I never read anything philosophy related but want to get into

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>thought Wittgenstein would be a good starting point for someone with a mathematical background.

Read at least Aristotle's Categories.

Read Frege first. In particular
- The Concept of Function.
- Sense and Reference

I reccommend reading an introductory work to his whole work. See Anthonny Kenny Intro to Frege. Some familiarity with Kant's philosophy of mathematics is handy.

Then Russell. The paper On Denoting. Also some introductory book to his work, so you don't have to tackle down the Principia Mathematica by youself. Maybe Russell by Grayling, it is good if I am not mixing authors in my head.

Read Moore. Principia Ethica. Not strictly needed.

Read an introductory book to the TLP. How to read Wittgenstein by Ray Monk is a good choice. Wittgenstein by A.C Grayling is decent as well, and it covers both TLP and PI.

Watch some lectures AFTER you have read the former books and papers. Not strictly needed, but it can be useful to hear a professional sum up the main points after studying, in order to no lost sight of the forest for the trees.These are good
https://www.youtube.com/watch?v=S1RPRp5bDgg
https://www.youtube.com/watch?v=TNaBRR-XeAs
https://www.youtube.com/watch?v=EQHiGrCNwJI

Read the TLP by youself.
Good luck.

>>8589285
this is actually all sensible, this is no memepost. Though you can get all the Frege you need from secondary lit, but I probably will be stoned for saying that.

If you follow what anon says, you'll get a very strong basis for reading Wittgenstein (I recommend going at it chronologically if your basis will be that strongly in Frege), although you probably will quit before you get to Wittgenstein proper.

So, that's a great post, but not a great philosopher to start with.

>>8589285
Thanks for the post. I supected it to be not as easy to understand Wittgenstein as I wanted to.


I have two more general questions.

Is it essential to understanding to read the original works of philosphers rather than reading secondary literature? Is it likely that secondary literature corruptes the original?

Is there a place where I can find full lectures to philosophic concepts/authors? Im not the autodidactic kind of person to be honest.

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>>8589359
>Is it essential to understanding to read the original works of philosphers rather than reading secondary literature? Is it likely that secondary literature corruptes the original?
This can be a controversial question, some people will say no on the basis that the secondary source is clarifying and explaining what the original book said, some people will say yes on the basis that the secondary source may be putting to much of his thought in his reading. An recent example of the latter is the book Wittgenstein on Rules and Private Language by Saul Kripke, which presents a Wittgenstein that some people have come to name Kripkenstein because of how much of Kripke's own ideas are in his reading of Philosophical Investigations. It is a great book nonetheless, regardless of who say what and when.

My answer is that it is not essential, and it is preferable to have read secondary sources before the original work. The thing is they need to be sourceS, so you can spot points people can disagree on, instead of learning that a particular reading is correct in all that says. Secondary literature by no means corrupt the original.
In any case, the basics about any work are the same and there is a consensus about those points. It is not probable that you will find any secondary literature published by a reputable house that offer something that deviate from the norm in the main points of the work. The little differences that may appear are regarding very specific arguments in the work, about which there is no need to worry unless you have plans to publish a paper.

>>8589359
>Is there a place where I can find full lectures to philosophic concepts/authors?
Not that I'm aware of. Most of what can be found is spread over the net.
A few youtube channels that may work for you:

Daniel Bonevac
https://www.youtube.com/user/PhiloofAlexandria/videos

Gregory Sadler
https://www.youtube.com/user/gbisadler/videos

Massimo Pigliucci
https://www.youtube.com/user/MassimoPigliucci/videos

Hoyningen-Huene
(most lectures are in german, but he also has a very nice lectures in english)
https://www.youtube.com/channel/UC4yBDbab-abnWC6yrysAL3w

Wes Cecil
https://www.youtube.com/channel/UC9ff15w4ufviWfv9UfIuByA/videos

Philosophical Overdose
https://www.youtube.com/user/soultorment27/videos

Philosophy Bites, a podcast
http://philosophybites.com/2016/03/365-bites-podcast-interviews-arranged-by-theme.html

Coursera
https://www.coursera.org/browse/arts-and-humanities?languages=en#philosophy

>>8589215
I have a soild knowledge of maths, especially in statistic and logic. To me it is quiet clear what he tries to show, but it is certainly a factor, that i'm german native speaker.

