has had to take place for the disagreement you choose to focus on to even be considered...
It was the wrong theory - and if it had been blindly accepted without questioning, we could still have it today.
Critical thinking is a skill to be encouraged. Group think is the biggest danger to science.
The article cited in the OP struck a cord with me. I had been considering the threads created by the likes of @Bartricks and others; the not-quite-batshit-crazy stuff. They seem to be the result of applying critique before understanding.
That's exactly wrong. It's those who have taken the time to understand the topic who are in the best position to critique it.
This does not agree with my personal experience. Add a new person to a subject matter group - they may not be fully unto speed - sure they will make a few errors / say some dumb stuff - but they also usually bring new ideas and a new perspective.
A car mechanic can think critically about repairing a car. I, and I dare say most of you reading cannot. Teaching us critical thinking strategies instead of car mechanics is likely to be useless.
— John Sweller
This is very much wrong, and I'm saying this as someone who largely trusts car mechanics. A car mechanic will have certainly a vast body of knowledge about the inner workings of a car, just as a doctor will have a vast, vast body of knowledge about medicine.
So lets say I go to a doctor with a cough one day; clearly, at least in theory, it could indicate a billion different ailment. Coughing might be a sign of bubonic plague or AIDS, but a doctor who is hopefully able to critically think doesn't just thrust his entire encylopedia of conditions at me and instead is about to critically reason that it's most likely a seasonal cold and check for that first before moving onto bigger, rarer ailments.
This. You don't learn to improvise first. Seeing the relevant holes in things requires first knowing what is relevant to them. Learning what's relevant to what is learning; when you know what's relevant to what you can ask better questions, when you ask better questions you can learn better.
And over-abundant. Proper critique, on the other hand, is not.
Or maybe I just like the word.
My point is they would not properly understand the topic without a base of critical thinking. They would understand how to repeat information, sure, but they wouldn’t understand if what they were repeating was true or false without some ability to objectively and rationally form judgements.
Not what I said. I'm highly aware of the provisional nature of all scientific knowledge. I'm reading Karl Popper right now, it's his main position. Nevertheless, some components of our knowledge are more stable than others. Newtonian mechanics is no longer adequate as a cosmology, but it continues to suffice for much of our day to day needs. Euclidean geometry, calculus.
Edit: fittingly for the OP, Popper's take on scientific realism is that it is precisely criticism (critical thinking) which validates all objective knowledge. Excellent read.
So actually, if you don't mind my saying, you are both correct. Critical thinking is critical, and it does need to be substantive. (again, it's Popper, sorry, we do tend to see through the lens of our current focus). :)
Edit: He also says, the more different the backgrounds, the more fruitful the argument....
Agreed. The percentage of our knowledge that is sound/stable increases with time. But I don't quite think that percentage is currently high enough to abandon critical thinking.
I'm of the opinion that people should not be discouraged from posting articles critical of science/maths just because they are not a subject matter expert:
- There are enough folks on the forum to straighten out the odd error in OPs
- It is a learning experience
- More posts mean we are more likely to come up with some good stuff
Coming from one who has come to understand that my own past critiques have sometimes been based on a misunderstanding, I would readily concur with this. It's exactly right.
I do not think that critical thinking is something that can be taught. Questioning authority is not equivalent to critical thinking. Doubt without adequate ground is not the result of critical thinking. It's the result of something else much less worthy... much less admirable.
Learning context matters lots (as far as I can tell).
Incidentally one of the reasons why I think good, accessible education is important.
In terms of context, it is a matter of much debate to say what that is.
From one point of view, that is the only argument. We cannot get past the framing of a question to try and answer it.
On the other hand, there are arguments that question why any arguments are necessary.
So, the notion that the nature of arguments could satisfy a bunch of of arguments may be a hope misplaced.
Which that?
The starting place where one says this is the starting place.
Deductive reasoning, and the process of elimination involves knowing what to look for. Good mechanics and good doctors perform the same process of elimination... House aside, it's a bit fantastical, real doctors do much the same. I've recently watched it happen. Interestingly enough, she was as absolutely certain as she could be, but would not dismiss the possibility of being mistaken...
...turns out she was right.
All that said, deductive reasoning and the process of elimination involved in identifying a problem or a cause is but one aspect of critical thinking, not the only one.
Here’s the other thing...
Authority can be built on inadequate ground, and in that case critical thinking can show its great worth.
Oh, I am not at all dismissing the crucial importance of critical thought when it comes to becoming aware of conventional historical mistakes. It is a crucial element. Sometimes what was once thought to be true turns out to be mistaken in some way or other. We all know this.
We are fallible creatures. We form and/or hold false belief. When they are held across the spectrum of an entire population or society, and they are false, we could have a case of operative false belief with a tremendous amount of power. Such beliefs are considered to be common conventional wisdom by most if not all of those members.
Here...
"Thinking outside the box" has some weight so long as it's not so far outside that it becomes utterly irrelevant. The revolution of conventional wisdom always comes in amenable terms.
I don't know about cosmology, but in mathematics I don't know where you get the "huge" from; most mathematicians sail along successfully oblivious to this issue. Those relatively few in foundations of mathematics might be disturbed. Keep in mind math developed over many thousands of years, becoming more and more effective in describing and predicting physical effects, but placing all that math on firm foundations is a recent effort and is rarely required to practice the Queen of the Sciences effectively. (math is not really a science)
As for critical thinking, I taught college courses for many years and I suppose I fall into the nature category vs the nurture. If someone isn't born with the skill, some aspects of that skill can be taught in specific areas but for a very general kind of CT I'm not convinced. But I certainly could be mistaken.
Indeed, and it's usually a form of crude belief, of credulousness. As @Banno mentioned, those who don't know math nevertheless believe that they can detect massive mistakes at the foundations, somehow overlooked by people who have given their lives to the discipline.
This 'less worth, much less admirable' thing you mention is even 'the' enemy that we as thinkers primarily contend with --our own intellectual vanity. What such rebels are overlooking is that they merely enact the spirit of our times (an accidental conformism that mistakes itself as revolutionary.)
Quoting creativesoul
I like your humility here. I also look back on my petty resistance to certain thinkers and theories as based on a misunderstanding that was itself based on sloth and vanity. We are haunted by the fantasy of the short cut, and 'idle talk' that shallowly misunderstands various famous philosophers only supports this. In short, (as I currently see it), philosophy hurts. The conceptual difficult is secondary to emotional difficulty.
