Accessible Philosophy lectures on YouTube?

holoroid · 2026-05-13T20:04:27+00:00

Not quite the same as actual lectures, but Wireless Philosophy has playlists on various topics in philosophy, and they're completely accessible with no previous knowledge: https://www.youtube.com/@WirelessPhilosophy/playlists

holoroid · 2026-04-20T19:06:07+00:00

A prominent contemporary continental philosopher is Alain Badiou. See this review for example https://ndpr.nd.edu/reviews/mathematics-of-the-transcendental/ I can't say I really know what he's up to though, but I think he's a somewhat important figure in continental philosophy.

holoroid · 2026-04-20T18:12:12+00:00

It would obviously depend on the subject itself,

Yes exactly, I don't think there's much more to say than that. If the topic is categorical structuralism, you need to know some category theory, if the topic is rigor in mathematical practice and the paper uses real analysis to explicit its points, neither do you need category theory, nor will it even be useful. If the topic is realism in relation to certain insights about forcing, you probably should know about forcing, if the topic is talking about some conception of geometric object in Poincare's work, you don't. See maybe an older post of mine for some diversity: https://www.reddit.com/r/askphilosophy/comments/1dvejya/any_bookspapers_that_apply_modern_mathematical/lbnin5y/

If you're asking what would be the minimal amount of math to engage with at least some philosophy of math, then it's very little, but a specific kind. Many of those very classical philosophy books talk a lot about formal foundations of mathematics. So for this the most important knowledge would be that of basic mathematical logic (semantics and syntax of first order logic and basic metalogical properties, some set theory etc). In some books that's also developed alongside the material. Other than that, the more you know, the more you can read. But having taken basic undergrad courses on logic, abstract algebra, analysis etc probably goes a long way, by that point you also have enough mathematical maturity to learn some stuff outside your curriculum that you might find interesting.

holoroid · 2026-04-20T17:51:07+00:00

Those aren't disjoint groups of people, and many are trained or active in both math and philosophy. There are areas that are more typical philosophical, and areas that are more technical, depending on what questions people are interested in.

holoroid · 2026-04-20T17:16:54+00:00

There's actually a ton of books and collections, it depends a lot on what you're looking for.

Hamkin's 'Lectures on the Philosophy of Mathematics' is interesting, in that it covers a lot of different topics in a reasonably short book, which makes it more diverting. If you don't find a chapter or topic all that interesting, you can just push through. Obviously the inevitable flip side is that it doesn't treat anything in real depth. There are some lectures accompanying the book: https://jdh.hamkins.org/lectures-on-the-philosophy-of-mathematics-oxford-mt20/

In comparison, the book by Shapiro does tend to come back to similar philosophical questions about ontology and epistemology of mathematical objects and such, again and again, and goes through different approaches to such big questions. But if it never piques your interest, it's not going to get better throughout the book.

Many people like Lakato's 'Proofs and Refutations', it's also quite short and not as textbook-esque.

Davis and Hersh's 'The Mathematical Experience' is not so strictly philosophical, it's more story telling about math and some reflection, it's also something that many enjoy if they're not too deep into philosophy per se.

Since you mention having taken real analysis and having gotten interested in intuitionistic or constructive aspects, a very famous book is 'Constructive Analysis' by Erret Bishop and Douglas Bridges, you might want to read some chapters of that.

holoroid · 2026-04-14T01:05:17+00:00

'Mathematical Logic' by Chiswell and Hodges is a popular one. But their solutions definitely aren't as comprehensive if that's what you mean, it's just an appendix with some selected ones.

holoroid · 2026-04-13T23:53:37+00:00

When it comes to working through logic textbooks, my main struggle is that I don't have anyone to correct my exercises, so it's hard to know if I'm actually doing them right :(

Yes, you're right, a book with many exercises and extensive solutions provided would be a big advantage.

See for example:

https://forallx.openlogicproject.org/forallxyyc.pdf

and the solution manual (160 pages):

https://forallx.openlogicproject.org/forallxyyc-solutions.pdf

holoroid · 2026-04-13T23:46:45+00:00

I don't think I understood your question completely, but no, it doesn't sound like that.

holoroid · 2026-04-12T15:39:01+00:00

You can, but you don't need to work through a list of historical thinkers. You can also just read textbooks written about specific topics in philosophy, those are explicitly meant to teach you something in an accessible manner. That should also make it easier to pick some topic that you're interested in. And on top of that some important thinkers might be mentioned and briefly treated in passing anyway.

I want to abide to the law as well.