>>8589359
>Is there a place where I can find full lectures to philosophic concepts/authors? Im not the autodidactic kind of person to be honest.
Not lectures but make use of the stanford encyclopedia of philosophy, it's well maintained and a great resource.
>>8589477
>An recent example of the latter is the book Wittgenstein on Rules and Private Language by Saul Kripke, which presents a Wittgenstein that some people have come to name Kripkenstein because of how much of Kripke's own ideas are in his reading of Philosophical Investigations. It is a great book nonetheless, regardless of who say what and when.
Hehe yeah that's a fun read, I wrote a short essay about it way back. As you point out it's probably a good lesson in how a reading from any particular point of view should be approached and appreciated.

>>8589215

Wittgenstein's regular use of the word "function" is almost always in reference to truth functions, which do satisfy the modern mathematical notion of what a function is, the arguments are instead merely logical, or propositions, truth values, etc, depending on exactly what you're doing at the moment ---- as opposed to numbers.

If Witty says "function", simply assume he's referring to truth functions unless context suggests otherwise.

Wittgenstein spends a big chunk of the Tractatus working out truth tables, truth functions and so on for basic two-valued (true-false) logic, which if you really have a mathematical background you should already be familiar with. Other logicians of the day were doing pretty much the same thing at the exact same time; Witty is credited with inventing truth tables but other logicians developed the idea around the same (earlier) time. The issue is to translate for yourself Witty's "old" version of these same truths into notation that you are familiar with.

A great logic review to read in parallel with the Tractatus is this current wiki:

https://en.wikipedia.org/wiki/Truth_function

Especially compare with 5.101. (just blow up the comments)

http://www.tractatuslogico-philosophicus.com/#node/n5-1

Witty simply recognizes that when you have, for discussion, exactly two propositional variables in a two-valued logic, you have 2^2 = 4 possibilities, depending on the actual truth values that the two variables may assume, for the compound proposition entailing both atomic propositions itself to assume. And since each thing is two-valued, EITHER true OR false, you have 2^4 = 16 distinct possibilities for truth function which must be accounted for. Then, depending on what those truth values actually are for a given compound proposition, you can map some equivalent truth-function (itself a compound proposition, usually an elementary version) to that thing. And sure enough, Witty starts mapping familiar logical connective jargon straight-away to all 16 possibilities: "if p then q", "neither p nor q", tautology, contradictions, etc. Notice how this maps directly to the layout of the above wiki.

1/2

2/2

The Tractatus is so short and the accompanying literature about it would tend to hew to Witty's notation, that there isn't really much to be gained by "updating" Witty's old notation except for your personal notes for your own understanding; if you can't get comfy simply using a slightly different notation to convey the same ideas rather quickly, then perhaps your math background needs work (this type of shifting gets way easier if you do math regularly). It seems like your trouble is simply "decoding" that Witty is really talking about two-valued logic for much of the more technical parts of the book. This is part of why the above wiki is so great for this: several different symbols have been used for the truth-functions over the past century (and it gets even more diverse with the introduction of computer languages which must necessarily use certain strings of symbols to convey the exact same ideas) and the wiki just summarizes them all, which allows you to much more rapidly make sense of Witty's notation. In particular, the backwards-C - thing is his "implies", and IIRC the dot-thing is "and" and the little v is "or", but check this.

There are these goofy connection diagrams toward the back as well; one can rapidly make sense of them by recognizing that they (poorly) illustrate truth functions like "if p then q" and similar. Witty explains them in the text.

Some pseud who didn't know what he was talking about tried to tell me that certain basic math does not appear in the text and is not essential to understanding the text (it is); in particular that "sigma notation is not used" in the tractatus, and I shut him down, kek. He never did reply back.

But it doesn't really matter because at the end of the book Witty goes all mystical and says whoops we don't need to do all of that anymore. Further, Witty did not intend the book to be "explanatory" as-such, he instead simply had his ideas and wrote the book for someone who has already articulated much the same ideas in the future and who might then derive some gratification from reading his little book in the future.

Irrelevant to reading Wittgenstein (though Wittgenstein likes him), with your background you might find Charles Sanders Peirce a good read - very strong philosophical tradition in his writing (and what he talks about) and a top logician/scientist/mathematician of his day. Interesting from the perspective of history of logic and mathematics as well.

>>8590491
>(just blow up the comments)
It really is so easy to read in this format compared to the book.