'Critical thinking' is self-sacrificing thinking, and this sacrificed self is the petty self.
[quote=Delphi temple inscription, allegedly]Know thyself.[/quote]
I think we are. I think that knowing one's self also reveals the 'viscosity' of thought. Large changes in our networks of beliefs and desires are traumatic and rare, and this suggests/explains that intellectual growth is a kind of continuous drift, punctuated now and then by a leap one is ready for.
I connect this viscosity to identity, by which I mean how the subject is attached to seeing itself. Harold Bloom's notion of the anxiety of influence is useful here. If I am attached to understanding myself as a genius, then I do not want to discover myself to be merely repeating what has already been said. I must read a kind of 'swerve' into my own offering to rescue it from coming too late. But more usual threats to identity are the 'death of god' or the realization of 'my' complicity in that which I understand to be guilty and other.
I don't pretend in the least that these are new themes or realizations. For me 'knowing myself' has largely been about experiencing the force and aim of the words of others. In my view, philosophy is not just the isolated ego knowing itself but more like our self-knowledge. This 'our' as opposed to 'my' is IMV fundamental and constitutes a part of our self-knowledge.
Critical thinking all by itself, without a solid, tangible or conceptual topic, is not possible.
If critical thinking has no topic, or the critics have limited or no knowledge of the topic, critical thinking is a waste.
But we are criticising pure critical thinking.
And critical thinking has been shown to be useless without a topic.
So we are critically thinking about something that is critical thinking with no topic.
---------------
Let me explain.
F(x) only has meaning when x is not equal to zero.
F(F(x)) therefore only has meaning if X is not equal to zero.
We wish to examine F as a function.
But we do it with a conceptual approach, where we in effect examine F(F(0)).
Therefore this discussion is only worthwhile if we approach the topic with actual examples, and not with conceptual megadescriptions.
Yet the notion that F(0) is meaningless was postulated while talking about F(0) in terms of F(F(0)).
Go figure.
Critical thinking is certainly dangerous without large doses of humility.
Was chatting about this sort of thing recently. The reason why ‘scientists’ are generally more capable of critical thought is likely because they are happy when their ideas/theories are proven wrong - that is exciting for them. When it comes to more dogmatic areas of interest (where ‘correct’ and ‘incorrect’ don’t fit so readily) the opposite is sought out: that is people look to be shown right in order to develop a sense fo ‘understanding’. At the extreme end the dogmatically religious types seek proof to rest on and do their upmost to deride any contradiction.
Reason and critical thought must go hand in hand right? If so, we’re starting at a disadvantage as we’re terrible at basic logic in abstracted forms. I don’t think this can be ‘taught’ and probably the best means of pedagogy would involve greater emphasis in the Arts rather than expecting people to make conceptual leaps from concrete examples to abstract rules.
Like all human trait, there are environmental factor that help to nurture them. Also, some traits will necessarily hinder other traits. Quite often what many see as detrimental to X actually boosts X in the long run.
Critical thinking is largely absent from the cultural paradigm. If everyone was busy in such an act, it would be impossible to differentiate the creative people from the followers. Most Scientists also tend to be followers in a sense. Even though they can be more open minded to changing their opinion on certain matters than most religious people on religious matters. To give an example that will bring clarity to my claim. Consider Einstein, he was incredibly critical to come with a theory that fundamentally changed what had been accepted for perhaps 300 years. Yet all that critical thinking did not let him accept the parallel development that was taking place in the quantum physics. He obviously understood it better than most of us but he insisted that the theory was incorrect and it took quite sometime for him to get used to the viewpoint. Another important example is feynman, he did not like the field theory of Schwinger as it was more tedious. Even though it was far more rigorous than what Feynman had presented. The scientists are also human beings and will always end up being partial to one way of thinking over another in the field of science. Let's move away from science and focus on philosophy. The rift which existed between analytical philosophers and the continental philosophers or to put it more accurately, the complete indifference of each other to the others development is yet another example of a category of people,the academic philosophers being close minded, contrary to the opinion that philosophers are always open minded.
It is quite easy to target the religious people and take a jab at them. Dogma is comforting to the common man who doesn't really care about the technical details or whatever the fuss theologians have created. This is the way the social consciousness works and probably will in the future. The apologetics are really too close minded and do not represent the majority. I am sure most of them do notice the weakness of their arguments but for sake of defending their religion, still use them nonetheless. If you really want to understand some religions, you also need to look at them from a psychological point of view. A lot of philosophers who were deeply in touch with the human spirit were against apologetics and one of the best examples is Kierkegaard. He really understood what was the problem at hand.
Who is an expert in God to know what they are talking about?
Who is an expert on consciousness to know what it is they are talking about?
Who is an expert on knowledge and truth to know what it is they are talking about?
Who is an expert on morality to know what is good and bad for everyone?
If these fundamental questions can't be answered by experts, then is it safe to say that anyone is an expert on anything?
Those open to shifting their world views are more open to taking criticism on board. I wasn’t saying for a moment that scientist, philosophers or pious people are automatically one more than the other, only stating inclinations instilled in them.
It kind of seems like you are saying, it is possible to think critically 'about' something specific, but it isn't possible to think critically about critical thinking?
Karl Popper has highly-regarded and expansive epistemology called "Critical Rationalism" that is entirely based on the concept of critical thinking.
In that case, a certain amount of dogma is absolutely necessary in order for a person to gain knowledge of the subject before applying critical thinking on it. The vastness of the knowledge in the world means that there will always be people who are experts in a certain field and other people will have no choice but take their words for it. Further more, the ability to think critically is totally different from the will to think critically. Consider a scientific theory which needs some refinement and despite the will and effort of many scientists to improve it, only a few will be able to think critically and succeed in improving it. I think we are confusing the will to think critically and the act itself.
I think inclinations are due to human nature itself and not the subject beforehand. It manifests itself in different forms. In religious doctrine, you will find a relative freedom in the interpretation of their texts but within the fold of the belief system.For science it is opposite, you will be able to claim anything but the freedom will also require you to provide a more rigorous justification of your thesis on basis of mathematics and experimental evidence. Dogma exists in different forms in every activity human beings take part in.
