# User talk:Ancheta Wis/l

Kurt Lehovec (1918- ) b. Ledvice, Czechoslovakia. Professor Emeritus, University of Southern California. Resides in the Los Angeles area. Doctorate, Prague University in 1944. He immigrated to the United States following World War II under Project Paperclip, a U.S. government program designed to recruit German and other foreign scientists for their considerable talents needed to fight the Cold War. He worked as a consultant to U.S. Signal Corps from 1947 to 1952. MAJOR SCIENTIFIC CONTRIBUTIONS

by Kurt Lehovec

CONTRIBUTION: REFERENCE:

1. SOLAR CELLS

• First explanation of mechanism Phys. Rev. 75, pp. 463-471, 1948

2. LIGHT EMITTING DIODES /LED/

• First explanation of mechanism Phys. Rev. 83, pp. 603-607, 1951

3. SOLID ELECTROLYTE BATTERIES

• Initiation of the field J. Electrochem. Soc. 101, pp 208-209, 1954

4. SPACE CHARGE AND LATTICE

DEFFECTS AT THE SURFACE OF IONIC

CRYSTAL J. Chem. Phys. 21, pp. 1123-1128, 1953

5. LIQUID EPITAXY

• Earliest work J. Appl. Phys. 24, pp. 1482-1484, 1953

6. SURFACE STATES

• Initiation of the C/V method Phys. Stat. Sol, 3, pp. 447-464
• Equivalent circuit of MOS Solid State Electron.7, pp.65-73, 1964

7. P/N JUNCTION ISOLATION U.S. Patent 3,029,366 (1962)

• Invention

8. PHOTOELECTRIC UNDUCED P/N

JUNCTION DEVICE U.S. Patent 3, 473,032 (1969)

• Forerunner of charge coupled device Reissue 27,775 (1973) 7

9. FIELD EFFECT TRANSISTORS

• Current linearity with gate voltage due I EEE Trans. Electron Devices ED 15,

to drift velocity saturation pp. 987-989, 1968

• Modelling Solid State Electronics 13, pp. 1415-1426, 1970

10. WAVES AND PHOTONS

• Photons as consequence of the uncertainty

principle. Submitted to the Phys. Rev. in May 2000

THE SOLAR CELL

The name SOLAR CELL is relatively new for a device, which converts solar radiation into electricity. Semiconductor structures, which achieved this, were already known, since the later part of the 19th century. Made from selenium, they were used commercially as photographic light meters in the 1930s. However the underlying phenomenon, called the PHOTOVOLTAIC EFFECT, was not understood until I explained it.

The early solar cells were semi-conducting rectifiers illuminated through a transparent electrode. The mechanism of the rectification, as explained by Schottky and Mott, invoked a built-in space charge layer. My paper THE PHOTOVOLTAIC EFFECT [Phys. Rev. 74, 463 (1948) describes how electrons and holes, generated in a space charge layer by appropriate illumination, are driven in opposite directions by the electric field of the space charge layer, causing the solar cell effect. I provided a complete quantitative analysis of the operational characteristics of a solar cell, viz. the dependence of its current and voltage output on the intensity and spectral distribution of the illumination. By relating them to the properties of the semi-conducting material, I pointing the way toward the modern Silicon based solar cells, which utilize the built-in space charge layer of a p/n junction. However it took about two decades before the interest in solar cells exploded with applications in space among others.

TESTIMONIALS

"A semiconductor photovoltaic cell converts solar energy directly into electrical energy by mmeans of a p/n junction. Incident photons with energies greater than the band gap of the semiconductor create electrons and holes which are separated by the junction, A potential is thus created across the junctionm and energy can be delivered to a resistive load [ref. 1 - 12]"

J. J. Vysocki and P. Rappaport: "Effect of Temperature on Photovoltaic Energy Conversion" J. Appl. Phys. 31, 571 (1960)

My paper of 1948 is ref. #1. All the other references are from 1954 or later.

"The first theoretical investigations of the photovoltaic effect in photoconductors have been published by Lehovec."

