Jump to content

Talk:Tractatus Logico-Philosophicus (5.101)

Page contents not supported in other languages.
From Wikipedia, the free encyclopedia
This is an old revision of this page, as edited by Ancheta Wis (talk | contribs) at 01:07, 21 May 2005 (Relevance to electrical engineering: IEEE Transactions). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

"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)

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)[reply]
I will comment out the Note. Ancheta Wis 09:29, 13 May 2005 (UTC)[reply]

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)[reply]

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)[reply]

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)[reply]
Maybe I should read the article first. --Wtshymanski 20:36, 12 May 2005 (UTC)[reply]
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)[reply]
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)[reply]
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)[reply]

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)[reply]

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)[reply]
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)[reply]
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)[reply]
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)[reply]
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)[reply]
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)[reply]

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)[reply]

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)[reply]
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)[reply]

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)[reply]


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)[reply]

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)[reply]
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)[reply]
Here is a /draft of the page with citations. Comments invited. Ancheta Wis 09:57, 20 May 2005 (UTC)[reply]

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)[reply]

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)[reply]
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)[reply]
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)[reply]
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)[reply]
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)[reply]

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)[reply]

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.

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)[reply]

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)[reply]

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

  • 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.

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)[reply]

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)

"... 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.

File:Cat-on-mat.GIF
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. ...

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)[reply]

See /draft for references with respect to Electrical Engineering. Especially the IEEE Transactions. I know for a fact that the referenced series has existed for decades. I don't think I am the only person who knows about these materials. Ancheta Wis 01:04, 21 May 2005 (UTC)[reply]