>>8591591

I like the above website. Its translation is distinct from my book and I really should read it sometime, rather than just citing it. The text really is meant to be read/experienced as a web page on the one hand, but on the other hand Witty ordered the things in the way that he did for his own personal editorial reasons, and so it should be read "linearly" as well.

The major fault with the above website is that it does not entail in-line reproductions of the figures, or graphical content of the book. It would be very easy for them to fix this, and then they would have a "complete" site. But anyway these are easy to find.

It's so good that it even correctly annotates what are some faults in Wittgenstein's comment-nesting convention, which in my view takes the book down a peg. I wonder if this can be attributed to Wittgenstein's purported/possible dyslexia (I heard this once but I never substantiated it). In particular, just play around with all the comment numbers in 2.xxx, and get a copy of the book and look up Witty's opening footnote, which explains the nesting structure of the comments. Although (now that I re-read again, pic related is a great illustration of this) the middle bits of the book do have early comments of the form "2.00etc", "3.0etc", they yet generally lack a comment of the form 2.0, 3.0, etc, and despite their internal consistency on this point (I had forgotten this), they yet lack a consistency with the few comments which comprise 1.etc. This bears a re-read on my part, but there does seem to be consistency issue about the comment structure, though I had misremembered part of it - I was about to be more critical of how 2.0 etc is where it goes all fucky, but it turns out that 1.etc is the real exception; I had misremembered this. But even so, not including comments of the form 2.0, 3.0 as-such is yet inconsistent with Witty's opening footnote.

Anyway obviously 1.etc and 7 are by far the shortest segments of the book, while 2.xxx-6.xxx are the meat, so internal consistency is practically most important for these middle five segments.

Getting back to OP's original difficulty though, he raises a good issue and now I'm wondering about it again.

I hope this thread stays alive for another day (having a very limited internet connection).

>>8589285
>>8589477
Thank you so much, Guys. This Threat is Gold.

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Oh, I forgot to mention one book. Frege's Logical Investigations.

It was written after the papers I mentioned above. You can think of it as a follow-up of Frege's philosophical and logical thought, and in some sense, Frege's attempt to think about "tractarian" problems on his own.

The books contains three essays: Thought, Negation and Compound Thoughts. The interesting thing about it is that the first two essays were written while Wittgenstein was at war, the third essay was written after the publication of the TLP. It is widely considered that the TLP undermines Frege's crucial arguments in the LI, although Wittgenstein had no chance to read the essays before writing the TLP.

>>8589285
Is it not necessary to go through a formal logic textbook before the TLP?

Writing in this thread has piqued my interest again in the Tractatus. I may endeavor to explain each statement which contains a diagram, figure, or other complex series of formulas which go beyond the simplest statements of basic logical forms, and do not use "natural language", but instead formulae or pictures of some kind. There are about 12-20 of these throughout the book depending on how you choose to count.

One thing that needs to be said with direct reference to OP's difficulty is that in Russell's paradox, the elements of the paradoxical set /are themselves sets/, so that the purported set and the objects that are supposed to be contained in the set are the same type (in the simple, literal sense of the latter word, leaving aside any of Russell's more technical senses of same word) of thing. The thrust of 3.333 then is that Wittgenstein considers related math-logic objects (functions, or truth functions per the above) and indicates that they cannot "nest" in this same way, for certain reasons. What I take Wittgenstein to mean when he says that "Russell's paradox vanishes", then, is that it vanishes /in his analogous treatment of his analogous objects/, and possibly by extension back to Russell's distinct situation. It (this historical project of building modern logic, of which Witty is one participant) just a way of feeling out "no you can't do that", because if I'm reading everyone properly, Witty and others recognize that the paradox, which I shall call RP, is a real thing that needs to be dealt with, and not something superfluous. Therefore Witty is in this case(!) not dismissing Russell's idea, but instead suggesting a way of getting round RP by setting things up in a certain way is a "good" thing in that it causes the paradox to vanish. It's just a "dude you can't do that that's not how it works.", in response to Russell's correct identification of the paradox.

