Polytopos

Karma: 134

Polytopos 10 Aug 2022 18:09 UTC
1 point
0
in reply to: ChristianKl’s comment on: What are some Works that might be useful but are difficult, so forgotten?
Science and Sanity looks pretty interesting. In the book summary it says he stressed that strict logical identity doesn’t hold in reality. Can you say more about how he builds up a logical system without using the law of identity? How does equational reasoning work for example?

Polytopos 10 Aug 2022 0:35 UTC
8 points
0
on: What are some Works that might be useful but are difficult, so forgotten?
Great question.

My joke answer is: probably Hegel but I don’t know for sure because he’s too difficult for me to understand.

My serious answer is Graham Priest, a philosopher and logician who has written extensively on paradoxes, non-classical logics, metaphysics, and theories of intensionality. His books are extremely technically demanding, but he is an excellent writer. To the extent that I’ve managed to understand what he is saying it has improved my thinking a lot. He is one of those thinkers who is simultaneously extremely big picture and also being super rigorous in the details and argumentation.

Ever since I first studied formal logic in my first year of undergrad, I always felt it had promise for clarifying our thinking. Unfortunately, in the next decade of my academic education in philosophy I was disappointed on the logic front. Logic seemed either irrelevant the questions I was concerned with or, when it was used, it seemed to flatten and oversimplify the important nuances. Discovering Priest’s books (a decade after I’d left academic philosophy) fulfilled my youthful dreams of logic as a tool for supercharging philosophy. Priest uses the formalisms of logic like an artist to paint wonderous and sometimes alien philosophical landscapes.

Books by Priest in suggested reading order:

An Introduction to Non-Classical Logic: From If to Is. Cambridge University Press, Second Edition, 2008.
- It’s a great reference. You don’t need to read every page, but it is very helpful to turn to when trying to make sense of the rest of Priest’s work.
Beyond the Limits of Thought. Oxford University Press, Second (extended) Edition, 2002.
- Presents the surprisingly central role of paradoxes throughout the history of philosophy.
- The unifying theme is Priest’s thesis that we humans really are able to think about the absolute limits of our own thought in spite of the fact that such thinking inevitably results in paradoxes.
One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford University Press, 2014.
- A study in the metaphysic of parts and wholes
- A deeply counterintuitive but surprisingly powerful account based on contradictory entities
Towards Non-Being, 2nd (extended) edition. Oxford University Press, 2016.
- An analysis of intensional mental states based on a metaphysics of non-existent entities.

Polytopos 6 May 2022 18:08 UTC
3 points
on: What are the best examples of catastrophic resource shortages?
Various fisheries have become so depleted as to no longer be commercially viable. One of the obvious examples is the Canadian Maritime fisheries. Despite advanced warning that overfishing was leading to a collapse in cod populations, they were fished to the point of commercial non-viability, resulting in a regional economic collapse that caused depressed standards of living in the maritime provinces to this day.

Polytopos 12 Mar 2021 3:04 UTC
5 points
in reply to: Joe Carlsmith’s comment on: Grokking illusionism

according to the story that your brain is telling, there is some phenomenology to it. But there isn’t.

Doesn’t this assume that we know what sort of thing phenomenological consciousness (qualia) is supposed to be so that we can assert that the story the brain is telling us about qualia somehow fails to measure up to this independent standard of qualia-reality?

The trouble I have with this is that there is no such independent standard for what phenomenal blueness has to be in order to count as genuinely phenomenal. The only standard we have for identifying something as an instance of the kind qualia is to point to something occurring in our experience. Given this, it remains difficult to understand how the story the brain tells about qualia could fail to be the truth, and nothing but the truth, about qualia (given the physicalist assumption that all our experience can be exhaustively explained through the brain’s activity).

I see blue and pointing to the experience of this seeing is the only way of indicating what I mean when I say “there is a blue qualia”. So to echo J_Thomas_Moros, any story the brain is telling that constitutes my experience of blueness would simply be the qualia itself (not an illusion of one).

Polytopos 10 Feb 2021 21:11 UTC
1 point
in reply to: Jameson Quinn’s comment on: Why everything might have taken so long
For an in depth argument that could taken to support this point, I highly recommend Humankind: A Hopeful History by Rutger Bregman.