F. Forlani and N. Minnaja:" Photovoltaic effect in photoconductor -dielectric -metal sandwiches " Phys. Stat. Sol. 8, 177 (1965).

"Under conditions of maximum output, a photovoltaic generator can deliver almost 90% of the generated power to a load. This was first pointed out by Lehovec in 1948"

P. Rappaport "The Photovoltaic Effect and its Utilization" RCA Review 20, 373 (1959)

THE LIGHT EMITTING DIODE [ LED ]

With the onset of radio communications in the 1920s, there was a great interest in crystal detectors to rectify the radio signal received by an antenna. These detectors consisted of a semi-conducting crystal to which a point contact was made. Lossew observed in the early 1920s that some Silicon Carbide crystals emit light, when a current is passed through the point contact.

I reproduced Lossew's observation in 1949 and explained it by recombination of minority carriers, injected over a p/n junction, with the majority carriers there and I verified this explanation experimentally with my coworkers [ K. Lehovec, C. A. Accardo and E. Jamgochian "Injected Light Emission of Silicon Carbide Crystals", Phys. Rev. 83, 602 (1951) ]

TESTIMONIALS

"Our understanding of the mechanism of the Lossew effect stems from the work of Lehovec, Accardo and Jamgochian.... Although many refinements have of course been added to this simple model, it still forms the basis of our understanding of the electroluminescent effect in p/n junctions.

C. H. Gooch: "Injection Electroluminescent Diodes".John Wiley & Sons, N.Y. 1973, page 2.

"Electroluminescence, the direct conversion of electrical energy to light energy in a semiconductor was first observed by O. Lossew in 1923....This phenomenon remained unexplained and unexplored until 1951, when Lehovec, using the theory developed for p/n junctions in transistors, produced a theoretical explanation and renewed interest in the electroluminescent properties of semi-conductors."

C. Rowland and R. C. Bottomly: Gallium Phosphide".British Communications and Electronics #2, 12, p. 90, (1965)

"Nearly twenty years elapsed before Kurt Lehovec and coworkers at the Fort Monmouth Signal Corps Engineering Labpratory pointed the way in 1951 and explained the puzzling phenomenon of low voltage generated light emission. in Silicon Carbide crystals. This explanation, which has since stood the test of time, had eluded not only Lossew and other investigators of this puzzling phenomenon, but many additional scientists studying the nature of a closely related puzzle, rectification in semi-conducting diodes."

E. E. Loebner; "Subhistories of the Light Emitting diode", Trans. Electron Devices ED-23, p. 680 (1976)

I visualized several aspects and future applications of the light emitting diode, which are mentioned in the review article INJECTION ELECTROLUMINUSCENCE, Sol. State Elect, 2, 232 (1961) by A. G. Fischer:

"The possibility of the conversion of heat into light in a wide band gap p/n junction, first mentioned by Lehovec [Phys. Rev. 83, 603,(1951), Phys. Rev. 89, 20, (1953)], was further substantiated under idealized thermodynamic assumptions by Weinstein."

"The possibility of using p/n injection light emitting diodes in connection with photoconductors for relays, switches and optical amplifiers has been pointed out by Lehovec" and "Graded-seal p/n junction, made for instance from Ge/Si or Te/Se alloys have already been proposed by Lehovec" [ U. S. Patent 2776367, 1957]."

"In this connection the following model, which would make an injection electroluminescent powder cell for a. c. operation, must be rementioned [ K. Lehivec, Proc. I. R. E. 40, 1407, (1952)]"

THE SOLID ELECTROLYTE BATTERY

Ordinary batteries derive their power by a chemical reaction at one electrode promoted by ion transport through a liquid electrolyte inserted between the two terminals. I have initiated with my coworker J. Broder a new class of battery, which uses ion transport through a solid electrolyte. These solid electrolyte batteries provide extended shelf life, but only comparatively small currents. My solid electrolyte battery was improved in cooperation with mycoworker D. Smyth and patented [US Patent # 3 036 144]

TESTIMONIALS

J, N. Mrgudich, J. Electrochem. Soc. Sept. 1968

MICROCHIPS

Since resistors and capacitors could be made from the same semiconducting material as transistors, entire electric circuits on a single semiconducting chip were envisioned in the later 1950s. The main obstacle for achieving this objective was the problem of how to isolate the individual devices or subcircuits from each other, that they are not short-circuited by the semiconducting substrate. I solved this task by using p/n junctions for this isolation and obtained the US patent 3 029 366 for it on April 10, 1962, filed April 22, 1959.