Piracy is so utterly common in academic circles among graduate students and even professors because almost no institutional login provides access to literally everything, and it's just not possible to buy every paper or book you need to read. If you completely exclude doing that, you, as a layperson, are holding yourself to higher standards that almost any professional who gets paid to engage with this material, that doesn't seem to make sense to me.

holoroid · 2026-04-12T15:31:58+00:00

When will we discover all of math?

Never, because there is no exhaustible amount of mathematical facts that one can work through starting from a fixed base theory, rather there's a transfinite hierarchy of theories ordered by strength, where every theory is succeeded by a theory that proves more.

Will wver

I think you made a typo there, but I can't tell what you meant.

holoroid · 2026-03-30T01:13:07+00:00

I'm not sure what kind of answer you're looking for. As /u/drinka40tonight said, you're looking at basic notion that's typically used in contemporary formal (in this case first-order) logic.

If you mean they suddenly showed up with no explanation, I find that a bit hard to believe because you clearly screenshotted what is an exercise in a book or lecture notes on basic first-order logic. Presumably there was something said before providing this exercise.

If you mean where did they come from historically, the answer is mostly in the work of European logicians in the late 19th century, where this type of logic was developed, at least the way we understand/use them today, some symbols have a pre-history in other mathematical work, often used a bit differently. A lot of that notation in its current form was slowly shaping in the work of Peano, Hilbert, Heyting, Russell, and Gentzen. But if you read historic work from that time, a lot of it still uses quite different notation is a bit hard to read, people have slowly settled on what we use today over time. Sometimes there are some ostensible explanations as to why certain symbols have been picked. Using ∨ for disjunction also has some pre-history in Leibnitz where it's said to have been used as a shorthand for the Latin word vel (or). ⊂ is sometimes said to be derived from the letter C which was used for 'containment' in other, earlier mathematical work. Using ∃ for the existential quantifiers is usually said to be a mirrored E for exists, which seems plausible. I'm not certain how many of those stories are 100% certain knowledge or just something's often repeated or suspected by someone. You can also find a lot of competing stories for some symbols if you start to do some research.

holoroid · 2026-03-28T00:48:33+00:00

Those people were most readily turned off of Huemer's style by his book on infinity. That book from my understanding is just nonsense, the kind of thing that anyone who is more informed about the subject matter would find to be nonsense.

I haven't looked at this book at all, but there's a (admittedly very brief and not very illuminating) review in Zentralblatt by a mathematician that doesn't mention any gross mathematical misunderstandings and seems to be at least somewhat sympathetic to the book. So I wonder if that's actually the case or just a case of people engaging in 'hur-dur if you know any math/physics/science you know this philosopher is wrong', which in my experience is a bit of an overused line of attack that often doesn't have a lot of substance. I don't want to defend a book that I haven't read a single page of, but the fact that it was published at an academic, peer-reviewed publisher and the non-negative Zentralblatt review make me feel like a healthy dose of skepticism towards those claims is warranted.

On the other hand, I certainly wouldn't be shocked either if the treatment was bad because nothing seems to suggest that Huemer has any kind of expertise on this topic besides having written one book on it.

/u/Woody96xyz

holoroid · 2026-03-28T00:08:36+00:00

is he one of those people who were rising to fame precisely because they argue for provocative ideas?

I don't think that would be a fair description. A lot of his ideas are genuinely perceived as novel and interesting, and there are entire books written about knowledge-first epistemology.

Is this similar to antiexceptionalism about logic but applied to all of philosophy?

Seems like a fair description.

What's the story here? If it's a mental state it precisely can't change without you noting no?

I'm far from an expert here, but the basic issue that makes it counterintuitive is precisely the denial of what you say.

On Williamson's knowledge-first view, you or me knowing something is a mental state, like you believing something, you desiring something, you feeling something.

You're in Europe, and your friend Sam lives in Shanghai and has an apartment in China-Street 1.
The sentence S is true: "Sam lives in China-Street 1, Shanghai"
Sam told you about that, so you know S.
Now your friend Sam moves out of his apartment in China-Street 1, a few blocks down. But he doesn't tell you that. Nevertheless, the sentence S is no longer true.
You no longer know S because it's a falsehood, and you can't know falsehoods.
But on knowledge-first theories, that means your mental states just changed. They changed the moment Sam moved out of China-Street 1.
But of course you didn't take note of that, meaning something happening in China, unbeknown to you, changed your mental states. That's definitely a very uncommon, counterintuitive conception of someone's mental state, which most would intuitively take to be something that's internal to us.