Polytopos 10 Feb 2021 15:30 UTC
1 point
in reply to: TAG’s comment on: Philosophy: A Diseased Discipline

it generalises. Logic and probability and interpretation and theorisation and all that, are also outputs of the squishy stuff in your head. So it seems that epistemology is not first philosophy, because it is downstream of neuroscience.

I find this claim interesting. I’m not entirely sure what you intend by the word “downstream” but I will interpret it as saying that logic and probability are epistemically justified by neuroscience. In particular, I understand this to include that claim a priori intuition unverified by neuroscience is not sufficient to justify mathematical and logical knowledge. If by “downstream” you have some other meaning in mind, please clarify. However, I will point out that you can’t simply mean causally downstream, i.e., the claim that intuition is caused by brain stuff, because a merely causal link does not relate neuroscience to epistemology (I am happy to expand on this point if necessary, but I’ll leave it for now).

So given my reading of what you wrote, the obvious question to ask is, do we have to know neuroscience to do mathematics rationally? This would be news to Bayse who lived in the 18th century when there wasn’t much neuroscience to speak of. Your view implies that Bayse (or Euclid for that matter) were unjustified epistemically in their mathematical reasoning because they didn’t understand the neural algorithms underlying their mathematical inferences.

If this is what you are claiming, I think it’s problematic on a number of levels. First, on it faces a steep initial plausibility problem in that it implies mathematics as a field is unjustified for most of its thousands of years of history until some research in empirical science validates it. That is of course possible, but I think most rationalists would balk at seriously claiming that Euclid didn’t know anything about geometry because of his ignorance of cognitive algorithms.

But a second deeper problem affects the claim even if one leaves off historical considerations and only looks at the present state of knowledge. Even today when we do know a fair amount about the brain and cognitive mechanisms, the idea that math and logic are epistemically grounded in this knowledge is viciously circular. Any sophisticated empirical science relies on the validity of mathematical inference to establish it’s theories. You can’t use neuroscience to validate statistics when the validity of neuroscientific empirical methods themselves depend on the epistemic bonafides of statistics. With logic the case is even more obvious. An empirical science will rely on the validity of deductive inference in formulating it’s arguments (read any paper in any scientific journal). So there is no chance that the rules of logic will be ultimately justified through empirical research. Note this isn’t the same as saying we can’t know anything without assuming the prior validity of math and logic. We might have lots of basic kinds of knowledge about tables and chairs and such, but we can’t have sophisticated knowledge of the sort gained through rigorous scientific research as this relies essentially on complex reasoning for it’s own justification.

An important caveat to this is that of course we can have fruitful empirical research into our cognitive biases. For example, the famous Wason selection task showed that humans in general are not very reliable at applying the logical rule of modus tollens in an abstract context. However, crucially, in order to reach this finding, Wason (and other researchers) had to assume that they themselves knew the right answer on the task. i.e.., the cognitive science researchers assumed the a priori validity of the deductive inference rule based on their knowledge of formal logic. The same is true for Kahneman and Tversky’s studies of bias in the areas of statistics and probability.

In summary, I am wholeheartedly in favour of using empirical research to inform our epistemology (in the way that the cognitive biases literature does). But there is a big difference between this and the claim that epistemology doesn’t need anything in addition to empirical science. This is simply not true. Mathematics is the clearest example of why this argument fails, but once one has accepted its failure in the case of mathematics, one can start to see how it might fail in other less obvious ways.

Polytopos 9 Feb 2021 22:20 UTC
9 points
on: Book review: The Geography of Thought
This is a fascinating article about how the concept of originality differs in some Eastern cultures https://aeon.co/essays/why-in-china-and-japan-a-copy-is-just-as-good-as-an-original

Polytopos 8 Feb 2021 21:24 UTC
1 point
on: Living Metaphorically
An interesting contribution to is this book by Hofstadter and Sanders

They explain thinking in terms of analogy, which as they use the term encompasses metaphor. This book is the a mature cognitive sciencey articulation of many of the fun and loose ideas that Hofstadter first explored in G.E.B.

Polytopos 8 Feb 2021 21:16 UTC
1 point
on: Philosophy: A Diseased Discipline
I’m curious how many people here think of rationalism as synonymous with something like Quinean Naturalism (or just naturalism/physicalism in general). It strikes me that naturalism/physicalism is a specific view one might come to hold on the basis of a rationalist approach to inquiry, but it should not be mistaken for rationalism itself. In particular, when it comes to investigating foundational issues in epistemology/ontology a rationalist should not simply take it as a dogma that naturalism answers all those questions. Quine’s Epistemology Naturalized is an instructive text because it attempt actually to produce a rational argument for approaching foundational philosophical issues naturalistically. This is something I haven’t seen much on LW, it usually seems like this is taken as an assumed axiom with no argument.

