Talk:Tractatus Logico-Philosophicus (5.101)

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[edit] "All philosophical problems are solved"

5.101 is a demonstration of the mapping between natural words like AND, OR, NOT, IF-THEN and binary number patterns.

To me, it does not follow that all philosophical problems are solved. The ForAll and ThereExist symbols, and the problems of object-oriented programming with Class definitions, for me, are still unsolved with the 5.101 notation.

Wittgenstein was probably quite aware of this, having studied under Russell and Frege, who invented said logical apparatus. (That said, the distinction between propositional and predicate logic was not fully worked out until a good decade later). But the view expressed in the Tractatus of things like variables and names suggests that this may not have been a problem: W. arguably viewed universaly generalizations as unanalyzed propositions which, fully analyzed, would turn out to be about--to name--each specific individual object. Quantified logic could in this way be reduced to something like propositional logic (An extensional one: not, for example, counterfactually or modally robust, nor even able to accommodate unknown information.) It was, of course, problems with "hooking" up such a view of language to the actual world that (among other things) led W. to reconsider these views.
In any case, your remark is confused: You say that not all philosophical problems are solved, and as evidence you present (1) Two symbols which you call unsolved. What does that mean? Do you perhaps mean that there were residual philosophical problems only formulable using those symbols? No doubt there are, but you don't present any. (2) The problems of object-oriented programming etc. But since programming didn't exist in 1922, how could any programming problems have existed then? This doesn't vitiate W's claim to have solved all philosophical problems, and even if programming problems are a kind of philosophical problem (which is rather dubious), it wouldn't vitiate a claim to have solved all philosophical problems that then existed.
Re: it does not follow that all philosphical problems are solved: Wittgenstein realized this in his later life and wrote the Philosophical Investigations... although it doesn't address the formal logic problems, but rather philosophical problems with his methodology. --Wikiwikifast 02:26, 18 Apr 2004 (UTC)

[edit] Note

Um, I'm a little confused by the "note" at the top of the page. While some of the implications may not be for the "layman", most of the article is perfectly readable. It certainly doesn't take "years" to understand a truth table... they're not that complicated. func(talk) 02:50, 13 Nov 2004 (UTC)

I have to agree here. First, the "note" is not necessary. Also, the discussion as to how boolean expressions are represented in C is also not necessary.--Antiframe 17:57, 12 May 2005 (UTC)
I will comment out the Note. Ancheta Wis 09:29, 13 May 2005 (UTC)

[edit] Wittgenstein was trained as an engineer

This man was trained as an engineer. His family was one of the most wealthy and cultivated in Austria. He had the intellect to anything he wanted. The world beat a path to his door because of his work. He attained fame even when he was working as a gardener in Austria. Please respect the background of a man who started the Computer Revolution, decades before his time. Ancheta Wis 17:32, 12 May 2005 (UTC)

I haven't read "Tractatus" myself, though I know someone who has (and I was baffled at the few passages of "Philosophical Investigations" that I did try to read). I mean no disrespect of Wittgenstein, but I've never heard of "Tractatus" influencing any electrical engineering practice and as far as I can tell has had no trace of influence on the so-called "Computer Revolution". For example, the article on Claude Shannon only mentions Boolean algebra, (which came along much earlier than "Tractatus" as the article itself mentions). The biographical information in the article on Wittgenstein shows only a couple of years in mechanical engineering and no sign that he ever practiced - most of his post-graduate education seems to be under Bertrand Russell.
No! He was NOT educated by Russell. He had the ideas before he came to England. Tractatus was written in German 1914-1916 and then translated to English 1921-1922 by people who understood the importance of what he was doing. But he indeed tried to fit in and then eventually rejected Russell's concepts. This is very important because Russell's concepts were implemented as the Theory of Types which have become computer language concepts (Classes, Object-orientation, etc), after 60 years. But Wittgenstein's ideas (post-Tractatus) have yet to be formulated in computer language. Someone will do this, after they take the time to understand what he has done.
I have been bold and deleted the category and link to electrical engineering. Someone more qualified than I should decide if computer science needs to be unlinked from here as well. --Wtshymanski 17:45, 12 May 2005 (UTC)

You find him quoted in many places. E.g.

Thus, complete analysis of the possible values of true and false requires us to consider a only finite number of cases. Truth tables were first formulated by the philosopher Ludwig Wittgenstein.

http://www.cs.uwyo.edu/~jlc/courses/5880/book.pdf

Pjacobi 18:19, 2005 May 12 (UTC)