Another technical way of getting round RP is found in one of the axioms of Zermelo-Fraenkel set theory or "ZFC", a commonly accepted theoretical foundation of modern mathematics , which I will not endeavor to explain in further detail beyond linking it. It's quite clear from the language, however, that what we have in this other case a similar technical specification right at the top of "no you can't do that, don't do that." In order to banish RP. In crude terms, they (everyone I've mentioned ITT) basically recognizes that RP is a real problem that must be dealt with and in one way or another they say "no don't do that" in their foundational premises, to get rid of it.

https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory#3._Axiom_schema_of_specification_.28also_called_the_axiom_schema_of_separation_or_of_restricted_comprehension.29

>>8595142

I cannot overstate how helpful reading and understanding the wiki in >>8590491 is to reading TLP. It's a crash-course in two-valued logic which is directly pertinent to the text, and also gets the reader used to the idea that different symbols have been used historically to connote certain logical operations, which you need to understand to get TLP. What you should look to do is to build yourself up a list of examples of these functions and convince yourself of why they are the way they are.

For the math stuff, I would also recommend self-teaching a bit about sigma notation, combinations and powers of two. I intend to say a bit more about this ITT per the above.

For now, I want to link a good pdf of the book which includes the diagrams that I have referred to above. I intend to explicate these a bit futher.

Navigate to https://www.gutenberg.org/files/5740/5740-pdf.pdf for the full text of TLP (English in front, German in the back. I will only concern myself with the English). In this pdf, the statements involving figures or complex formulas can be summarized as follows, where the statement is followed by the pdf's page number (as opposed to the in-document page number):

https://www.gutenberg.org/files/5740/5740-pdf.pdf

4.27 52
4.31 53
4.42 53
4.442 54
5.101 58
5.5423 73-74
5.6331 77
[6, 6.01, 6.02] 77-78
6.1203 80-81
[6.241] 85
6.36111 88

The setup of Witty's formula used in 6 isn't a complex formula as-such, but he sets it up throughout the document and so it deserves a separate discussion.

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>>8595142
I think it may be useful, but is not needed. When the TLP was written, formal logic was something relatively new. It had been around a few years, but received no much attention until Russell read Frege and gave it a kick.

Any formal logic textbook that you can read nowadays will go far beyond the formal logic needed to read the TLP. Paradoxically, it will also fall short, since there are concepts that are NOT present in any standard textbook on formal logic but were introduced in Fregean logic, some of them criticized by Wittgenstein in the TLP. That's why I recommend reading Frege or an introductory text to Frege. If someone is able to read On Denoting, an obscure text on its own, then should be able to read the logic in the TLP; needless to say, understanding how it works and fits into the system is different story, but the lack of understanding will hardly come from lack of knowledge in formal logic.

>>8595274
>>8595272
you're the bomb, my man

Let us first of all consider 4.2:

4.2 "The sense of a proposition is its agreement and disagreement with the possibilities of the existence and non-existence of the atomic facts."

What this basically says (once you get the context which I will fill in here according to my take on things) is that a proposition is potentially composed of "atomic facts", which may either be true or false in a two-valued logic, giving rise to /general two-valued possibilities/. Perhaps a given atomic fact in the overall arrangement is either true or false, as the case may be. There is the specific example of some one given (compound) proposition composed by certain atomic facts (or propositions), but this is distinct from the two-valued logical space which requires us to consider ALL (two-valued) possibilities, which is what Witty is driving at. Just roll with this for a moment, because 4.27 is of course a comment on 4.2:

4.27 "With regard to the existence of n atomic facts there are K_n = [SUM] possibilities. It is possible for all combinations of atomic facts to exist, and the others not to exist."

This is effectively his way of saying "let's consider all the possibilieis when n atomic facts are variously either true or false."

Now, the sum is important (yet a bit opaque to the average person) because Wittgenstein directly considers powers of two in this two-valued logic that he discusses. The essential observation is this: /that complex sum stands for powers of two., it means precisely two raised to the power of n/. And how is this?

Pascal's Triangle is the simplest illustration. The form at right of the sigma in vertical parentheses is read "n choose nu", and stands for /mathematical/ combinations. It is interesting that this English mathematical word coincides with the English translation of the word, though I suspect that this is somewhat accidental/not important.

Every nth row (starting with 0) of Pascal's triangle ranges from (n,0) through (n,n). It is /these/ entries that the sum adds up. And as you can clearly see by checking yourself (do this), they always add up to successive powers of two. This is what 4.27 really means. To add another atomic fact into an arrangement is to immediately double the logical possibilities, exactly because that one atomic fact may itself either independently be true or false.