My patent was challenged by J. Kilby of the Texas Instrument Company, who claimed priority. However the board of patent interferences of the US Patent offices decided on March 16, 1966 that I am the inventor of the p/n junction isolation, which is now used in every microchip of the world.I quote from the decision of the US Patent office. It starts with:

"Count #1 reproduced below is representative of the five counts involved.

Count 1

A multiple semicomnductor assembley comprising a semiconductor slice having a plurality of regions of alternating p and n conductivity types to thereby provide a plurality of p-n junctions, at least two semiconducting components assembled each on one of said regions of said slice, said components being separated by a plurality of said regions so as to provide therebetween at least two p-n junctions thereby achieving electric insulation of said components through said slice by the impedance of said p-n junctions."

And it ends with:

"Since Kilby has no reduction to practice prior to the filing date of Lehovec, and no diligence has been asserted, priority of invention of the subject matter of counts 1 to 5 is awarded to Kurt Lehovec, the senior party."

TESTIMONIALS

"During the early years significant developments were made in the techniques for batch processing of Silicon devices. These developments culminated in the invention of the p-n junction isolation technique by Lehovec and the planar process by Hoerni.

The Lehovec patent allowed the engineer for the first time to recast microelectronics as "the logical synthesis of complex electronic functions by the interconnection of separate components in a single block of semiconductor material." This effectively transferred their implementation from the realm of new device invention to the application of well developed active circuit synthesis techniques. Concurrently, the Hoerni patent allowed the practical realization of these functions by significantly increasing the fabrication yield. It is safe to say that these patents paved the way for the logical development of a large number of sophisticated, reliable microcircuits. The rapid growth of microelectronics from that time bears evidence to this fact.'

From the preface of Sorab K. Ghandi, The Theory and Practice of Microelectronics, John Wiley and Sons, Ne York, 1968

"Robert Noyce, Jean Hoerni, Jack Kilby and Kurt Lehovec, all took part in developing the integrated circuit."

Caption of a photograph of the four inventors from COMPUTOR BASICS, Time Life Books Inc., 1985

These four inventors are included in a chart of the 40 key people, who contributed most to Electronics since the sixteenth century, I find myself in the company of Franklin, Galvani, Volta, Faraday, Maxwell, Marconi, Edison, Tesla, Lee de Forest, Brattain, Bardeen and Shockley, among others.

Introductory DC/AC Circuits and Introductory DC/AC Electronics 4e Chapter, pp. 2-4.

"The integrated circuit accomplishes the separation and interconnection of transistors and other circuit elements electrically rather than physically. The separation is accomplished by introducing p/m diodes, or rectifiers, which allow current to flow in only one direction. The technique was patented by Kurt Lehovec at the Sprague Electric Company."

R. N. Noyce, "Microelectronics", Scientific American,Vol. 237 #3, 1977.

"1959: Kurt Lehovec and Robert Noyce pave the way for integrated circuit development Integrated circuit technology allows etching many electrical switches, perhaps thousands, on a single semiconductor element.

From page 2 of a historic table in COMPUTORS AND CULTURAL TRANSFORMATION by Jaishree K. Odin, University of Havaii http://www.hawaii.edu/aln/cul imp.htm

"3000 miles away, in North Adams, Massachusetts, the research director of the Sprague Electric Company, Kurt Lehovec was looking for a better way to make alloy junction transistors. The Czech born physicist's work led to a technique of alloying from a liquid column to a semiconductor wafer, that was called capillary alloying. Lehovec began thinking about how to put several transistors on one wafer in order to get smaller size and save separate encapsulation. Lehovec proceded to write up the patent application for a MULTIPLE SEMICONDUCTOR ASSEMBLY and filed it himself."