I note that this is a computer science paper. I'm not sure that it is the case that Wittgenstein first formulated truth tables. Since truth tables are universally used to illustrate Boolean algebra, I've been lead to believe that George Boole originated the truth table notation. I note from an [English copy of "Tractatus"] that Wittgenstein doesn't call 5.101 a "truth table" and that it does not resemble the usual form of truth table; it is a list of word-translations of a compact form of logical notation, for all possible logical relationships between two propositions (boolean variables). In fact the more I look at the figure the less I understand it...how to get 16 cases out of only two boolean variables? becasue 2 bits gives 4 rows, which can be populated with exactly 16 distinct combinations of 1's and 0's Surely the technique of perfect induction pre-dates both Boole and Wittgenstein? Can anyone explain the table figure in 5.101 to me? Could Wittgenstein have read and been influenced by Boole's much earlier work? Are there any other electrical engineers in the house? This is fun, I'm learning something and not just fixing spelling mistakes. --Wtshymanski 19:48, 12 May 2005 (UTC)
Maybe I should read the article first. --Wtshymanski 20:36, 12 May 2005 (UTC)
2^4 is 16 possible truth functions. Wittgenstein formulated this concept. The obscurity of his notation in Tractatus is clear evidence he invented the concept, as he was blazing new ground. And he was perfectly clear that it solved some problems and created new ones, just like the computer revolution. Both he and Emil Leon Post were doing this before Turing. Post just had the bad luck not to publish for 10 years, but he was sick. Every college kid goes around muttering "the world is all that is the case", and its not an obscure statement. Obviously Wittgenstein read Boole etc. and Frege also. But he wrote this in the trenches in WWI. Ancheta Wis 21:53, 12 May 2005 (UTC)
Shannon's paper "A Symbolic Analysis of Relay and Switching Circuits" does not list "Tractatus" in the bibliography, but Shannon does mention George Boole. The IEEE "Encyclopedia of Computer Science Third Edition" has articles on both Boole and Boolean algebra, but does not have an article on Wittgenstein. Can anyone show me a link between "TLP" and electrical engineering? I'd like to remove the category as I think the connection is remote at best. --Wtshymanski 02:17, 18 May 2005 (UTC)
It's worse than that. I can;t see any justification for this article existing as a distinct item. It is flawed throughout. See below. Banno 08:08, May 18, 2005 (UTC)

I do not disagree that 5.101 belongs in the main article. Ancheta Wis 15:50, 18 May 2005 (UTC)

Wtshymanski, are G. Spencer-Brown's Laws of Form cited in IEEE "Encyclopedia of Computer Science Third Edition"? I am curious. I know for a fact that several electrical engineers were influenced by this book. Ancheta Wis 20:32, 18 May 2005 (UTC)

[edit] Truth Tables

See the discussion of their origin at Truth table. Wittgenstein was brilliant, but he did not create truth tables, nor is there any evidence that he forsaw an engineering use for them. His role was to show how the can be placed in a series and to relate them to axiomatisation; the popularity of his work perhaps led to their wider use. The attempt made here to blame Wittgenstein for the computer revolution is misguided.Banno

The article makes no claim that 5.101 caused the computer revolution. If you want to blame someone, blame Maxwell, Boole, Shannon, Shockley, von Neumann, etc.
See Karnaugh map (1950), Bell Labs. Freshman Electrical Engineers are taught to layout their logic circuits using them. They are identical in concept to 5.101 (1921), which had the non-standard notation (but it was first, and therefore excusable). Don't you think it obvious that W., trained as an engineer, would have tried to lay out the functions systematically? Boole, Peirce, etc were on the ground floor, but did not try to see if there were only 16. Note the Truth table article only lists 5. Not the exhaustive list of Boolean Functions of two binary-valued variables. I am not claiming utter priority for W. but his insights were seminal. Note too that he is only a part of the story, including Alonzo Church, Emil Post etc. I think I am becoming persuaded that we need an article on the History of Computer Science and Electronic Engineering. Then his place could be noted, along with the rest of the Pantheon. Ancheta Wis 23:21, 12 May 2005 (UTC)
If you follow Karnaugh Map, you see it came from Quine, which came from Carnap which came from Wittgenstein. Ancheta Wis 23:31, 12 May 2005 (UTC)
Ancheta, with all due respect, none of this demonstrates that 5.101 was written with the intent ascribed to Witgenstein in this article. Banno 10:50, May 14, 2005 (UTC)
Did you look at Karnaugh map? Ancheta Wis 10:55, 14 May 2005 (UTC) -- Perhaps I need to point out that a Karnaugh map is a device for minimizing the cost of implementing a Boolean expression. It is useful when a CPU is too expensive. That sounds ludicrous today when you can buy one for several dollars but there was a time not long ago when long division was worth a Master's degree. But if you look at Karnaugh's layout, he clearly uses the idea that you could map the possibilities for binary-valued functions in a systematic way. That is 5.101. But Quine has a better way. And Quine got his training from Carnap, among others. And W. quit talking to the Vienna Circle when he detected that Carnap was "stealing" his ideas. Ancheta Wis 11:08, 14 May 2005 (UTC) I guess I also need to point out that Bell Labs was enjoined from building computers by virtue of the monopoly agreement that AT&T enjoyed with the US government. Ancheta Wis 11:58, 14 May 2005 (UTC)
A few points: Firstly, Wittgenstein did not originate truth tables in this form - they were fairly common by the time of the Tractatus. Secondly, Wittgenstein says explicitly in the introduction that little of his work is original. Thirdly, it is plain from your account that the connection with engineering was made by Karnaugh, not Wittgenstein as the article alleges. Forth, the link between Karnaugh, Quine, Carnap and Wittgenstein is tenuous, since we don't know exactly what ideas were being "stolen" - and W. and Carnap share more than one idea. Finally, no independent source has been cited that supports the case made int he article unequivocally. Banno 21:13, May 15, 2005 (UTC)
I do not disagree that Wittgenstein did not originate truth tables. He uses the term truth-function ala Proposition 6 etc. And it is quite clear that Frege was his intellectual progenitor, and that Russell undercut Frege's program via his Theory of Types. I have found a historical description for the use of the term truth-function in Alonzo Church's Introduction to Logic, but have not dug into the pages (I only have the version of his book where there are some chapters missing). The article makes no claim about W's priority for truth tables. Church is important here because his lambda notation takes the next step beyond Wittgenstein, which was used in the programming languages like Lisp, ML, etc Ancheta Wis 10:04, 16 May 2005 (UTC)
Upon reading lambda calculus#Recursion, I see that W's 3.333 can be used to define recursive functions when working under the restrictions of lambda notation! (But there are additional concepts needed, per the lambda notation article) We need W's Tractatus text in the Wiki-series somewhere. Ancheta Wis 10:18, 16 May 2005 (UTC)
I think the main TLP article should use the term truth function rather than truth table. That would get rid of some of the tension about claims, etc. It is quite clear that his truth function notation was part of the basis for some mainline developments as shown above. The truth tables are important as a basis for discourse, and for engineering and computing. But W's picture theory of language, and the graphical notations of Frege, Peirce etc are more akin to the truth-function, the lambda notation, etc. Ancheta Wis 10:36, 16 May 2005 (UTC)