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>>8595364
>What this basically says (once you get the context which I will fill in here according to my take on things) is that a proposition is potentially composed of "atomic facts", which may either be true or false in a two-valued logic, giving rise to /general two-valued possibilities/.
What are "atomic facts" ?
There are no atomic facts in a proposition, but these are represented by names.(which are unanalysable terms). And it is not potentially composed of names, IT IS composed of names. Names are taken as the elementary terms, the language-equivalent of atomics facts in the world.

>which may either be true or false in a two-valued logic, giving rise to /general two-valued possibilities
Truth must be understood in the sense a sentence mirrors or not a state of affairs. In which case we say the sentence is true or false. This is not to be understood in the classical logic sense, because in this latter sense propositions are either true, false or contingent, but in the TLP every sentence is contingent, because sentences mirror a state of affair and states of affair in the world are not necessarily true nor necessarily false. This is, a "true" sentence can still be false and a "false" sentence can be true, provided we find that there is a mistake in our judgment of the state of affairs.

>This is effectively his way of saying "let's consider all the possibilieis when n atomic facts are variously either true or false."
Atomics facts cannot be true or false. The TLP only speaks about truth in relation to the relation world-language.

Just commenting to say this is good stuff.

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>>8595491

2.01 "An atomic fact is a combination of objects (entities, things)."

From this context (and, I take this statement to mean that) Wittgenstein's atomic fact can be a variously a logical/mathematical object, a representation of physical reality, and all of the above. It is worth mentioning that at http://www.tractatuslogico-philosophicus.com/#expanded , the phrase "atomic fact" is instead translated somewhat consistently instead as "state of affairs", which loses the /singular/ sense of "atomic fact".

This part gets pedantic/academic, but simply put I am not at all convinced of your assertion that "there are no atomic facts in a proposition". I did scroll through Witty for something to try to use to BTFO out of you but admittedly the closest I got was

4.21 "The simplest proposition, the elementary proposition, asserts the existence of an atomic fact."

Which could be argued in a vague :^)-tier way in my direction but I'm not going to bother about it because it's not a direct thing that interests me at the moment, and frankly it's a bit beneath our intelligent discussion and your intelligent pushback. There's also a long pedantic discussion to be had here about what it means for an atomic fact to be "in" a proposition, but I leave that aside for similar reasons and also because I'm going out in a bit.

It seems to me that your differentiation between formal logic and, say, physical reality is appropriate, although of course Witty uses both in the course of a narrative. But in your second paragraph your contingencies seem to me to reinforce the two-valued logic which is indisputably an element of what Witty is driving at (the math part), even if we have disagreements over the philosophy part. Indeed your second paragraph seems to me to conclude by affirming the basic idea of two-valued logic, that we must in principle have to consider that any one proposition (whether itself atomic, compound, a truth-function or whatever name we prefer to describe an entity which may in principle be judged EITHER true OR false for discussion in certain circumstances) may in vacuous principle be considered as either true or false. This is what I take you to have tacitly conceded by putting "true" and "false" even if the concrete fact, proposition etc is obvious to us a la the sky is blue, 2+2=4, etc. (provided we agree about these in a common-sensical way).

I admit that I may be confusing atomic facts with certain other primitives somewhat vis-a-vis the math bit but I'm about sketching the math part out, which indisputably entails that some entities may be judged in principle to be either true or false, irrespective of their actual circumstances. and thus instead of using "The Chinese Flag is mostly red" (an atomic fact?), we might use "p" instead.

pic related is the pascal's triangle I mentioned above and failed to post. everyone should note that the horizontal rows sum to powers of 2; this is what Witty meant in 4.27 and 4.42.

I finally thought I had figured out Wittgenstein a bit and then I met some 30 year Wittgensteinian guru professor and he told me it's all bullshit. I asked whether I'd need good logic abilities, need to read Frege and Russell, and he said forget all that shit, forget the positivists.

>spend 20 years avoiding Wittgenstein because I think he's some final boss of philosophy
>decide to read up on him this week on a whim
>he was a literal meme retard
>Tractatus was B+ at best, same shit done by a dozen other guys in the 20th century except they actually worked out their ideas instead of just being a trendy celebrity with them
>Investigations is exact same thing, just read Heidegger ten other guys instead
>only a trendy celebrity because horrendous parody-of-themselves-tier analytics like Moore, Russell, Carnap greased the wheels for him to be famous
>would have been nobody if (also a shit hack totally derivative of Frege fuckup moron) Russell hadn't launched him to fame while at the peak of his own fame
>these famous analytics didn't even understand him, even HE thought they didn't understand him
>unpleasant as fuck, just a weird dude who acquired celebrity status
>beat kids constantly, kept beating kids all the time
>may have killed a kid
>every coverage of his """""""""ideas"""""""" is 90% composed of WASN'T HE QUIRKY???
>SO QUIRKY!!!!
>also faggot Cult of Logic & Latter Day Common Sense anglos sucking his dick every time he entered a room
>which was usually followed by him gesticulating and grumbling to no effect, and then they'd scribble down "His ideas come to us as if by revelation. He is a divine god and I want to suck his cock."
>literally a meme
>literally a retard
>just the analytic Slavoj Zizek of a bygone generation