M. P, Wolff, "Innovation", IEEE Spectrum, August 1978

THE C/V ANALYSIS OF SURFACE STATES

Using Hoerni's planar technology and my p/n junction isolation method, the large scale integration of microcircuits was still prevented by an uncontrollable feature of the Metal-Oxide-Silicon transistors: the surface states at the Silicon/Oxide interface. The solution was first to determine the amount of these surface states in each processing batch of a microcircuit, and then to compensate for it by an appropriate dose of implanted ions.. I introduced the C/V analysis for determination of the amount of surface states by analyzing the voltage dependence of a test metal-oxide-silicon capacitor, inserted now on each silicon slice for microchip production...

TESTIMONIALS

"The equivalent circuit shown in Fig. 2a is a simplified version of the one given by Lehovec and Slobodskoy."

E. H. Nocollian and A. Goetzberger, MOS Conductance technique for Measuring Surface State parameters", Applied Physics Letters, 7, #8, (1965)

### The "lost years": life after the Tractatus

At the same time, Wittgenstein was a profoundly changed man: he had embraced the Christianity which previously he had opposed, faced harrowing combat in World War I, and succeeded in crystallizing the upheavals in his intellectual and emotional life with the exhausting composition of the Tractatus. It was a work which transfigured all of his past work on logic into a radically new framework that he believed offered a definitive solution to all the problems of philosophy. These changes in Wittgenstein's inner and outer life left him both haunted and yet invigorated to follow a new, ascetic life. One of the most dramatic expressions of this change was his decision in 1919 to give away his portion of the family fortune that he had inherited when his father had died. The money was divided between his sisters Helene and Hermine and his brother Paul, and Wittgenstein insisted that they promise never to give it back. He felt that giving money to the poor could only corrupt them further; the rich would not be harmed by it.

Since Wittgenstein thought that the Tractatus had solved all the problems of philosophy, he left philosophy and returned to Austria to train as a primary school teacher. He was educated in the methods of the Austrian School Reform Movement which advocated the stimulation of the natural curiosity of children and their development as independent thinkers, instead of just letting them memorize facts. Wittgenstein was enthusiastic about these ideas but ran into problems when he was appointed as an elementary teacher in the rural Austrian villages of Trattenbach, Puchberg-am-Schneeberg, and Otterthal. During his time as a schoolteacher, Wittgenstein wrote a pronunciation and spelling dictionary, in the vernacular, for the use of his students; it was published and well-received by his colleagues. This would be the only book besides the Tractatus that Wittgenstein published in his lifetime.

Wittgenstein's teaching methods were intense and exacting, and his students enjoyed a level of education very rarely available in impoverished rural schools. At times, he would take his students on field trips to Vienna, where they stayed overnight at his sister's school. However, Wittgenstein had very little patience for his slower students, and his severe disciplinary methods (often involving corporal punishment) — as well as a general suspicion amongst the villagers that he was somewhat mad — led to a long series of bitter disagreements with some of his students' parents, especially in Otterthal. During this period, Wittgenstein was prone to bouts of depression. In April 1926, he resigned his position and returned to Vienna, feeling that he had failed as a school teacher.

After that, he worked as a gardener's assistant in a monastery near Vienna. He considered becoming a monk, and went so far as to enquire about the requirements for joining an order. However, at the interview he was advised that he could not find in monastic life what he sought.

Two major developments helped to save Wittgenstein from this despairing state. The first was an invitation from his sister Margaret ("Gretl") Stoneborough to work on the design and construction of her new house. He worked with the architect, Paul Engelmann (who had become a close friend of Wittgenstein's during the war), and the two designed a spare modernist house after the style of Adolf Loos (whom they both greatly admired). Wittgenstein found the work intellectually absorbing, and exhausting — he poured himself into the design in painstaking detail, including even small aspects such as doorknobs and radiators (which had to be exactly positioned to maintain the symmetry of the rooms). As a work of modernist architecture the house evoked some high praise; G. H. von Wright said that it possessed the same "static beauty" as the Tractatus. The effort of totally involving himself in intellectual work once again did much to restore Wittgenstein's spirits.