I don't speak for him but l think there is some truth to it. The tools we use can only be applied to something other than themselves. If we try to improve the way we think. We will only end up with a conclusion that was pre-supposesd in the beginning. It will be a circular task.
To this I can only suggest you check out Popper. His is a comprehensive survey and analysis of induction, probability, testability, demarcation, etc. etc. Naturally, he uses examples, but he does really examine what constitutes criticism. Moreover, he concludes that criticism produces an objectivity that is more fundamental even than perception (which is 'uncritically theory-laden').
I think it is possible, as meta-analysis.
It doesn’t make sense to me to suggest an absence of skepticism falls in line with ‘critical thought’.
It can make sense, as l explained here.
Sure, so far l have only checked his falsification principle in science and he does seem to engage in a meta epistemic study. Recently l had a discussion with a friend of mine on that topic and we could not reasonably draw a line between what constitutes scientific thesis and which doesn't. For example, a lot of modern psychology is in a midway between science and psuedo science.
But what's your take on it. Do you believe that we can think critically about critical thought itself. I think we can but it will always be a circular task. Even though all results may not be wrong, their reasoning can always be challenged.
Can dogma exist in an absolute form and encompass knowledge totally. I think that would be an exaggeration.
People can have fundamental dogmatic beliefs and based upon them exercise a limited critical thinking. Limited critical thinking can also happen when the person does not stand on dogmatic grounds, simply because of the limitation of the human mind. I understand why dogma doesn't change but it can provide a base for other thoughts to evolve. For example physicists dogmatically accepted that time is absolute, yet they still managed to think critically on a lot of their topics based on time. Only in the 20th century, this conception of time was again challenged.
Any novice will have to select a certain viewpoint to follow or adopt and l believe critical thinking at that time is not possible, simply because of the absence of knowledge. Hence, it will be a lighter form of dogma
‘Dogmatic’ can be used to suggest a degree of close mindedness.
Dogma means to disregard evidence for or against. There is no ‘premise’ in dogma only absolute truth (that is how the term is used). That is what the word means. For that reason I cannot see how anything that can be considered ‘critical thought’ when there is no weight of evidence in play.
How about the example l gave before and l will quote again.It was a matter which could not be decided on basis of evidence and a lot of other problems in religion, philosophy and even science cannot be decided on basis of evidence. Here is the example, it was treated as an axiom. You have to change your conception of dogma in order to include other forms of dogma.
I’m not interested in this kind of word play tbh. Have at it with someone else please.
I think it is just another form of meta-cognition. Thinking about thinking. You can criticize the way something is done. You can criticize the way that you or someone else performs criticism. I.e. Do your criticisms tend to be substantive versus methodological? You have performed critical thinking about critical thinking. Are your criticisms effective? Why not? Are they couched in polemical versus interrogatory fashion? Critical thinking about critical thinking.
You don't have to but we were using the same word differently.
Btw, don't you sense the deep irony
hmm :sad:
You should read Thomas Kuhn, a philosopher who argued for the presence of dogma in science. :smile:
Critical thinking is the analysis of facts to form a judgment.[1] The subject is complex, and several different definitions exist, which generally include the rational, skeptical, unbiased analysis, or evaluation of factual evidence. Critical thinking is self-directed, self-disciplined, self-monitored, and self-corrective thinking. It presupposes assent to rigorous standards of excellence and mindful command of their use. It entails effective communication and problem-solving abilities as well as a commitment to overcome native egocentrism[2][3] and sociocentrism. I don’t think he was suggesting scientists ignore all evidence.
Dogma:
The point being - which I still don’t see an argument against - that ‘critical thought’ does not align with dogma. It is not possible to think rationally about something you hold as a dogma that necessarily (as a dogma) requires no evidence or explanation, other than ‘it just is’.
Furthermore, from wiki:
I think the bold makes my point more clearly here. Dogma is the antithesis of the above, being irrational, non-skeptical, biased and lacking analysis, and completely unconcerned with evidence of any kind.
I don't think that is what Wittgenstein is saying. I think he is saying it is possible to be dogmatic, in the sense of holding some traditionally held "primary theses" about the world (Relativity is correct) and yet still be capable of advancing your knowledge by way of critical thought. Perhaps critical thought doesn't target dogmatic core beliefs initially or directly, but it can eventually penetrate them.
Certainly, as W says, that is Thomas Kuhn's position, and the man did come up with the notion of the paradigm shift.
Great stuff. Unfortunately, education trends are going in the exact opposite direction. We (to be fair, I only know the American system well) are abandoning content to teach "skills" like critical thinking. And very smart people (see the many in this thread) seem blind to the fact that you must have something to think critically about, and without a knowledge base, you might be thinking, but there is nothing critical going on.
And after my first read through the thread, every post that even slightly disagrees provides no example of how to teach critical thinking separate from content...unless I missed it.
Good point. It reminds me of history education. There are theories now that history education can be a mish-mash hodepodge of time periods and events, as long as it is taught using "critical thinking" skills. In other words, the aversion to "grand narrative" history is so great, that the basic eras, periods, and change over time is lost to "thinking exercises" or collaborative projects, or whatever else is considered more important than content itself. However, without the basic narrative, there is no way to properly understand it, deconstruct, or do anything else meaningful with it. It is devoid of context. If you don't understand the Enlightenment, the American Revolution makes little sense. If you don't understand the Reformation, the Enlightenment makes no sense. If you don't understand the Silk Road, you miss out on the globalization that lead to Renaissance, etc. To take things out of context and to just use historical subjects as a means to some some ludicrous critical thinking goal, that has nothing to do with history itself is to create a real disservice.
@Banno Maybe you'd agree.
:rofl:
I think it is possible to think about the methods and obstacles that are present when one is using critical thinking and after reflecting on it. The whole post-positivist movement that was initiated by Popper as you have mentioned falls under that. But as you have seen with my discussion here, it is impossible to convince another person that there can be something wrong in the application of critical thinking in a highly critical field. People usually take that for granted, especially in science.
Thank God. Someone understands my point here finally. I was going to lose my mind and l was beginning to think whether l was spewing complete garbage.
Quoting Banno
Everything is dangerous when you live under the yoke of tyranny whether that be a single powerful dictator or the so-called "democratic" majority.