Alright, no more joking around. Analytic philosophy people are fucking morons. Carnap, Moore, Russell, I kept forgiving and forgiving and forgiving you people for worshiping actual autistic children like these fucks, thinking Wittgenstein was going to be some top secret German spice like Frege 2 Electric Boogaloo. And it's just more shit. You are actually all morons.

This isn't banter. If you are an analytic philosopher, or a fan of any analytic philosopher, YOU are a MORON.

>>8595835
jeez dude did an analytic philosopher take your lunch money and kiss your crush?

>>8595806
Isn't it best to just analogise atomic facts as essentially axioms?

This is what I got from The Tractatus is that its a reference to Greek Atomist's terminology ie something fundamental that can't be divided further to use physical metaphors.

>>8596050
*missing commas.

>>8595835
If you don't like Tractatus fine, but Philosophical Investigations is genuinely decent philosophy and an enjoyable read. Especially, for me at least, the whole seeing-as discussion (duck/rabbit).

Also his takedown of Solipsism is fascinating which is developed in his other writings outside of PI.

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>>8595806
>2.01 "An atomic fact is a combination of objects (entities, things)."
I know the TLP definition. I was just puzzled because you used " ", saying "atomic facts" instead of simply atomic facts. My bad, sometimes the use of quotations marks can be confusing.

>>8595806
>but simply put I am not at all convinced of your assertion that "there are no atomic facts in a proposition"
Because atomic facts belong to the world. A proposition is a lingustic construction, and its structure mirrors the tractarian ontolgy. Using the first fragment you quote, it states clearly that an atomic fact is a combination of OBJECTS, objects are IN the world, not IN the proposition. They are instead, mirrored by elements of the proposition. You can speak of atomic (or elementary) propositions, but not of atomics facts in the proposition.

I was wrong regarding what I said in my lost post. I said that these are represented by names but I should have said elementary propositions instead of names.

Horwich presents the basic structure clear enough:
>(a) that there is a stock of basic entities (objects), the ultimate constituents both of our world and of all merely possible worlds
>(b) certain combinations of these entities actually exist, forming atomic facts
>(c) that all the other facts that make up the real world are constructed, with the help of logic, on the basis of the atomic ones.

>By combining the picture theory of meaning with his metaphysical doctrines Wittgenstein can deduce what character any language will need to have if it is to be capable of representing reality. It must contain
>(a*) unanalysable terms (names) that refer to the basic objects,
>(b*) elementary propositions, each consisting of some of these terms combined in a certain way (i.e. embedded within a certain logical structure), and true if and only if the referents of those terms are actually combined in exactly that way
>(c*) various other propositions, but only in so far as their truth values are logically determined by those of the elementary propositions.
(Horwhich, Wittgenstein's Metaphilosophy p.76)

>we must in principle have to consider that any one proposition (whether itself atomic, compound, a truth-function or whatever name we prefer to describe an entity which may in principle be judged EITHER true OR false for discussion in certain circumstances) may in vacuous principle be considered as either true or false.
I agree with this, as I did before when I said "In which case we say the sentence is true or false". I don't think there is a problem when, "in vacuous principle", we talk about a proposition being true or false, have in mind that these sentences hold their truth value in virtue of the (apparent) mirroring relation with the world.
The two-valued logic certainly is something Wittgestein holds, and of that we can be sure because of the Brouwer dispute.

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>>8596598
cont'd

It is not part only of the TLP, but also of the PI. The "inner contingency" of which I talked earlier, in the sense that a sentence must be either true or false because of its mirroring relation (which does not need to hold through time, thus the "contigency"), is giving later by the relation of sentences to language games.