Secondly, toward the end of his work on the house, Wittgenstein was contacted by Moritz Schlick, one of the leading figures of the newly formed Vienna Circle. The Tractatus had been tremendously influential to the development of the Vienna positivism, and although Schlick never succeeded in drawing Wittgenstein into the discussions of the Vienna Circle itself, he and some of his fellow circle members (especially Friedrich Waismann) met occasionally with Wittgenstein to discuss philosophical topics. Wittgenstein was frequently frustrated by these meetings — he believed that Schlick and his colleagues had fundamentally misunderstood the Tractatus, and at times would refuse to talk about it at all. (Much of the disagreements concerned the importance of religious life and the mystical; Wittgenstein considered these matters of a sort of wordless faith, whereas the positivists disdained them as useless. In one meeting, Wittgenstein refused to discuss the Tractatus at all, and sat with his back to his guests while he read aloud from the poetry of Rabindranath Tagore.) Nevertheless, the contact with the Vienna Circle stimulated Wittgenstein intellectually and revived his interest in philosophy. He also met with Frank P. Ramsey, a young philosopher of mathematics who travelled several times from Cambridge to Austria to meet with Wittgenstein and the Vienna Circle. In the course of his conversations with the Vienna Circle and with Ramsey, Wittgenstein began to think that there might be some "grave mistakes" in his work as presented in the Tractatus — marking the beginning of a second career of ground-breaking philosophical work, which would occupy him for the rest of his life.

### Modal logic versus Deontic logic

Banno, Might you agree that scientific reasoning uses Modal logic?

During my work on the Tractatus article, I learned about the distinction between Modal logic and Deontic logic. These articles state clearly that there is a Deontic logic operator which is not truth-functional. Thus, for example, a myth need not rely on whether it is true or not, but people who subscribe to the myth (perhaps learned in childhood), are free to act on it (for example, the belief that one should do good deeds, as we are taught in Boy Scouts).

On the other hand, during my work on the Wittgenstein article, I learned that he was compelled to include a Deontic element (duty based -- keyword must) based on aesthetic considerations within the Tractatus. (Proposition 6.41)

## Semantic theory of truth

The semantic theory of truth holds that some statement of truth 'any p is true' can be only a formal requirement on the language P which is expressing p. ... It is generally necessary ... to set the instance of the "object language P" one is talking about, apart from the instance of the "use language U" one is using to talk about P. ...

Wittgenstein: meaning is use.

## Friedrich Waismann

Friedrich Waismann was a member of the Vienna Circle (Wiener Kreis), which espoused a philosophical program of logical positivism, a program of logical empiricism, where analytic means provable per either the empirical observation or via logical deduction from an established point. This deconstructs a lot of Hegel etc.

This program set out to reconstruct philosophy along the lines of physics and biology, as in, for example the International Encyclopaedia of Unified Science (University of Chicago Press).

Waismannis remembered as one of the principal conversants with Wittgenstein, 1927-1931.

He was also author of:

• Friedrich Waismann, Ludwig Wittgenstein und der Wiener Kreis, B.F. McGinnis, ed. (Oxford: Blackwell, 1967)
• Friedrich Waismann, An Introduction to Mathematical Thinking

## Socratic question

the Socratic question: "How should I live my life?"Edward Craig, p.12

• ^ Edward Craig (2002), Philosophy: a very short introduction, ISBN 0-19-285421-6 132 pages.
• Garrett Thomson (2003), On the Meaning of Life ISBN 0-534-59580-4

p.9

"Why should I live when I could commit suicide?"
"What should I do with the rest of my life?"
"What sense can I make of my life up to now?"
"What could have been different about my life?"