I will get back to you with more examples of science undergoing a paradigm shift and removing fundamental axioms or assumptions that were taken for granted because of the the general consensus of the scientific community. Dogma in science is under the cover of a paradigm. The paradigm shift can not take place for a few centuries, yet scientists are still able to produce new science. The Newtonian physics and Einstein's physics are completely different in their fundamental principles. Even though they may reduce to the same nature when we apply them to daily life, the difference lies in the details.
Besides that, a religious doctrine can have a wide range of interpretations around it. Anyways l rest my point here. I have probably said all l had to say.
Critical thinking shouldn't only involve criticism but also an ability to correct the mistakes you have found. That aspect is largely missing and is not possible to cultivate in the minds. Certain people just happen to be more gifted and hit the targets we can't even see. Feynman did remarkably well in his Putnam tests without any preparation. An even better example would be Galois, who invented galois theory at the age of 18 and died an year later from a duel. His theory was so ahead of his time that even the mathematicians of the highest calibre struggled to understand its importance. One of the biggest lie that we are all told is that everyone is creative.
Quoting Banno
It is not very complicated. The work of critical thinking reveals how assumptions shape various arguments.
So, how does one separate those various arguments?
Ugh, you are so right here it hurts. I actually have my teaching credentials in history. They haven't driven me from education yet...but I sure have rolled my eyes during a few teacher's meetings.
Quoting schopenhauer1
I wish this was understood by more people (shouldn't it be obvious?)
Quoting schopenhauer1
Why learn about the Enlightenment, the American Revolution, the Reformation, the Enlightenment, or the Silk Road when you can spend weeks learning about the Janissaries or Rasputin :roll:
Quoting schopenhauer1
:cheer:
I'm glad to know I'm not the only one who sees this.
Who is saying that everyone is me?
Yeah, that's a big fat lie! My gawd, the world would be in a heap of trouble.
:yum:
Ironically in philosophy, the simple things are left unnoticed. The most cryptic philosopher is usually the one who is studied the most too cause it is easy to argue about topics that can be misunderstood easily.
:smile:
I apologize for any copyright infringement. Please don't press any legal charges.
Hah!
I voluntarily put what I think I know, even when I think I know it's novel, out there for all the world to see!
:wink:
My income doesn't depend so much on philosophy! Good thing too!
I just like puzzles.
That is certainly fair. I just don't want the "most cryptic philosophers" being taught in an introductory (or anything at the high school level) philosophy course. They need to know the basics BEFORE getting into the cryptic stuff.
And philosophy would be much trickier to define content for. Is philosophy taught/learned or practiced?
My point remains the same. Dogma is against critical thought because it doesn’t care about evidence. You’ve presented why you disagree with if you actually take the word for what it means. I doubt you do disagree. It seems you were just looking to ‘jab’ at me for no good reason.
Dogma simply isn’t the same as holding bias or psychological fixedness. When people only see the world as being explained via science that isn’t even ‘dogma’. That is ‘scientism’ - a term philosophers enjoy to use when they face scientific facts they don’t understand.
Totally. l had a discussion a few weeks ago, where the other person wouldn't acknowledge that scientific statements are not a priori.
Indeed. I had trouble with it when I first encountered it in 1962. :yikes:
Before addressing anything else, l want to assure you that l didn't want to take a jab at you or anything like that. I felt what you wrote was really interesting and l couldn't resist attacking it. It was all done in good mood. Nothing to worry about.
I want to know what do you think on the assertion that a paradigm shift occurs in science after it has come to a halting point. Do you think that the paradigm shift removes "psychological fixedness" ? I have read on that and it does capture some aspects of why science comes to a halt but it doesn't capture the details. I think certain viewpoint are not due to psychological fixedness but due to a consensus among the scientific community. You can disagree with my opinion obviously .
That's a long time ago. I still have to learn a little more group theory before l can begin to appreciate it deeply. I wish he lived longer though. Who knows what he might have done later on had he lived.
I don’t really consider a paradigm shift to be anything other than a human item, so to refer to a paradigm shift in art, science, religious thought, aesthetics, political or anything else, is not something I can quite get my head around in the context of this discussion.
I guess a good Marxist would insist that such ‘revolutions’ are part of a necessary conflict of opinions. I think it was Schiller who said something along the lines of humans being a kind of creature likely to destroy perfection out of sheer boredom - we’re ‘anti-dogmatic’ in that sense, because I believe stagnation always instigates a revolution of some kind (by way of exploration and/or death). This makes sense in terms of a ‘paradigm’, as once everyone is pulling roughly in the same direction things go swimmingly, when things ‘halt’ - a term I’ve been very interested in regarding this subject matter - anyone can shift the momentum. Maybe that is a biased analogy though that adheres to strictly to Newtonian mechanics?
In the sense of a paradigm shift I’d relate this more to disrupting the axis mundi (or weltanschauung if you prefer) rather than just ‘psychological fixedness’ (which sounds too tame a term for a societal shift, but fitting for individual cases). For the individual we’ve learnt a fair bit about brain functioning and it doesn’t take much to see how IOR (inhibition of return) and neural priming effects our world views. The successful communication of a new perspective is what instigates the beginnings of an evidence based paradigm shift in terms of science.
Who is more likely to say “Wow! We were wrong. How fascinating!”, and who is more likely to say, “We’re not wrong! Evidence doesn’t matter, I just KNOW what the truth is.”
Paradigm shifts open up a whole new way of ‘viewing’ the world. Some are fearful of this for various reasons, including commitments to areas now deemed worthless, financial investment (the genome project is an example of that - pharma companies bought up genes to research for huge sums, but now few think such research into individual genes is of any significant use as the whole genome is far more complex and interactive than anyone had imagined). Is that ‘dogma’? Nope. That is politics, and politicking in science causes some people to deceive others - Feynman pointed this out with his famous words about ‘mother nature’ after the shuttle disaster. Newton was hardly a ‘scientist’ by any modern standard, but none of that matters to the OP as far as I can see?
How/Why do you see paradigm shifts as important to critical thought? I can see the relation, but not where you’re going. Keep in mind a ‘paradigm shift’ has adapted its use since Kuhn.
Expansive means "can be expanded". So it can be shrinked. Because whatever is expansive, is elastic.
So Popper's expansive theories can be reduced and disregarded, if one shrinks them, instead of expands them.
----------
Does the book "Critical Rationalism" describe the process of critical thinking without any topic as the topic of the critical thinking, or does the discussion discuss critical thinking without any topic?