[edit] First para

This increases the confusion. Let's try to determine what it is that is claimed on Wittgenstein's behalf in the article, and then we might be able to see if it is supported. The first sentence reads:

In Ludwig Wittgenstein's Tractatus Logico-Philosophicus (1921), Proposition 5.101 is a pioneering insight from the point of view of a computer or electrical engineer.
The literature clearly shows influence on both computer science and on engineering. See draft. Ancheta Wis 00:33, 21 May 2005 (UTC)

This is the ambit claim; that Wittgenstein made a contribution to engineering. Well and good; all that is needed is to show what that contribution was, and to show that it was indeed Wittgenstein that made it. The next reads:

Wittgenstein simply demonstrated that some ordinary English words (or originally German words), "and, or and not", have exact mathematical counterparts.

Now it is surly not the case that Wittgenstein was the first to show that words such as and, or and nothave mathematical counterparts. Rather, this was done fifty years earlier by George Boole. Furthermore, the phrase "mathematical counterparts" is misleading, since Wittgenstein maps sentences against their truth value, not against 1's and 0's.

Mappings are what functions are about. One finds a mapping from Domain to Co-Domain, and evaluates expressions to find the Range of valuation. Truth functions map the set of {Propositions} (also called the Domain of discourse) to the set {True , False} (These are Truth values), which W. explicitly maps to the set {Not(0), 0}. In retrospect, these are valuable statements to be added to the article, for the nonmathematical reader. Ancheta Wis 14:05, 20 May 2005 (UTC)
The counterparts are shown in the truth function table below. A truth function simply means a mapping (or function) between values (true or false) and propositions (or the meanings of sentences).

Further on in the article the point is made much clearer :

...Wittgenstein demonstrated that bit-patterns, such as "TFTT" can correspond directly to word concepts, such as "If C then A".

Is this mapping original? It appears to me to be no more than a consequence of Boole's algebra. A similar approach is used in Principia mathematica and from my reading I suppose it was fairly common at the time; What is possibly original is the way in which Wittgenstein tabulated this mapping - however, that claim is not demonstrated by reference to any source or citation, and even if it is, so what? Banno 21:36, May 17, 2005 (UTC)

I trust that my interpolated statements are showing that W. had a grasp of the situation and understood the issues well enough to make a valuable contribution to the state of logic at the time. He still is providing value to the Engineers who are working out his ideas, per the citations in the draft, given below. His statements about Ethics and Aesthetics have yet to come to realization, but there is time. Ancheta Wis
"The obvious is that which is not seen until someone states it clearly" -- Christian Morgenstern
The stages of an idea:
  1. Non acceptance
  2. Grudging note of the claims
  3. Statement that the claim is obvious
  4. Claim of priority and retrospective assignment of credit
It is quite unfortunate that these ideas are taking the classic sequence, like the history of the circulation of blood. We are currently at #3 in the course of this thread.

Let us be clear that Boole made no splash in his lifetime. It took De Morgan (duals), Jevons (who built a computing machine), Peirce (who envisioned logic gates, and a rational graphical language), Frege (who had the vision of logic as the basis of it all -- W's progam), Sheffer (who established the NAND gate), Russell & Whitehead (who bravely set out to prove the vision of proof from postulates, and burned out with the effort -- "We could only look on logic with nausea"), Wittgenstein (truth functions etc.), Bothe (the AND gate), Shannon (telephone switching circuits as Boolean logic gates), Gödel (first-order logic only for fulfilling the vision), Church (lambda notation and the Church boolean), etc. etc. to build the topic. That is what it takes to build the science. Boole distinctly did not build up the topic on his own. Boole's contribution is far more linguistic and expository, as befits the pioneer. Ancheta Wis 00:52, 18 May 2005 (UTC)

English has the fortune to have a logical double negative. The English OR is not quite the Mathematical OR (i.e. binary +). The English AND is exactly the Mathematical AND (i.e., binary times). Some dialects of English, do not show these characteristics, to this day. But English is not entirely logical; for example the English question "Aren't you going outside?" is logically answered "Yes. (I am not going outside.)", but current usage is "No. (I am not going outside.)"