The value of attempting to make the arguments for naturalized epistemology explicit is that they can then be critiqued and evaluated. As it happens, when one reads Quine’s work on this and thinks carefully about it, it becomes pretty evident that it is problematic for various reasons as many mainstream philosophers have attempted to make clear (e.g., the literature around the myth of the given).

I’d like to see more of that kind of foundational debate here, but maybe that’s just because I’ve already been corrupted by the diseased discipline of philosophy ; )

Polytopos 8 Feb 2021 20:51 UTC
2 points
on: Against Modal Logics
You might be interested to look at David Corfield’s book Modal Homotopy Type Theory. In the chapter on modal logic, he shows how all the different variants of modal logic can be understood as monads/comands. This allows us to understand modality in terms of “thinking in a context”, where the context (possible worlds) can be given a rigorous meaning categorically and type theoretically (using slice categories).

Polytopos 12 Jan 2021 7:15 UTC
5 points
on: The Power to Teach Concepts Better
I really enjoyed this post. It was fun to read and really drove home the point about starting with examples. I also thought it was helpful that it didn’t just saying, “teach by example”. I feel that simplistic idea is all too common and often leads to bad teaching where example after example is given with no clear definitions or high level explanations. However, this article emphasized how one needs to build on the example to connect it with abstract ideas. This creates a bridge between what we already understand and what we are learning.

As I was thinking about this to write this review, I was trying to think of examples where it makes more sense to explain the abstract thing first and then give examples. I had great difficulty coming up with any examples where abstract first makes sense. The few possible examples I could think of came from pure math, and even there I wonder if it wouldn’t still help to start with examples.

The most abstract subject I’ve ever studied is category theory. Recently I was learning about adjoint functors, and here indeed the abstract definition make sense entirely independent of any examples. However, having learned the definition one can’t really do anything with adjoint functors until one has seen it in some examples. So this might be an example where the abstraction-example-abstraction order or explanation makes sense. On the other hand, once I learned about the free-forgetfull adjunction, I thought that would have been a good example to start with to build intuition before introducing the abstract definition. I realized that my favorite teachers of the subject still use a lot of examples. Like Bartosz Milewski, who comes at category theory from the perspective of a programmer.

Learning to program is also a good example where in advance one might think it would make sense to learn a bunch of abstractions first. However, in practice, one learns to code by example, then after having mastered some examples, learning the principles behind them.

Polytopos 12 Jan 2021 6:24 UTC
3 points
on: The Power to Teach Concepts Better
Excellent article, thank you. I particularly enjoyed your images and diagrams. To me concept diagrams are another superpower for explaining things. Have you written anything about that?

Polytopos 12 Jan 2021 6:16 UTC
1 point
in reply to: Ruby’s comment on: The Power to Teach Concepts Better
Personally, I thought “mind-hanger” was ok. I got an image of a coat-hanger for the mind. You could even include that image explicitly in your concept mapping pictures.

Some other ideas that stick with the coat-hanger variant would be “idea-hanger”, “concept-hanger”.

Another term you might consider is scaffolding. This also has a strong concrete image of construction scaffolding, but the metaphor lends itself to the idea of building on top of the skeletal example, just as we start a building project with a scaffold and then build the real building around it. Often the scaffold is removed at the end, which can also happen with abstraction, where we can throw away the pedegogic examples once we’ve mastered the bigger idea. We don’t really build anything on top of a coat hanger (nor a ship’s anchor).

Polytopos 11 Jan 2021 23:35 UTC
2 points
in reply to: Slider’s comment on: Fittingness: Rational success in concept formation

I think I can fruitfully engage in truth evaluation of grue things wihtout agreeing or supposing that grue is fitting.

As indicated in the post, fittingness is dependent on the domain D under study. If we take grue to be a term in the study of colour, it is profoundly ill-fitting. I think it is a fair assessment that no researcher who studies colour would find it fruitful or salient to evaluate the truth of propositions involving grue. The picture changes however if we let D be philosophy of science. In that case, grue is fitting, precisely because it illuminates an important paradox in our theories of induction. Here the truth evaluation of statements formulated using grue is fruitful, but that’s not a problem because grue is fitting.