This is a question only you can answer, Pantagruel, since you are the only one who has read the book in these parts.
Please also be careful you read the passages in the book that are about critical thinking, not about merely critical rationalism. I wish you to avoid building an argument on a strawman.
How do you measure the size of a lie? You put them side-by-side, and the taller lie is bigger? Or you put them on a scale, and the heavier one is the bigger lie?
"Dear, they do it with smoke and mirrors."
It’s why they taught the trivium before the quadrivium in classical education. One needs the requisite understanding in order to grasp the more complicated topics. Most importantly, as with the liberal arts, one needs an education worthy of a free person. Without critical thinking I’m not sure that’s possible.
Assuming you were 20 year old back then, you are approximately 77 right now. You are probably the oldest user here then
I simply look at the type of people who are believing it. If they happen to be critical, it is a well constructed lie ( a little lie ). If they happen to be simple minded, it is a big lie.
:lol: :lol: :grin:
Can Hempel help out here? Is there such a thing as philosophy/theory of mind that can meet Hempel's criteria of adequacy?
Yes. The only way the shift will take place is that we abandon philosophy. If no one asks a question, there won't be any answers to find. Everything will be neat and tidy.
Are you agreeing that we are in dire need of an acceptable theory of mind(thought and belief on my view)?
Are you also claiming that logical empiricism has the only acceptable criterion for what counts as an adequate theory/explanation of human thought and belief(mind)?
That's seems quite odd to me at first blush. Are all notions of mind incapable of meeting Hempel's criteria?
I'm just happening upon Hempel... so...
An acceptable theory of mind is beyond the scope the philosophy and even science in my opinion. Logical empiricism has it's own faults too.
:worry:
I hope my toxic defeatist attitude leaves your beautiful creative soul alone and alive.
No worries. Curious to see it argued for though.
Indeed, I am paying more attention to the focus applied to the critical component since joining the thread. Certainly overall it is the use of critical thinking in validating scientific knowledge in general which is the heart of the matter. However he does comment, compare, contrast various types of criticality.
Honestly, per my comment on metacognition, I think it is trivially evident that one can critically evaluate one's own critical thought processes. Why would you not be able to? It is simply a tool, like any other?
I have to say, I get a lot of 'word-games' feeling coming from your general direction. This comment really has no substantive merit other than polemic. Expansive primarily means extensive in scope, at least, that's my experience with the word.
And the word you are looking for is "shrunk".
A workable, acceptable, or even just merely descriptive theory of mind is beyond the human mind to construct.
We are stuck in this together. We would need to invent an apparatus or mechanism or process whereby we can pull our own selves out of the quagmire by our own hairs.
Somebody, don't have the reference or the author's name, said that philosophy should not seek to have its questions answered; instead, it should seek a cure to treat itself.
You're right on both counts.
Damit, I admit: guilty as charged.
Well, the thesis was that the tool (critical thinking) is useless, or even undefined, non-existent without an application, without a piece of material that it can work on.
If, and only if, that is true, then my earlier conundrum stands.
I've been guessed to be hugely different in age from the real one on one philosophy internet forum. Forgot which of the four I was active on at the time. It pleased me to no end.
What's my age ?? :wink:
I'd say, five or six... but a very precocious five or six. A child genius. A prodigy. A pedagogical miracle.
I'm 82. Oh, for the days of youth (77)! :cool:
(Is there a chance that you may be dyslexic? transposing digits and characters in your writing? And your age is 28?
In months.)
My mind is going. It is horrible to have early-onset Alzheimers at such a young age that i'm at. (Mommy just brought me home from the hospital, I still have some raw umbilical cords hanging off of my belly.)
In different words... I agree with this sentiment.
I'm always confounded at what seems to be a rather broad-based general consensus across the philosophical spectrum that we cannot take proper account of our own thought and belief.
Upon what basis does this consensus rest?
Do you have an argument and/or reasoning process... some intelligible coherent line of thought that has led you to such a conclusion?
Could you explain why and/or better yet how an acceptable theory of mind is beyond the scope of both science and philosophy?
https://thephilosophyforum.com/discussion/comment/362707
Notice that Devans does not look to the previous work done in mathematics, but straight away applies his own understanding of division in order to find a solution.
My reply:
https://thephilosophyforum.com/discussion/comment/362716
I, on the other hand, went to a reliable source, trusting that others with far more mathematical expertise than I had already considered the issue. I went there because I had previously read sufficient mathematics to understand that the answer was not undefined, but uncountable; but insufficient recall as to why this was so.
Devans erred in dividing by zero. Now it seems to me that this should have been an end to the discussion. But instead, Devans says
Quoting Devans99
It leaves one nonplussed. Devans is not stupid; but then again...
Can you elaborate on what you think this broad consensus is? I think most people would agree you can take some sort of self account of thoughts and beliefs...so Im curious what you mean.
The full explanation of the point I was making is given in this post:
https://thephilosophyforum.com/discussion/comment/362723
What is going on here? Why can't Devan's see that division by zero is an illegitimate act?
That we cannot take proper account of our own thought and belief. That we cannot know what thought and belief is. Broad-based belief of that 'nature'(for lack of a better term).
I know it is illegitimate; that is why I say it equates to UNDEFINED.
But the definition of a point, as having zero extents, is also equivalent to division by zero:
- You want to divide a line segment length 1 into 0.25 length chunks: 1/0.25=4
- You want to divide a line segment length 1 into 0 length chunks: 1/0=UNDEFINED
So I hope you can see the problem - the definition of a point as having zero extents enshrines into maths that division by zero can produce a defined result (?).
I'd previously put this down to mere psycoceramics, but that's not I now think sufficient.
Rather, the Cult of the Maverick provides an incentive for folk to critique without first doing the work of understanding the topic.
Simply explaining to the Maverick were they have gone wrong is insufficient; their purpose is not to find out the truth, but to smash it in order to demonstrate just how clever they are.
One sees the same thing in, for example, @Bartricks repetition of "there are no actual infinities".
I think it interesting - and the popularity of that thought in this thread seems to back me up here.
https://thephilosophyforum.com/discussion/comment/362723
Ok, and what is meant by “properly”?
here is the second place I addressed your reply: https://thephilosophyforum.com/discussion/comment/362728
A third time: do not divide by zero.
I know, that's why a write 1/0=UNDEFINED - I know it is an illegitimate operation - so I write UNDEFINED. This is the normal convention from maths.