W's contribution was incremental and undeniable. The fact that it seems obvious from our perspective is proof of its success. But at the time, it was nontrivial. His demonstration that there are exactly 16 truth functions (read predicate or logic gate or expression depending on your POV) of two boolean variables is 5.101. It is the completion of the mapping begun by Boole. It is instructive to look at the original ordering of the integers in W's original 5.101 table; he started with what he felt he could rely on - Truth. Then he adds truth functions, line by line, til he wound up with Falsity (contradiction). The numbering of the truth functions was not sorted in a logical order. He added them as he figured it out. The truth-functions (logic gates, from an engineer's POV, or predicates from a philosophical POV, or expressions from a computing POV) lead naturally to the lambda notation for open sentences. See also G. Spencer-Brown's Laws of Form which notation can be viewed as a form of NAND but which starts from a blank page (Falsity).

Russell and Whitehead worked on the integers, like the original implementation of computers -- all decimal-based machines; they didn't get to binary for years. Principia could only get to 2+2=4 ("though the proof is long" -- Russell). I should mention that Herbert Simon used his Logic Theory Machine to recapitulate and go beyond Russell. Russell himself was gratified that there was a better way. But that was after computers came into their own, 3 decades after 5.101.

In our own time, we are seeing the same sorts of efforts being expended on the qubit, etc. Ancheta Wis 15:36, 18 May 2005 (UTC)

Indeed, W. showed that there are 16 possible binary functions. That is not worthy of its own article. Despite your discursive argument, I still think this article does not make a sufficient case for special treatment of 5.101. Banno 21:15, May 18, 2005 (UTC)

My comments at http://en.wikipedia.org/wiki/Talk:Tractatus_Logico-Philosophicus on 5.101 still stand. As well, if the authors cannot provide citations that show the import of 5.101 to engineering, then this must stand as original research, which is inappropriate. Banno 21:21, May 18, 2005 (UTC)

See below. But in answer to the cited comments, 5.101 stands a Rosetta stone with the bit-patterns of the truth table rows set side by side with English propositions. The C-language is merely translation of the English, no more than that. The Electrical engineering logic symbols are the same thing. This is "the equivalence of Hardware and Software" or the "equivalence of Random Logic (the propositions) and Memory". These are EE theorems. Not part of the article, just stated gratis in the talk. Ancheta Wis 21:52, 20 May 2005 (UTC)

As I said above,the article must show what Wittgenstein's contribution was and show that it was indeed Wittgenstein that made it; if it is to stay an individual article, we must add that it must show the significance of that contribution.

It's a mathematical statement. 2 binary variables is 4 possible states. The truth functions have 2 states. 2^4 is 16. That has got to be what convinced W. The perfection of the list. It wasn't 13 or 17 or some other prime number. Ancheta Wis 21:52, 20 May 2005 (UTC)
W. made a contribution to Gödel number, as well, which was the machinery behind Gödel's Undecidability theorem. He did talk to the Vienna Circle and thus indirectly to Gödel

You say the contribution was to show that there are 16 possible binary functions. Well and good. Now show that this is an original idea. But read the preface to the Tractatus again first. All you need do is cite a reliable opinion that supports your contention.

As for its significance, another reference from a published history should suffice; not too difficult, I hope. Banno 09:52, May 19, 2005 (UTC)

This is a clear statement of the goal which is sufficiently restricted in scope for me; I seek to provide it. Ancheta Wis 10:28, 19 May 2005 (UTC)
Here is a /draft of the page with citations. Comments invited. Ancheta Wis 09:57, 20 May 2005 (UTC)

Reply moved to end of discussion. Banno

[edit] AND gate 1924, ...Truth Functions

To demonstrate that Wittgenstein's concepts were part of the Zeitgeist, note that Post's machine and Bothe's coincidence circuit (1924)- Nobel Prize 1955 for the AND gate were all formulated during this time. Post's machine is a superior method for determining some computability issue, compared to the Turing machine. Computer Science was not even an academic subject then. It was all mathematics at that time. To segment a paper based on the Academic Tribe (as we see it today) is specious. It's all the same subject. There is an Electrical Engineering theorem on the equivalence of Random Logic and Memory - I assume you have heard it. Well, all this logic came from somewhere and Post, Wittgenstein, Boole, Russell, Shannon, Peirce formulated all this before it got into the textbooks of today. I am restoring the Electrical Engineering category. You have to realize that Bothe's circuit was revolutionary because it handled pulses. That was distinctly not part of the electrical engineering of the time. Bothe was a Physicist. Are you going to remove the Category of Electrical Engineering from the AND gate because a Physicist invented it before it became part of Electrical Engineering? Ancheta Wis 22:15, 12 May 2005 (UTC)