Nine mistakes paraphrased pp154-5

1. Only the infinite has meaning...
2. The meaning only per a goal
3. Meaning only per happiness
4. Meaning must be invented
5. Material universe cannot imply meaning
6. Value judgements reducible to reasons for action
7. Meaning of one's life cannot extend beyond boundaries of one's life
8. Only linguistic items can be meaningful
9. Meaning consists in living in accordance with a self-determined life plan
• ^ Robert Audi, ed. The Cambridge Dictionary of Philosophy ISBN 0-521-48328-X
• ^ Francis Crick (1994), The Astonishing Hypothesis: the scientific search for the soul. ISBN 0-684-19431-7

### 6.41

Banno, there may be a way to "fix-up" 6.41: if some reader were to interpret Propositions 1 and 6.41 as expressions (in the sense of a series of symbols, as in a mathematical notation), then W's 6.41 wording: "sense of the world" amounts to an expression evaluation (as in a mathematical procedure). W explicitly states that the "sense" is not part of the "world" (the expression). From our viewpoint, however, if we were to view the expression as a time-series of states, say, themselves expressions, then the problem vanishes.

It is as if you were to perform a computation using only two registers A and B. The world is saved to register A. The evaluation (or the sense) is saved to register B. A computer program could continue to operate, using A only, and the evaluator could continue to operate, using the parallel register B.

If B can read A, but A cannot read B, then it is as if B did not exist (according to everything known in A). But Wittgenstein explicitly states that we have sense. (In other words, the readers are the evaluators). When A cannot read B, then in computing circles, A does not share B's namespace. In computing circles, the idea that A can read B is called namespace pollution

However, I have not seen this fix-up anywhere; thus this cannot be published as there is no citation for it. Ancheta Wis 18:24, 27 May 2005 (UTC)

• 6.41 "The sense of the world must lie outside of the world. In 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.
If there is a value which is of value, it must lie outside all happening and being-so. For all happening and being-so is accidental.
What makes it non-accidental cannot lie in the world, for otherwise this would then again be accidental.
It must lie outside the world.

Here he confounds his view of the world with the world, a fallacy which begins with Proposition 1. However, it is understandable, as his view is linguistic.

A formal modal logic represents modalities using modal sentential operators ${\displaystyle \Box }$ and ${\displaystyle \Diamond }$.

I investigated this mapping but decided that contingency reads better.

If there is an A which is of V, A ${\displaystyle \Box }$ outside( all ${\displaystyle \Diamond }$). For all ${\displaystyle \Diamond }$is accidental.
What makes A non-accidental cannot lie in W, for otherwise A would then again be accidental.
A ${\displaystyle \Box }$ lie outside the W.
• 6.42 "Hence also there can be no ethical propositions. ...
• 6.421 "... Ethics are transcendental. ...
• 6.423 "Of the will as the bearer of the ethical we cannot speak.
• 6.5 "For an answer which cannot be expressed, the question too cannot be expressed.

## 6.5

In Tractatus Logico-Philosophicus of Ludwig Wittgenstein Proposition 6.5 seeks to ground his philosophy of action (Proposition 7: "Whereof one cannot speak, thereof one must be silent").

• 6.5
"For an answer which cannot be expressed, the question too cannot be expressed.
"The riddle does not exist.
"If a question can be put at all, then it can also be answered.