>(...) while Wittgenstein qualified his earlier insistence that every proposition must be bipolar, he continued to cleave to the requirement of bivalency. (He had, as far as I know, nothing to say concerning truth-value gaps, about which debate erupted in the 1950s apros Strawson's criticisms of Russell's Theory of Descriptions.) He explicitly denied that Brouwer had discovered propositions of arithmetic that lack a truth-value. Rather, he said, Brouwer had discovered structured that looked like propositions but were not.
(Baker, Hacker. Wittgenstein: Understanding and Meaning: Vol. 1, p. 354)

This is something I personally find it hard to agree with. It looks like Wittgenstein would extend his claims to any kind of mathematical proposition, but 12 years after Wittgenstein's death, the continuum hypothesis was shown to be neither true or false in the ZFC. In this point, arguing that the continuum hypothesis merely looks like a proposition but in fact it isn't one, seems to me very hard to hold.

>"The Chinese Flag is mostly red" (an atomic fact?),
In fact, there is no obvious example of what an atomic fact is. Wittgenstein gave no examples of atomic facts, and the lack of these was something that was one of the reasons the second Wittgenstein rejected large parts of the TLP.

>Russell and I both expected to find the first elements, or 'individuals', and thus the possible atomic propositions, by logical analysis... And we were both at fault for giving no examples of atomic propositions or individuals. We both in different ways pushed the question of examples aside. We should not have said "We can't give them because analysis has not gone far enough, but we'll get there in time"
(Ray Monk, The Duty of Genius, p. 329)

I really like his ontological reevaluation of perpetuating inelastic language forms of semiotic and lexical duplicity in terms of anarithmia. Reminds me of Kant's demarcation of hermeneutic interpretation, and the subjective dichotomy of metaphysical and structuralist deontology.
Well worth reading all of his works if you're a serious philosophy fan.

>>8596606
this is how bullshit looks like

Thanks for the great help, guys. 3.333 is still not clear to me, though.
1) F(u) and Fu are not the same thing it seems. F(u) represents the function itself (like for example negation) whereas Fu is a sentence, right?
2) The formula translates to

There is a phi such that F( phi u ) and phi u equals F u .

The point of this is to show that the expression contains no self-reference, is that right? Why doesn't this work with Russell's system?
3) How do I get from the above formula to Russell's paradox?

>>8597876
>3) How do I get from the above formula to Russell's paradox?
I meant from F(F(u)) to Russell's paradox

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>>8597876
(1) F(u) and Fu are the same thing. In predicate logic it is common to write Fx, Qy, etc instead of F(x) or Q(y). Parenthesis are added hen clarification is needed. Take F(Fu) for F(F(u))

(2) Exists ϕ such that F( ϕ (u) ) ∧ ( ϕ(u) = F(u) ), or you can separate it into two sentences:Exists ϕ such that F( ϕ (u) ) ∧ ϕ(u), exists ϕ such that F( ϕ (u) ) ∧ F(u).

You can't construct F(F(u)) in the theory of types

If u is a (n-1)-order function, ϕ has order n, and F has order n+1, then F(u) has no sense, because for F to take u as an argument it needs to be of ONE higher order.

https://en.wikipedia.org/wiki/Axiom_of_reducibility

(3) I'm afraid I'm unable to help you. I don't think I fully understand it, and even if I did, it would be hard to clarify it only with ascii characters.
See pic related, is a fragment of the paper by Urmas Sutrop, Wittgenstein and Russel. Paradox.

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>>8597880
>>8598151

this thread is shit

can we go back to dfw?

>>8598151
That paper seems to be exactly what I was looking for. I don't understand it yet; I need to learn the basics first. But I have some free time and with the help of the links in this thread I will work on it.

>Exists ϕ such that F( ϕ (u) ) ∧ ϕ(u), exists ϕ such that F( ϕ (u) ) ∧ F(u).
So the "." means logical product here, looks like I read the it incorrectly.
One last question.
Would it be wrong to say "there exists" instead of "exists" at the start of that sentence?

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>>8598416
As long as it is clear what you're trying to convey, I wouldn't say it is wrong, I would understand it, so I wouldn't be picky with that. That said, I have never heard nor read "there exists" for such cases, and "there" said like that sounds like it's pointing to some place, like saying "there exists ϕ , there, inside the honeycomb."
"There is" is much more common.

>>8598688
>"There is"
Oh yeah, that's what I meant. I wasn't sure because "exists ϕ" sounded like an implication (like "if a exists than b") in my head.