At one point a Wikipedia article claimed that Tesla patented the AND gate, but the patents that were cited didn't seem to claim the idea of "AND" implemented electrically as an original claim. I'm sure the idea of a mechanism doing one function AND another predates Tesla (and Boole) by a long time. I believe Wittgenstein's ideas and notations were not an influence on the field of electrical engineering, because I think the George Boole ->Claude Shannon connection is much better documented and I think is the origins of the fusion of formal study of logic with the design of electrical (and later electronic) switching systems. --Wtshymanski 17:33, 13 May 2005 (UTC)
The pulse circuits of the coincidence circuit (the Geiger counter 1908 and improved 1928, etc.) were very esoteric electrical engineering which didn't become mainstream until RADAR circuits were built in WWII. This was all after Wittgenstein. Ancheta Wis 18:41, 13 May 2005 (UTC)
Wtshymanski, I see that you are interested in IC's. I have Horowitz and Hill too, and also Mead and Conway etc. If you have time, you may have noticed that the CMOS process is the only one that I documented in the IC article. You may wish to augment and review the IC article to include other semiconductor processes. Ancheta Wis 22:26, 12 May 2005 (UTC)
Duly noted - I will add it to my ever-lengthening to-do list, though my knowledge of semiconductor fabrication processes is rudimentary. --Wtshymanski 17:33, 13 May 2005 (UTC)
Wtshymanski, if you have time, I am also interested in your read of ground (electrical).
I'll have a look at it in my copious spare time - skimming over it just now I think it's a little long and perhaps not clear to the non-electrical-specialist but it will take some thought to see if it can be improved. --Wtshymanski 17:33, 13 May 2005 (UTC)

I quote from the article: Wittgenstein simply demonstrated that some ordinary English words (or originally German words), "and, or and not", have exact mathematical counterparts.

The 16 values 0 to 15 could be part of a CPU's microcode, with 1011, for example, the microcode for IF A THEN B, where A and B are the values of 2 registers in a CPU. If we take a stream of nybbles (a 4-bit stream of tokens laid directly into computer memory using the above architecture, there is then an exact correspondence between the 16 values and 16 logical functions, such as AND, OR, NOT. etc. These are all obvious concepts to an Electrical Engineer. I count Computer Engineering as a specialized subset of Electrical Engineering, which itself is a technological application of Physics, etc. etc. I do not count Computer Engineering as part of Computer Science, which is properly an application of Mathematics. Ancheta Wis 22:54, 12 May 2005 (UTC)

Note that the PDP-11, for example, mechanized these logical functions as part of its architecture. I am sure that lots of other computer companies (which employ a LOT of electrical engineers) have microcode to do this, they probably just don't use Wittgenstein's mapping to the logical functions.

[edit] One of the simplest propositions of Tractatus!

When we step back and look at 5.101, it's dog-simple to an Engineer of today. Yet look at all this commentary. Can you imagine what grief the propositions which are a little more vague than this one are causing? It has to be true, that they are simply being ignored. But can you imagine the treasures that lie in them? Ancheta Wis 23:41, 12 May 2005 (UTC)

Didn't Wittgenstein later renounce the "Tractatus"? Anyway, I'll try not to lose sleep tonight over the idea that there's hidden treasures in "Tractatus" yet to be implemented. --Wtshymanski 17:33, 13 May 2005 (UTC)

Ancheta Wis 10:35, 14 May 2005 (UTC):Just choosing 3.33 ... 3.334 as an example:

  • 3.33 "In logical syntax the meaning of a sign ought never to play a rôle; it must admit of being established without mention being thereby made of the meaning of a sign; it ought to presuppose only the description of the expressions.
  • 3.331 "From this observation we get a further view -- into Russell's Theory of Types. Russell's error is shown by the fact that in drawing up his symbolic rules he has to speak about the things his signs mean.
  • 3.332 "No proposition can say anything about itself, because the propositional sign cannot be contained in itself (that is the "whole theory of types").
  • 3.333 "A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself.
    • "If, for example, we suppose that the function F(fx) could be its own argument, then there would be a proposition "F(F(fx))", and in this the outer functions F and the inner function F must have different meanings; for the inner has the form ψ (fx), the outer the form ψ ( φ (fx)). Common to both functions is only the letter "F", which by itself signifies nothing.
    • "This is at once clear, if instead of "F(F(u))" we write "( there exists a φ ) such that F( φ u) and φ u=Fu".
    • "Herewith Russell's paradox vanishes.

In modern terms, "F" is an unresolved symbol, which a compiler marks in its symbol table, but any expression involving "F" is simply jammed onto a stack until F is resolved to a defined function. Once F is known, the compiler can resolve it, and eventually the CPU can evaluate the expression. But if the elements of any expression which involve F remain unresolved by the end of the production, the compiler has to emit an error message for the programmer.

I chose 3.33 as an example because it mentions Russell's Theory of Types, which is the basis for the Type definitions which are in use by many programming languages. -- in this case, it looks like there is technology to deal with the issues. You just need a programmer or a computer operator to watch over an expression until it can be fully resolved, and then evaluated by a CPU.

[edit] NAND gates

The main article points out that Proposition 6, in modern language is that all logical forms can be built from NANDs. That is something that all electrical engineers learn in school today. But that is like the fact that each bipolar transistor has 2 diodes in it, so the same form of statement could be said about diodes being a basic element (but at another layer of engineering design).

The editor points out that the Sheffer stroke (1913) is probably where W. got his idea.

I suppose that is the basis of the statement of the "equivalence of random logic and memory arrays", and the whole reason for the existence of the FPGA as an electronic product. Ancheta Wis 09:53, 14 May 2005 (UTC)

[edit] Truth functions and W's picture theory of language

5.101 is not about W's picture theory of language. I quote from the abstraction#Thought process article which is germane to truth-functions. W actually seems to conflate The World with Propositions. Peirce's existential graphs and Sowa's conceptual graphs (see graph below) have a family resemblance to W's picture theory. It is clear that they are about the same thing -- how we cognize the world.