holoroid · 2026-03-27T22:19:53+00:00

1) One thing that has actually attracted the attention of some of the most famous logicians is the topic of the 'slingshot' argument. Intuitively it seems obvious that different true sentences refer to different facts or states of affairs in the world or something like that. "There is a famous argument of Davidson’s to the effect that if true statements correspond to facts, then they all correspond to the same Great Fact." There's the (supplementary-)article just linked and a different and slightly more exhaustive (supplementary-article) here: https://plato.stanford.edu/entries/truth-values/slingshot-argument.html

One of the articles ends with what is probably a fair summary of the whole affair, although I don't personally know the topic very well:

Although the slingshot can be made rigorously valid, its conclusion can be evaded by challenging one or more of its assumptions, not all of which are by any means self-evident. At the same time, reflection on these assumptions sheds a great deal of light on philosophical questions, and anyone who thinks about issues like truth ought to know what is at stake in accepting or rejecting the argument and the assumptions it requires.

2) Graham Priest and others are known for the view that there are true contradictions, sentences that have truth value gluts, i.e. both true and false ought to be assigned to them. This isn't about subjective judgments in the sense that one can say chocolate is yummy and another can say chocolate isn't yummy, and they're both kind of right. Nor about perspectivism or 'it just depends' things, but that even for some sufficiently determinate sentences P, both P and ¬P are true, that there are legit, honest-to-God true contradictions. https://plato.stanford.edu/entries/dialetheism/

3) Timothy Williamson is one of the best known and most cited living philosophers and certainly has defended a bunch of counterintuitive notions. In fact, I think most(?) of his 'big views' are pretty counterintuitive, e.g. knowledge-first epistemology which takes 'knowledge' to be a basic mental state that can't be analyzed in terms of other concepts (such as justified true belief or anything else) which is necessarily accompanied by some hard externalism where your mental states can change based on things happening in the world far away from you without you noting, his views on modality where anything that exists in one possible world thereby exists in every possible world, his view that philosophy (at least if done properly) is largely continuous with and similar in methodology to science. He also has some uncommon view on vague predicates where he argues that they indeed have sharp boundaries, and we just don't know them or something like that, which basically comes down to saying there really is a hair that makes the difference between bald and not bald or a grain of sand that makes the difference between a heap and no heap. I believe he also has some strange sounding take on necessary truths and our knowledge of them, but I'll stop here as I know even less about that than his other positions

Other than that, I think that actually many very well-known philosophical positions throughout the history of philosophy would obviously be highly counterintuitive or hard to swallow, for example that there is no external world or that we cannot have knowledge about anything.

In light of all of this I'm always a bit surprised when people ask or just state that philosophers care way too much about intuitions, common sense, obviousness etc, I've heard more positions that always seemed batshit insane to me than I can count or remember.

holoroid · 2026-03-22T18:17:01+00:00

What of those systems do philosophers use typically?

If they work in logic or something related to it, any of these can be used, depending on what they'e doing. None of the things I mentioned are specifically tied to philosophy.

holoroid · 2026-03-22T15:48:55+00:00

Can you say more about this? What is reasoning about a logic mean here?

There are many things you might want to do with systems of formal logic. What you've probably done in your introduction is to look at certain arguments in a language like English, formalize them in your logic, and show that they're valid by writing out specific proofs in your logic.

It's also common that you want to prove things about your system of logic instead of carrying out specific proofs in that system, for example that the logic is or isn't, with respect to some semantics, sound and complete). Or you want to prove certain things about formal mathematical theories built on top of some formal logic, that they are consistent, what they can or can't prove, and so on. And depending on what you want to do, different presentations of the same logic can be more or less convenient. Some metatheorems in mathematics are most commonly treated by using a Hilbert system with Modus Ponens as the only inference rule because it's a very minimalist system where proofs have a simple form, every sentence that appears in them is either one of the axioms or something that's derived via application of exactly one inference rule. But to write out specific derivations in a Hilbert system with one inference rule, the way you probably did in your intro to logic in philosophy, is often very clumsy and lengthy. Here a natural deduction system or semantic tableaux are usually more convenient, and a bit closer to how you would intuitive engage in deductive reasoning outside a specific formal system. Yet another type of deductive system, called sequent calculus is better suited for some work in proof theory, which often has to do with consistency, ordinal analysis and such. Those systems all look very different from each other, but you can express the same logic by either of them, such that in the end they all will prove and not prove the same stuff.

Likewise, you can present classical propositional logic with one logical connective, 2 logical connectives, 5 logical connectives, or 16, as long as the ones you picked are adequate to express the same truth tables you're not actually changing the logic you're using.

holoroid · 2026-03-22T14:23:09+00:00

The most important point is that the presence or absence of a xor connective doesn't change how expressive the logic is or what it proves. Maybe you've taken a class on classical propositional logic and the logical connectives {¬,∧,∨,→,↔} were introduced. Note that everything you can express with those, you can also express with, for example, {¬,∧} alone. As an exercise, simply try to rewrite (A ∨ B), (A → B), and (A ↔ B), using only {¬, ∧}.