But maths, by assuming a point has zero extent - is legitimatising division by zero - a point composes a line so you have to divide by zero to find out how many points there are on a particular line segment.
So you know you shouldn't do it, but you just can't help yourself?
I don't know.
- You should not divide by zero
- (any number)/0 = UNDEFINED
http://mathworld.wolfram.com/Undefined.html
UNDEFINED is not a number. So any equation involving it is not well-formed.
It's shorthand for "Don't do it!"
Why are you using math if you reject its rules?
Its like you are fishing, and your friend catches a fish and says “i caught the biggest fish, 3 feet!”
And you say “no mines bigger”, but your friend protests after seeing your fish “its only 2 feet!” To which you reply “I dont use feet when measuring my fish, its way bigger”
Thats what you are doing here, propping up your argument using math but not using math when it shows your basis to be incorrect.
Is there another way of framing things not using math? If not, might be time to reevaluate.
UNDEFINED is a legitimate mathematical expression. It is perfectly valid to write 1/0=UNDEFINED. Or ?-1 = UNDEFINED (in non-complex maths). Or whatever.
It matters little, however, if you squabble with my syntax, the definition of a point as having zero extend implies divide by zero whenever we wish to know how many points constitute a line segment, a plain, etc... that was my point.
Yeah. You don't get it. I understand that. I'm not going to continue the discussion of the error of dividing by zero - that's not the point of this thread.
One that is rendered in evolutionarily amenable terms. One built upon universal criterion. One built upon knowledge of all thought and belief.
One without exception. One that is capable of taking account of that which exists in it's entirety prior to our awareness. One that is capable of taking account of that which is prior to our language. One that is capable of setting out a coherent account of all thought and belief.
Let me leave you with one thing to consider. The folk who get paid to do mathematics are on my side. They agree with me that the number of points in a line segment is uncountable, not undefined.
1/0 <> UNDEFINED
?
That seems apt.
How can you count something that does not exist? (if a point has zero extent, it does not exist). How can you flaunt basic mathematics. 1/0 is clearly not equal to 'uncountable'.
I guess this is the point of the thread - there are people (not just me) who disagree with the received wisdom of science and mathematics. Is it correct to dismiss/discourage them or engage with them to understand their issues?
So back to the topic of this thread - Devan's, and similar behaviour can be explained as entering into critique before having sufficient grasp of the topic.
We can see that clearly in Devan's case. He continues to attempt division by zero, despite it being pointed out that it is illegitimate.
Now to any one with a moderate grasp of mathematics, it might look as if Devans is making a legitimate point. That is, there is a certain level of mathematical competence that is required in order to see how far wrong he has gone.
And that means that someone like Tim, who knows what they are talking about, must spend an inordinate effort in showing where Devans goes astray.
But that's hard to do; hence, folk such as Devans can thrive in the gaps between legitimate discourse.
See? Devans lacks the understanding needed to see how he is wrong.
And here, learning stops.
Thank goodness this sort of thing does not happen in, say, politics - imagine the sort of President we might end up with if it did!
Engage with my argument for F**Ks sake.
If you have a point with zero length, how many are there on a line segment length one?
1 / 0 = ?
Again, the answer is that the number of points on a line segment is uncountable.
The topic here is not mathematics; it's why folk like you can't recognise when their argument has been defeated.
One might hope that Devans would go read some books and learn some maths.
But instead, he digs in, refusing to reconsider his position. Perhaps what is important for him is not being wrong or being right, but being the Maverick.
Witness the recent discussion concerning banning @Bartricks: https://thephilosophyforum.com/discussion/7115/banning-bartricks-for-breaking-site-guidelines/p1
That seems like an incredibly high standard of whats “proper”. What are some things you have this kind of account of?
No. I want a forum where the disagreement is legitimate.
Indeed. It's a universal standard. One without exception.
The questioning was about what counts as a proper account of all thought and belief, and hence "mind"...
The answers were about what an acceptable theory of mind needed to include in order to be a proper account of all thought and belief, and thus... of all mind.
[s]1/0 = undefined[/s] (n)
undefined(1/0) (y)
Or, colloquially, we may just call it nonsense.
You don't see mathematicians using = about undefined (unless, perhaps, there's an implicit context by which that's understood).
Whatever expressions are undefined we stay away from if we want to make sense.
You didnt answer the question sir. What are some things that you have this kind of account for?
Quoting creativesoul
1. No theory to explain the workings of the mind has been established.
2. Assuming the mind is a product of brain functions, we have no knowledge of how the brain works other than noticing blood flow and excited electron movement in some parts of the brain.
-------These first two points were empirically based. The next point is a priori based.
3. If we want to know how the mind works, we have to make a mental image of the mind. But to make a mental image of the mind, we need a storage capacity that equals the mental image, and then some more storage capacity to manipulate the thoughts that explain the mind. Therefore to explain the mind, we need a larger, better, more intelligent thing than our mind. Which is not achievable because you can't have something bigger than itself.
Students Have 'Dismaying' Inability To Tell Fake News From Real, Study Finds
"The kinds of duties that used to be the responsibility of editors, of librarians, now fall on the shoulders of anyone who uses a screen to become informed about the world."
https://www.npr.org/sections/thetwo-way/2016/11/23/503129818/study-finds-students-have-dismaying-inability-to-tell-fake-news-from-real?fbclid=IwAR29U7dZfZVbW9wmxBZuNg_JI1dxWDt_CuQB7mBg1sNgiJw6uP3POFv63do
In this climate of information crisis, better to be over- than under-critical.
I've found the critical tenor - i.e., continuously formulating objections as one comes to an understanding of a philosophical position - is as potent a learning-style as any. The key is not to neglect to - just as continuously - turn the critical eye back upon itself. Self-criticism should be as pointed and unforgiving as criticism of others.
A dovetailing or synergy of other-criticism and self-criticism can serve to purify and personalize our understanding of a difficult point or position.
I'm tempted to agree with you. But I do have concerns. The collapse of trust only emphasizes our passivity. The 'decapitated machine' of capitalism doesn't need anything from us but our mindless conformity to the usual buying and selling.
But I don't have any easy answers. I've just been thinking of this 'headlessness' and how it connects to the spectacle and the banalization of philosophy. My doubts are 'useless and unprofitable.' A short-term prudence dictates that I 'forget all that' and just gather coins. As long as fame and money are our gods, the philosopher is a comic figure, a cartoon.