Cat on Mat (picture 1)
Cat on Mat (picture 1)

"... Abstraction uses a strategy of simplification of detail, wherein formerly concrete details are left ambiguous, vague, or undefined; thus speaking of things in the abstract demands that the listener have an intuitive or common experience with the speaker, if the speaker expects to be understood (as in picture 1, to the right).

"For example, lots of different things have the property of redness: lots of things are red.

Conceptual graph for A Cat sitting on the Mat (graph 1)
Conceptual graph for A Cat sitting on the Mat (graph 1)

"And we find the relation sitting-on everywhere: many things sit on other things. The property of redness and the relation sitting-on are therefore abstract (as represented by the notation of graph 1, to the right). Specifically, the conceptual diagram graph 1 identifies only 3 boxes, 2 ellipses, and 4 arrows (and their 9 labels), whereas the picture 1 shows much more pictorial detail, with the scores of implied relationships as implicit in the picture rather than with the 9 explicit details in the graph. ...

[edit] Relevance to electrical engineering

The exhausting discussion above does not convince me that 5.101 has any relevance to electrical engineering and I requrest that it be removed from the electrical engineering category. If Wittgenstein had any influence on EE, it's impossibly tenous to trace - I can assure you that *this* practicing EE never heard of Wittgenstein as a contributor to computer science till reading this article. I can also assure you that being an EE does not necessarily give you any advantage in understanding "Tractatus", which I personallly found difficult to fathom.--Wtshymanski 00:53, 21 May 2005 (UTC)

See /draft for references with respect to Electrical Engineering. Especially the IEEE Transactions. Sorry you have to be a member to see the titles, but there is also a sales list which I can link to. I know for a fact that the referenced series has existed for decades. IEEE has existed a long time. I don't think I am the only person who knows about these materials. Ancheta Wis 01:04, 21 May 2005 (UTC)
I looked at a coule of the on-line references in/draft...I'm now using a dial-up connection, so it's slow work. The Kurzweil book is a dead loss, it's the only one I've had the patience to check out and doesn't seem to be about electrical engineering at all, just some AI stuff.
The reference was to Intelligent Machines. That is not just about CS. That is also EE. I would hope you see that in the purview of EE. If you disagree, then we need a discusssion about the boundaries of the EE category. If you do not think Intelligent Machines belong to EE then perhaps you can help me out in naming the proper category, which I do not happen to think is CS. Ancheta Wis 02:18, 21 May 2005 (UTC)
If Shannon had cited "Tractatus" in his paper, I would have considered that entirely sufficient to demonstrate the validity of leaving this article in "electrical engineering". I'm an IEEE member, but I'm not going to plow through the entire IEEE catalog looking for trace references to Wittgenstein. I think its misleading of Wikipedia to include TLP 5.101 as an item in the electrical engineering category. --Wtshymanski 01:40, 21 May 2005 (UTC)
Kurzweil is an innovator in Optical Character Recognition. That is clearly an Electrical Engineering field to me. If you disagree, then please identify what field he is in from your POV. I call his field EE and so does IEEE. Ancheta Wis 02:03, 21 May 2005 (UTC)
Hint: try Google. Enter IEEE Tractatus logic gate. That should considerably trim your search results. I get 90 hits.
Google Wittgenstein IEEE Man Systems Cybernetics. There ought to be a lot of results to demonstrate my point. I get 474 hits.
Ancheta Wis
Kurzweil's tone is decidedly philoosphical in the on-line book - and not like the way Shannon references Boole in his paper. Sorry, I'm not going to check out 474 Google hits on a dial-up connenction. Can you point to one in particular that justifies keeping {{Category:Electrical Engineering}} on this article? And shouldn't this article be merged with the main article on "Tractatus", anyway? (This is getting as frustrating as the Tesla issues on Wikpedia.) --Wtshymanski 02:32, 21 May 2005 (UTC)
I do not disagree that 5.101 should be part of the main TLP article. But if it is judged only a minor part of the main article, then the statement about 5.101 being a special case of a Gödel code should be kept, as that impacts the history of mathematics and philosophy. However W's theory of language (Proposition 2 etc) needs to be discussed. If there is no further discussion in Truth table or Truth function, then those are deficiencies in those articles which 5.101's content could be used to improve. I am inclined to believe that some of us would be happier with a general discussion of TLP, which would tend to gloss over some details just as sticky as 5.101.

[edit] Cybernetics cat

view of Tuolumne Meadows
view of Tuolumne Meadows

After this discussion with Banno and Wtshymanski, I propose to move the draft to the article page, but change one of the categories from EE to category:Cybernetics. I will wait one day before the move, if there are no objectors. Sorry if this has been a difficult climb for the participants. But we appear to be at a saddle point in the mountain range; we can see higher peaks ahead, and all around us; but in the valleys below, we can see where we have been before. Banno and Wtshymanski, I have learned something. Thank you. Ancheta Wis 10:46, 21 May 2005 (UTC) (Note this view from Lembert Dome can be approached from a steep side or an easy side. I once walked up the easy side with some 60 year-olds and a two-year old, who surprised some triumphant climbers.)

If there are further objections we can address them, of course.