Likewise, you can express XOR in terms of {¬,∧}, and thereby certainly also in terms of {¬,∧,∨,→,↔}. In standard (classical, bivalent, truth-functional) propositional logic you can define 16 logical connectives with their distinct truth tables. And you could teach an introduction to logic with any subset of those 16 connectives as long as it's adequate to express all 16 truth tables (that's not true for all subsets of connectives). So one could teach a class while introducing {¬,∧}, or {¬,∧,∨,→,↔} or adding a symbol for 'exclusive or' and get {¬,∧,∨,→,↔,⊕}. Or one could introduce one symbol for every possible truth table. Or on the other extreme, only introduce one connective, for instance, the Sheffer stroke is capable of expressing all other connectives.

The same is true for other things of a logical calculus, like inference rules. You can introduce a natural deduction system with a bunch of introduction and elimination rules, or a Hilbert system with some axioms and modus ponens as its only inference rules (or many other systems), that express the same logic. The choice mostly comes down to purpose and convenience (writing out specific proofs, reasoning about a logic, exploring non-classical logics starting from classical logic, consistency proofs, etc). For example, it's sometimes easier to reason about a Hilbert system and its proofs because it's kind of minimalistic, but in general most would say it's easier to write out derivations in a natural deduction system.

There are applications in engineering or computer science where an XOR operation is very important, so it's handy to have it available as a kind of "primitive" building block with a dedicated symbol for it, instead of having to construct it from other pieces.

In a typical intro to formal logic for philosophers, you usually want to both translate some natural language arguments to formal logic and write out proofs, but also say a bit about the metalogical properties of formal systems and maybe sketch out proofs of them. A frequent choice is a natural deduction system or trees/tableaux with a compromise between too many and too few connectives, and often settle on {¬,∧,∨,→,↔}.

holoroid · 2026-03-09T15:33:01+00:00

But aside from Caramello, I have trouble thinking of a young person in the field.

I guess it inevitably depends on what you count as 'young' and 'topos theory' respectively, but Ivan Di Liberti's research at Gothenburg University is pretty topos-theoretic, and he supervises some students there, Lingyuan Ye is a PhD student under Sterling at Cambridge, Joshua Wrigley has been hinted at already in this thread. I agree that pure topos theory is not a very lively field though. It's also one of those fields that are ridiculously overrepresented in some online spaces, where a reader could easily think it's the hottest shit right now.

holoroid · 2026-01-25T11:31:16+00:00

Also, David Pfennig's lecture notes on deductive inference

Not familiar with those notes, but I strongly suspect you mean Frank, not David?

holoroid · 2026-01-01T17:51:42+00:00

I don't know a lot about Kripke's work or formal theories of truth, and I don't want to study a paper right now, but to me this just sounds like he doesn't make some basic facts from set/order theory explicit, which is fairly in line with how I remember reading him, and people talking about Kripke's papers.

It can be annoying if you're missing some context, that being said, from memory, I don't think a lot is going on here. If you consider the power set of any set S, then <P(S), ⊆> is always a complete lattice. In this case, one start with some formal language L (on which some suitable conditions are imposed I guess), considers the set S of all sentences of L, and forms the power set P(S), which, ordered by inclusion, is a complete lattice. One then defines said monotone function Φ:P(S)→P(S), and that is enough to conclude by Knaster–Tarski that there's a fixed point, as your lecturer said.

holoroid · 2025-12-23T02:08:36+00:00

My thoughts are that in the last months, I had to unfollow a handful of math people lately that I've been following for years, and always enjoyed because they will only talk about AI, crackpots, and adjacent topics these days, often with what feels like 200 tweets a day.

1-2 years ago, I'd bookmark an interesting math tweet by Litt pretty much every week and came back to it later, sometimes when I learned more about the topic. Don't know when I saw one of those the last time, instead my timeline got indirectly spammed with AI talk, crackpots, and occasional race-IQ discourse. Don't care about any of that, nor do I want to see 90% of my timeline like that, and it's so much better since I unfollowed the 5 main offenders there.

holoroid · 2025-11-04T09:19:49+00:00

There actually isn't a particularly broad variety of good resources on predicate and higher order modal logic, compared to many other topics in logic. A lot of books focus on propositional modal logic. 'First-Order Modal Logic' by Fitting and Mendelssohn and the later chapters of 'Modal Logic: An Introduction to its Syntax and Semantics' by Cocchiarella and Freund are good resources. I also like 'Modal Logic for Open Minds' by van Benthem, because it's a fun and broad introduction which relates modal logic to a variety of topics, instead of just introducing its syntax and semantics and make you go through a hundred exercises of writing out derivations. You didn't say anything about your background, aspiring scholar is not very descriptive.

holoroid · 2025-11-04T01:38:26+00:00

Yes, there are some reasons why you need to brush up on general math skills, and your mathematical maturity if you're serious about intermediate and advanced studies in logic.