Quoting ZzzoneiroCosm
Well said.
Well...
Better yet to be well-informed. What is it that mathematicians, climate scientists, botanists and biologists actually say?
It's now astonishingly easy, from the point fo view of an old bastard such as I, to go to secondary or primary resources.
That the students in your cited report did not see fit to do so - yes, dreadful.
But are those in fact our gods? They're more the gilding of a god dauntingly out of reach. No matter how hoodwinked and hedon-hypnotized we are en masse, there is a fundamental craving in all of us for a peace-girding wisdom. It's what draws me to the Stoic pursuit of noble-mindedness and the Skeptic recipe for ataraxia.
In my mind it's crucial to draw a distinction between philosophy-as-position-making and philosophy-as-pursuit-of-wisdom. The former has nearly consumed the latter - no doubt the source of your dis-ease vis-a-vis the well-scoffed, cartoonesque abstractiphaster. There is nothing cartoonish about a sober devout pursuit of wisdom. Philosophy is banal insofar as it excludes it.
Wisdom and intellectual peace are still valuable and valued.
Thanks. I've been enjoying your posts. Welcome to the forum.
These days shifty academes - from what I understand - will fudge their research for a price. The pressure to publish has pushed a ton of bullshit into the scientific canon.
Those without the leisure to spend their days researching the research - the minutia of funding and the politics of such-and-such a scientific journal - had better be well-practiced and comfortable with a prudent suspension of judgment.
The notion of being well-informed has gotten almost inscrutably complex.
This is an ugly phenomenon indeed.
It seems to me that you guys are arguing about dogma, but strictly speaking you don't hold exactly equivalent definitions of what is dogma. Kind of like saying, "my definition of 'dogma'" is correct. As if it is debating ownership of the concept. When both positions have merit.
"All our hypotheses are conjectures, and anybody is free to offer
conjectures—even conjectures that may appear quite silly to the
majority of us. Only thus can we make way for bold, unconventional, new ideas"
Seems to illustrate the tension between the accepted dogma and the radically new insight.
Indeed. We are forced to trust experts, but only an expert can distinguish between a genuine and fake expert. There is too much human knowledge. The headless machine can somehow run without anyone grasping the totality of its operation. Those comfortable in their place in the mechanism are perhaps even happy that being well-informed becomes more and more difficult. Some are served by the general passivity and skepticism. But knowing this doesn't instantly cure one of that same passive skepticism.
I think I agree with you here. 'Fame' and 'money' are masks in a certain sense for some impossible enjoyment. In a narrow context, though, there is no time for serious thought, since time is money. Or rather time is understood in terms of exchange value.
To be sure, most of us offer a partial resistance to this. It's always the others who worship fame and money. We know better, but we must act as if we don't. This action is the 'truth' of the ideology, and others do our believing for us. Or that's one idea I've heard which has perhaps a grain of truth or value.
Quoting ZzzoneiroCosm
I feel that draw too.
Quoting ZzzoneiroCosm
I agree, and I think that's a valuable distinction. For me, philosophy as self-sculpting pursuit of wisdom is primary. At the same time, this seems connected to position-making, though not in the vain sense. Earnest position making is an attempt to further disclose reality or clarify existence.
Right now we are clarifying one of the difficulties of modern life, which is too knowledge with not enough credibility. I can ask myself sincerely: should I stop reading the news? Do I need to know about the sensational murder far away? Does a wise man read the news? At the moment I still read the news, wise or not.
Not really. I’m simply saying the other person is misusing the term to suit his purpose - the definition shows ways in which the context changes and I’ve made as explicit as I can what the context and definition is.
You may choose to use the term ‘banana’ to mean ‘sociopolitical’ and talk of the ‘banana influence in contemporary art’, I wouldn’t accept this as a reasonable thing to do as it is likely to cause confusion.
This all stems from my statement about ‘scientists’ being happy about being wrong whilst more ‘religious’ types are dogmatic - as in ‘dogma’ (where evidence is seen as of no value). And if we’re to talk about a ‘paradigm’ would it be right to call religious doctrines ‘paradigms’? Are they models? I guess that would depend on how willing you are to think of the context of ‘model’ in this sense, which basically means something like an adjustable set of ideas - clearly not something we relate to religions as they have the ‘true word’ at their disposal rather than a ‘model’ of something approximating a ‘truth’ (using ‘truth’ in a broad sense here to mean reality).
I’ve seen devans around for a few years here and there. They are willing to learn - not scared of making mistakes. That in and of itself is to be commended, and encouraged.
It’s good to see little groups of people having discussions across threads and feeling their way around. Some will float and some will sink.
Maybe this thread would’ve hit the mark if it focused on self-criticism more. It is important to know you don’t know. That way it seems there is some chance you’ll stumble across something useful and realise it is useful.
Each point corresponds to a specific real number. How many real numbers are there in the unit interval?
Quoting I like sushi
I would question whether "happy" is the appropriate description. In mathematics if I were to work trying to prove a theorem and then a colleague showed the theorem to be false, I would not be "happy" - rather disappointed but resigned to the acceptance of fact - and then cheer myself up by moving on to another project. :chin:
Even so the guy who solved Fermat’s theorem wasn’t exactly happy about solving it because it left him bereft of purpose.
I'm sure he's found something else to fill those lonely hours.
Isn't that exactly the same thing as I said, disputing the definition.? Anyway, it's been pointed out so I won't harp on it if it doesn't resonate at all.
You directed the post at me. I didn’t use ‘my’ definition, merely ‘the’ definition. I’m reasonably charitable with most words, but with some - in certain contexts - less so.
But I did answer. Those criterion are at work in my own philosophy which is based upon human thought and belief(mind).
This seems fraught throughout. The universe is bigger than us with much greater storage capacity, yet we know to some extent how it works, so clearly the above is wrong somewhere along the line.
"To some extent" leaves a huge margin of error, or a small margin of error, or no margin of error, or an unknown margin of error.
When I said "to know our minds" I meant no margin of error. That's all. Because to some extent, we already know our minds.
But thanks for noticing my previous post, and paying due respect by acknowledging its presence. I am actually grateful to you for that. Because earlier I had thought it would go down in history as a never-noticed post.