No objection here, I think the article will serve our hypothetical bright 12-year-old reader better in the "Cybernetics" category than in the "Electrical Engineering" category. --Wtshymanski 14:16, 21 May 2005 (UTC)

[edit] Draft

Ancheta, Why have you done this? Just edit them into the main doc. We can discuss them there. Why don't you use the Wiki conventions for referencing? Author first in the citation; and a citation should point to the entry in the article that discusses the Author (Wittgenstein, in this case) not to the bibliography of the article - what you have done means that the reader interested in checking your claims is forced to trace the comment from the citation. Clumsy, difficult and unhelpful. I am not an engineer, and so I will leave checking some of the references to others; but some things are clear. The link to Sowa leads to a bibliography that references anyone who touched logic in the last hundred years; it certainly does not support the claim thatWittgenstein simply demonstrated that some ordinary English words (or originally German words), "and, or and not", have exact mathematical counterpart as you claim - not surprising, since this is not an original claim made by Wittgenstein. Zach clearly and correctly states that W. did not develop truth tables. And the reference appears to be to a lunchtime seminar! The Schmid reference is to a footnote that W. "Deconstructed the purely true". What does that mean, and how does it help your case? None of these few I've looked at do what was required. I don't think you have supported your case. Banno 22:11, May 21, 2005 (UTC)

We speak across a gulf, due to our differing backgrounds. What is obvious to you is not to me and vice versa. I seek to build the case. In my readings, I have found support for the case, but in so doing, have realized that my work on the scientific method has a built-in POV which exemplifies the ontology of logical positivism (Vienna Circle, etc.) Historically, W. appeared on the scene with a framework built up from Frege and Russell (in his answer to R's Theory of Types), which the Vienna Circle simply subsumed, as W watched. I believe I can build up the case starting from Proposition 5, if I assume that it is the proper grounding. I am starting from a historical reconstruction of W's background in Janik and Toulmin (1973, 1996) ISBN 1-56663-132-7. This source also shows the point at which W turns away from TLP. However TLP is seminal for Engineering as the hits on IEEE above show, and Kurzweil is my source for the logical positivism link which all computer programming, electrical engineering, and business is following. (They are all implementing agents of one ilk or another). Since, by definition, an agent shares the ontology of its Principal, I need to include these factors in the case. Thus 5.101 is merely a small part (although crucial from an implementation POV) of the case. I hope that I do not have to go back further than 5. Kurzweil and the other engineers seem to be starting at 2. One of the reasons that TLP is good at what it does is that it is short. That brevity is what gives me hope that I can start at 5 and stop somewhere past 5.101 but not too much farther. Ancheta Wis 15:55, 22 May 2005 (UTC)

I don't think that our backgrounds are so dissimilar that we cannot communicate. But you have not in the above answered my critique of your post. Also, you should perhaps note the warnings against original research on the Wiki - http://en.wikipedia.org/wiki/Wikipedia:No_original_research Banno 08:04, May 23, 2005 (UTC)

I have taken your critique. The statement to which the first disputed template refers is replaced by statements about truth-functions which are directly taken from 5.101 with no other claim. The second disputed template is answered by the internal evidence of the words in 5.101 (the existence of and or not etc. in each row of Tractatus 5.101 in direct one-to-one correspondence to a row in 5.101). Ancheta Wis 14:18, 24 May 2005 (UTC)

[edit] Disputed

Thank you Ancheta. I appreciate that you have worked hard on this article. I have incorporated some of the material from here into the main article. But I have marked a few problems. In essence:

  1. I don't think that there is a strong case that the contents of 5.101 are original in the Tractatus. The material, as with most of the Tractatus, is a summary of the work of others, as W. says in the preface. There is original material in the Tractatus, but this ain't it.
  2. The article can be read as claiming originality on the part of W. that is simply not the case - for instance that prior to the Tractatus, Boolean operators were not seen as mathematical (as in "truth-functions... correspond to expressions using only some ordinary English words ...and, or and not" - this is Boole's work, not W.'s.).
  3. The references you provide do not support your case, neither for the originality of 5.101, nor for the impact of 5.101 on computing.

I think that this article should be listed for deletion, and some of its material re-incorporated into the main article. Banno 19:29, May 24, 2005 (UTC)

To repeat a comment from above I do not disagree that 5.101 should be part of the main TLP article. But if it is judged only a minor part of the main article, then I appreciate your edit to the statement about 5.101 being a special case of a Gödel code. However W's theory of language (Proposition 2 etc) also needs to be discussed. If there is no further discussion per the above talk, in Truth table or Truth function, then those are deficiencies in those articles which 5.101's current content could be used to improve. I am not tied to the 5.101 article, as it may appear, and do not seek its retention. 5.101's appeal is that it is clear, as opposed to some of the other propositions in TLP which appear obscure because of their pioneering character. One of these obscure items is W's acceptance of contradiction as a valid result. This was directly opposed by Turing, who stood up to W in his classes. (W. backed off, but ...) W. had a seminal part in the histories of positivism, of logic, of computing, and of cybernetics, even if this is seen only retrospectively and not in the direct line of attribution to Shannon, Zuse, Wiener etc. I do not disagree with your statements but rather believe there is yet value in 5.101. Ancheta Wis 20:11, 24 May 2005 (UTC)

I certainly do not disagree with you as to the worth of the Tractatus. But I do not see 5.101 as pivotal. It is certainly not the most important part of W's case. My contention is that the content of this article distorts W's argument. What is really needed here is comment from others. Banno 20:23, May 24, 2005 (UTC)