A true counter example to my claim would require that a concept C is ill-fitting for a given domain D and yet it is fruitful (for the purpose of rational inquiry into D) to evaluate the truth of statements which are formulated with C.

Regarding the quantum mechanics example, I would need more details to fully understand your claim. My hunch is that the mathematical concepts used to formulate QM could be fitting for the domain of physics even if we don’t have a good meta-interpretation of them. If you think this isn’t the case, please elaborate on why not.

Polytopos 11 Jan 2021 23:09 UTC
3 points
in reply to: Gordon Seidoh Worley’s comment on: Fittingness: Rational success in concept formation
The term I introduced is “fittingness” not fitness. Fittingness is meant to evoke both fit, as in whether a pair of shoes fit my feet, and also fitting, as in “that is a fitting word choice for this sentence”. It is possible that there is another term which would be a better label for the underlying concept. If you have suggestions for alternatives I would love to hear them.

I think it’s important that the word is specific, not general. As you point out, we could use a general term qualified with a lengthy phrase like: “success with respect to concept formation in the context of rational inquiry,” but that clunker is difficult to sprinkle throughout an argument. The advantage of a single term to encapsulate an important idea should be obvious. Nobody suggests we should replace the term truth with the phrase, “success with respect to belief in the context of rational inquiry.” Moreover, the metaphorical associations of fit and fitting give a clue about what this kind of success actually involves. It involves concepts fitting the structures found in reality, without implying the unsustainable idea that we can know what the natural structures are in advance of inquiry. We can size a shoe without knowing our foot size in advance, just by trying on lots of different shoes until one fits.

I admit that the concept I call fittingness is not often used at present. Indeed I believe in present discourse fittingness is often muddled either with truth or instrumental usefulness. This precise muddle leads to difficulties in understanding how Kuhnian paradigm shifts (or pre-paradigmatic science) can be understood as legitimate expressions of rational inquiry. I didn’t do more than hint at such problems in the post, maybe I’ll write another post about this.

The point of my post is to diffuse these muddles and make it easier to appeal to fittingness on the regular. I want it to be a part of our ready-to-hand conceptual repertoire as rationalists, in the same way that we have easy access to terms like truth, probability, evidence, etc. I make a case for why this would be of benefit in the section titled, “Why is this Distinction Important?” If you don’t find that section convincing please let me know what you see as the specific shortcomings and I will try to address them.

Polytopos 11 Jan 2021 17:45 UTC
3 points
on: What currents of thought on LessWrong do you want to see distilled?
I am a fan of johnswentworth’s gears sequence. It would be fruitful to have this distilled.

It would be good to have some some polling of which gears are tight and slack in the present state of the world for various big projects of interest to LessWrong members. e.g., for AGI research, for ethics, for various sciences, for societal progress, etc.

Polytopos 11 Jan 2021 17:02 UTC
1 point
in reply to: Slider’s comment on: Fittingness: Rational success in concept formation
Thanks, you are correct. I have updated the post to reflect this.

Polytopos 11 Jan 2021 5:38 UTC
1 point
in reply to: Gordon Seidoh Worley’s comment on: Fittingness: Rational success in concept formation
Fittingness is not the same as telos/purpose/concern. It is a success concept for a specific telos/purpose/concern, namely that belonging to rational inquiry. In other words, it indicates that one has formed a concept or ontology which is successful for the purpose of rational inquiry. Of course, there might be other purposes governing concept formation which would have their own success concepts. For example, if one’s purpose is to craft deceptive propaganda then the relevant success concept might be slipperyness or something.

Fittingness: Rational success in concept formation

Polytopos10 Jan 2021 15:58 UTC

6 points

9 comments6 min readLW link

Polytopos 10 Jan 2021 3:49 UTC
1 point
on: What are the open problems in Human Rationality?
I think a big open question is how to think about rationality across paradigms or incompatible ontological schemas. In focusing only on belief evaluation, we miss there is generally tacit framework of background understanding which is required for the beliefs to be understood and evaluated.
What happens when people have vastly different background understandings? How does rationality operate in such contexts?

Polytopos

Fit­ting­ness: Ra­tional suc­cess in con­cept formation

Fittingness: Rational success in concept formation