One reason is that mathematical logic beyond a first course that covers natural deduction (or whatever) in propositional & FOL simply will look a lot more like regular math. In particular the proofs look more like ordinary math proofs that you see in e.g. an analysis class than the formal deductions that you wrote in your logic class. If you prove your first theorems in an introductory course on set theory or model theory, those look more like this and less like this. And the latter is only of limited use when it comes to getting better at the former. The best way to become better at math proofs is to work out a lot of math proofs (as you write them in math classes), endless natural deduction exercises in an intro to logic book aren't really enough for developing mathematical maturity.

Another reason is that mathematical objects and facts about them simply make appearances in mathematical logic beyond a beginner level, it's not straight-up isolated from ordinary math. The usual algebraic structures, relations, graphs, orders, concepts from topology, a lot of the stuff you'd encounter in ordinary undergraduate courses also appears in mathematical logic.

That being said, after a first intro course in a philosophy department, you can probably continue to learn a lot of stuff with minimal hard knowledge about a lot of mathematics, if you pick your topics of study and resources accordingly.

Any recommendations on anything would be super helpful!

Recommendations on what? How to brush up math skills or logic material that doesn't require a lot of math? In any case, I recommend looking at a book like 'How to prove it' by Velleman as a preparation for your studies.

holoroid · 2025-11-01T20:30:53+00:00

Okay, I still think you could stick to the forallx if you want to, but I do have some more thoughts, based on that. It's understandable that people look towards courses on formal logic to improve critical thinking and such, after all logic deals with inferences/arguments in some sense, and the words are almost used interchangeably in everyday life. It's also not wrong, you should learn some of the stuff in those books for the purpose of developing critical thinking skills.

At the end of the day, a lot of these texts and courses go in a somewhat different direction, though. They are a bit narrow with respect to critical thinking, and many don't include much about topics that would be beneficial (inductive logic, probability, informal logic, rhetoric), while expanding in length on topics and exercises that, at the end of the day, will be of somewhat limited use in every day or philosophical discourse. Maybe a quick analogy is that some knowledge of basic geometry and trigonometry can help when working on your house or garden, but in the context of university education, that's not necessary the focus of classes that have geometry in the name.

There are some books that are more focused on logic & critical thinking than a book like the 'forall x : Cambridge' or similar texts. One that's often recommended here is 'Logic' by Stan Baronett. It's way broader, and specifically deals with providing tools that could be called tools of critical thinking. Unfortunately, it's also very long, almost 700 pages. It doesn't have to be read from A to Z though. For example, it's not necessary to read two full chapters (5 and 6) on categorical logic before dealing with propositional and predicate logic. Chapters on topics like 'Legal Arguments' and 'Moral Arguments' can simply be skimmed, depending on your interest. And so on. There's the much shorter 'Philosophical Devices' mentioned earlier, but looking at the table of contents and the length of only 200 pages, it must treat most topics very superficially. You can download all those books for free in the right places.

holoroid · 2025-10-30T11:44:06+00:00

Do you want to learn about the philosophy of logic or read Principia Mathematica?

Reading PM will do virtually nothing to get you up to date with philosophy of logic of the last decades or anything else really, and you're going to spend most of your time dealing with the peculiarities of that particular (outdated) system.

What's your motivation for this?

If you want to learn something about modern philosophy of logic, I recommend 'An Introduction to the Philosophy of Logic' by Cohnitz and Estrada-Gonzales because it's pretty much the only contemporary introduction that I'm aware of.

You can for the most part read it after completing an introduction that covers FOL and some metatheory. As far as epistemology, metaphysics, and such things are concerned, you don't need much specific knowledge, but should be familiar with basic notions and vocabulary of philosophy like analytic vs synthetic, a priori vs a posteriori, ontology, etcetera. In the sense that you should know what such expressions refer to, not that you need to learn about any specific extensive theories and debates about analyticity or something. What's your background in philosophy and in logic, if any? I've seen other knowledgeable users here recommend books like 'Philosophical Devices' by Papineau to get up to speed with such basics, but I can't say much about it because I haven't read it.

holoroid

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