So...your philosophy? Are you claiming to have achieved this standard with your own philosophy then?
Your philosophy is all this:
“One that is rendered in evolutionarily amenable terms. One built upon universal criterion. One built upon knowledge ofall thought and belief.
One without exception. One that is capable of taking account of that which exists in it's entirety prior to our awareness. One that is capable of taking account of that which is prior to our language. One that is capable of setting out a coherent account of all thought and belief.”
Bolded a couple of important words that highlight the magnitude of your claim.
Is that right? Is that your claim? If not, then can you help me connect the above with your statements? (And if youre inclined, how the above is NOT the claim you are making about your own philosophy)
Well, that's demanding perfection and/or omniscience.
Achieved?
:brow:
Those are criterion I use. A few here are redundant, but I was trying to emphasize the important bits of an acceptable theory of belief(mind).
Whats perplexing to me is terms like “acceptable”, which I take to mean nothing less will do, its your minimum standard and it doesnt even seem possible...but ok, I suppose I understand your criteria at least. Thanks.
Demanding knowledge.
Well if all you mean to say that all knowledge must be true... we are in complete agreement.
Well which bits do you find impossible?
Hehe... that was below the belt. But you're right.
“Universal criterion”, built upon “all thought and belief”, taking account of something in its entirety before being aware of it...pretty much that whole quote is full of lofty, impractical requirements for whats “proper”.
You are talking about infallible knowledge, and saying basically nothing less is acceptable.
Universally applicable is not equivalent to infallible.
With regard to an acceptable theory of human thought and belief, it must be able to take account of thought and belief that is prior to language, ad well as thought and belief that is informed by and/or mediated with language use. It must be able to bridge the divide between thought and belief that is existentially dependent upon language use, and that which is not.
Working from the premiss that at the moment of a capable creature's biological conception, there is no thought and belief, we arrive at the requirement to hold that thought and belief begin simply and grow in their complexity. Taking proper account of how that happens will be amenable to evolutionary progression.
Hence... the criterion put forth.
We must be working from different ideas of what's impractical... I use them, and have been since I began serious interest in philosophy twenty or so years ago.
So you are claiming you have a coherent account of ALL thought and belief?
Not exactly... I'm putting forth an outline(methodological approach) that is best suited to render one.
So its an ideal, not something you actually have or use, but something you strive for?
Both...
...ok then you are saying you have a coherent account of all thought and belief, aren’t you?
I'm saying that I've the beginnings of one.
Ok, I understand.
:ok:
This brings up a question that I think you may have a good quick answer for (it is off-topic, so I understand being ignored):
How are scientific statements not both? Some are a priori, but not all. Example: The tree is taller than the shrub. Does that NOT count as a scientific statement? I understand that foundational concepts of science are a priori, but wouldn't any scientific statements that stem from using the scientific method be entirely based on observation and experience?
Thanks. I was just using definitions before. But for me, that page would suggest that I am right and that many scientific statement are based on observation and experience and therefor NOT a priori???
I was responding to:
Quoting Wittgenstein
Which suggests that statements like, "the tree is taller than the shrub" are not scientific? Because surely that is not an a priori statement?
But @Wittgenstein used this as an example of something that is obviously right...so I feel like I am missing something...possibly it is a joke but my philosophy knowledge is too weak to get it?
I hope l don't get this messed up but l think these two examples will clarify a priori from a posteriori.
A priori
If John is taller than Mary and Mary is taller than Sam, then John is taller than Sam. Since this statement reduces itself to a logical property , If X>Y and Y>Z then X>Z.
A posteriori
John is taller than Mary. In order to make this statement, we need to have some empirical data.
On the point of science, foundational principles of science are a priori but l would put them into the category of metaphysics. Eg the statement, effect comes after the cause is an a priori statement.
An apple is a fruit.
Dogs are animals.
These statements are also a priori but in my opinion these statements should not be classified as scientific as they merely come from the category we assign to them. It is almost a matter of convention. Even if we give them a certain scientific veneer, they will be foundational.
My friend didn't only regard foundational topics as such but statements like " Gravity causes objects to fall towards earth" to also fall under a priori statement.
Oops! I need to learn to read. I missed the "not" in your previous statement (all scientific statement are NOT a priori). Suddenly it all makes sense. Thanks for taking the time to explain anyway. As I was reading, I was like, "this is exactly my point". Then I read your last sentence and realized I may have misread your original statement...and sure enough I did :grimace:
Thanks again for the patience, and yes, your friend is a bit crazy.
Okay. I will try to do better.
Kant objected to Hume's view of causality because it did not give a way to rank different explanations.
The objection on Kant's side was not so much about whether there were any way thinkers who could assign one agent or another as the cause of something but that Hume was cutting the enterprise off at the knees. Because every story as a story is just a story, there is no way to connect it to some kind of necessity that could provide proof of some explanation being more than that. A story.
So, on one level, the whole effort to object to an idea became a comprehensive theory of what could replace the disagreed thing.
As a matter of one thesis supplanting another, that is rather odd. The contestants are arguing about the rules of a fight rather than who has the correct view of a matter.
Fun with anonymity.
I think you're missing something about crackpots. For example, I struggled with the concept of compactness when learning topology. For some time, I thought: surely this isn't the natural complement to discreteness when generalizing finiteness to infinite sets. It wasn't until I learned topology from the perspective of computability theory that I understood the concept. Despite lacking knowledge and thinking critically, I don't think I ever became a crackpot about compactness.
Similarly, I read about the Riemann hypothesis before learning complex analysis. It never occurred to me to question whether the problem was actually within my grasp. I knew that thousands of people much smarter and more informed than myself have worked on the problem, and in order to fully understand let alone approach it I would have years of work ahead of myself. On another note, I avoid talking about the foundations of physics because I'm almost completely ignorant about the subject.
For whatever reason, crackpots focus on specific topics: the axiom of infinity, the Riemann hypothesis, P=NP, the ABC conjecture, and so forth. It's rare to find crackpots discussing the axiom of choice, the mean value theorem, the reality of transcendental numbers, or other actually problematic topics in mathematics (in particular, from the perspective of constructive mathematics). It must be a sociological phenomenon, but I'm not sure how to explain the choice of topics. Surely everyone learned mathematics in high school that are highly suspect and revised in more advanced courses; but those usually aren't the topics they choose to target. Anyways, my two cents.