This is actually amusing. When I re-instated this proposition some time ago, I certainly did not intend that it be one of the few entries in TLP. The original entries said more about the propositions here. How about nominating some proposition for reading, and then getting peo to write about it? I got something out of 3.33-3.334, and how W. considered it to be part of the response to the antinomy in the Theory of Types. But I would guess that that is a minor prop. as well in your view. Ancheta Wis 20:41, 24 May 2005 (UTC)
Based on my re-readings of TLP etc, I would venture that his propositions 6.* on Ethics and Esthetics rank in importance to the rest of the logic part. That is the thesis of Janik and Toulmin. I could write something about this. Ancheta Wis 20:57, 24 May 2005 (UTC)

Glad to provide amusement. My favourite is 7. But 6.5 might be a more appropriate response here ;-) Banno 21:10, May 24, 2005 (UTC)

He stayed out of big trouble using 7. I perhaps should follow that example. But I can make a first try at 6.5. Where do you want it, as a separate page, to keep the TLP article small? Ancheta Wis 21:13, 24 May 2005 (UTC)

[edit] 6.41

Banno, in Tractatus Logico-Philosophicus (6.5) I believe I can report that 6.41 does not follow from the chain of thinking beginning at 2.1 and ending at 7. There must be more to this point about 6.41, because he confounds the world with logic and rhetoric starting at Proposition 1. But on the face of it, since we can conceive of multiverses, there can be enormous numbers of possibilities of which our universe (the world) is merely one example, and not all that is the case. Ancheta Wis 08:18, 26 May 2005 (UTC)

[edit] 6.41 revisited

Because 6.41 is different in character from the other propositions, a review is appropriate. Here we use the machinery of deontic modal logic, with the following conventions, but tag 6.41's statements with the type of statement:

  • \Diamond happenstance or contingency is not necessarily so but which is actually so, and which could have been otherwise.
  • \Box necessity if it must be so
N.B.: John McCarthy (1996) notes that \Box is not a truth-functional operator
  • 6.41 \Box"The sense of the world must lie outside of the world. \DiamondIn the world everything is as it is and happens as it does happen. In it, there is no value, - and if there were, it would be of no value.
  • \Box"If there is a value which is of value, it must lie outside all happening and being-so. \Diamond For all happening and being-so is accidental.
  • Not \Diamond"What makes it non-accidental cannot lie in the world, for otherwise this would then again be accidental.
  • \Box "It must lie outside the world.

6.41 (1921) is an example of deontic modal logic (1926). Wittgenstein is making statements about the necessity of principled ethical action, rather than the basing of actions on contingent or accidental results, which he equates with the world. The doubling of the phrase no value is an indication that the statements are being made for different modalities.

  • From a humanist point of view, his actions taken, were to level-out the accidental parts of his life:
    • the accident of his wealth, which he attempted to level-out by giving away;
    • the accident of his position in society, which he attempted to level-out by volunteering for the ranks in the army, rather than accepting an officer's commission in the army (he was later promoted);
    • the accident of being a professor in wartime, which he attempted to level-out by becoming a hospital orderly.
    • Even his last words "tell them I've had a wonderful life" bespeak someone who was evaluating the sense of his life (and must have been so doing in the other examples just stated).
  • These actions can be taken as demonstrations of the meaning of life. This is pertinent, because 6.4 onward should not be parsed as meaningless; to do so, gives intellectual justification for suicide. As a Catholic, Wittgenstein could not justify suicide, even though 3 of his four brothers could. Wittgenstein simply chose to live out his life, while attempting to even out the accidental aspects of his life, apparently to achieve moral parity with his peers.
Banno, I revisited 6.41 because it was so different. I have just learned about deontic modal logic which includes some notation to express the big difference in the type of logic used in this item. I'm not sure it should be called a "proposition" because it is prescriptive in character. Ancheta Wis 03:43, 29 May 2005 (UTC)
Banno, I have just found the deontic logic article which actually seems to weaken 6.41 again. But if we were to take Wittgenstein's identification of the world as happenstance, and his identification of sense as necessity, then that mapping suffices for his case. Hence the chain of justification for 6.5 survives, because the deontic logic article does not take that mapping into consideration. Ancheta Wis 10:52, 29 May 2005 (UTC)
Sorry again, Ancheta; I don't follow this, nor do I see what its relevance is. I don't see that introducing modality does anything but confuse the issue. Banno 07:49, May 30, 2005 (UTC)

[edit] Merge and re-direct

Ancheta, since it appears only you and I are interested in this article, I suggest that it be merged and re-directed back to the main article. Since I find nothing of value here, I suggest that you make the move, taking anything you think worthwhile. We might then attract a bit more interest in the discussion. Banno 08:14, May 30, 2005 (UTC)

Banno, I threw out the ladder. 6.41 is problematic. John McCarthy (1996) notes that \Box is not a truth-functional operator Ancheta Wis 11:04, 30 May 2005 (UTC)
Yes, it is not a truth-functional operator; but since it is you, not W., who is introducing it, why is it a problem for W.? If language consisted only of atomic facts and their truth-functional concatenation, as the early W. contends, then both normative and modal utterances are without meaning. That is what 6.* is arguing. The W. of the Investigations had a somewhat wider view on the issue. In any case, let's take the issue to the other page. Banno 21:26, May 30, 2005 (UTC)