## Tractatus 1-2

Proposition 6.5 (and its consequence) can not be understood until one realizes that Wittgenstein was a son of a family at the apex of Viennese culture, the capital of an empire (now vanished)Jan73,pp28-29. In today's terms, the answer 6.5 is that from a man of the highest intellect, moral development, and worldly wealth. He literally could do anything he wished. But his father, Karl, thought him retarded, in comparison to the rest of the family, which included composers, musicians, and artists. He was schooled at home until age 14 (he later imposed the ideals of his tutors on his hapless students after he had completed Tractatus, and had undertaken training as a schoolteacher (1920)). He was assigned to study engineering and undertook the curriculum of an aeronautical engineer at the University of Berlin (1908). Thus he undertook the study of mathematics. But he refused to accept the propositions he encountered and brought his questions to Frege, who had undertaken a program to base mathematics on logic (1878). He later attended the University of Manchester in England as a doctoral student. Frege, unable to counter his questions, referred him to Russell. Russell, by this time, had completed a work on Frege's program (1903), and was collaborating with Whitehead on Principia Mathematica. He duly appeared at Cambridge, where Russell assigned him a tutor, K.E. Johnson, for logic. After one hour, Johnson reported that Wittgenstein was teaching him. But Russell had discovered some antinomies in logic, seriously calling into question Frege's program. Frege's program for logic as the basis of mathematics was now in shambles. Wittgenstein thus retired to Norway to work out his ideas (1912), and perhaps rescue Frege's program. This was the basis for his Tractatus.

While in Norway, his father Karl died (1913), leaving him heir to an enormous fortune, which he attempted to give away (much of it to his surviving siblings, on the condition that they not give any back to him). By 1914, the Austro-Hungarian Empire was at war with Russell's British Empire, and Wittgenstein volunteered to fight the British, for the Empire of Habsburg Vienna. While a soldier, before the serious fighting, he found a magazine article about a lawsuit involving a baby carriage and a truck. The court case re-enacted the incident with models. It was this event which made him realize that the subject of this process could be described by pictures as well as in words -- the genesis of his picture theory of language (Tractatus 2.*). But this idea was already endemic in Viennese thoughtJan73,p.31.

• 2.1
"We make to ourselves pictures of facts.

...

## Tractatus 3-4

• 3
"The logical picture of the facts is the thought.

...

• 4
"The thought is the significant proposition.

...

## Tractatus 5-6

• 5
"Propositions are truth-functions of elementary propositions.
• 5.2522
"The general term of the formal series a, O' a, O' O' a, ... I write thus: "[a, x, O' x]". This expression in brackets is a variable. ...

Wittgenstein thus gives a notation which expresses an inductive form.

• 6
"The most general form of proposition is [p, ξ, N( ξ )].

In this notation, ξ expresses the set of the series of negations of p, and N( ξ ) is the power set of ξ.

• 6.241 proves 2*2=4 in one sentence, a feat which took Russell hundreds of pages to prove 2+2=4, as his demonstration that he believes his method is more powerful.
• 6.33
"We do not believe a priori in a law of conservation, but we know a priori the possibility of a logical form.

He states this on the strength of 6.

• 6.41
"The sense of the world must lie outside of the world. ... In it, there is no value, - and if there were, it would be of no value. ...

Here he confounds his view of the world with the world, a fallacy which begins with Proposition 1. However, it is understandable, as his view is linguistic.

• 6.42
Hence also there can be no ethical propositions. ...
• 6.421
"... Ethics are transcendental. ...
• 6.423
"Of the will as the bearer of the ethical we cannot speak.
• 6.5
"For an answer which cannot be expressed, the question too cannot be expressed.
• 7
"Whereof one cannot speak, thereof one must be silent".

For me, the flaw is 6.41.

## Reference

Allan Janik and Stephen Toulmin (1973, 1996), Wittgenstein's Vienna ISBN 1-56663-132-7

TLP - an ontological basis for logical positivism

1) based on observation of fact (sensors triggering responses - behaviorism ala David Premack) 2) based on logic - expression evaluation of atomic propositions - not further analyzable (ala Max Born) 3) analytic statements are founded on facts, or expressions involving facts. - linguistic expressions only 4) truth-functions (logic expressions) or their equivalent embodiment 5.101 as syntactic units 5) no further basis for the ontology - an agent can be designed to act in behalf of a principal per contract - a logical expression. - a basis for action. 6) the facts are truth bearers. the agent can act on the facts.

## LW

Image:Wittgenstein2.jpg Ludwig Josef Johann Wittgenstein [IPA 'lʊdvɪç 'joːzɛf 'joːhann 'vɪtgɛnʃtaɪn] (April 26, 1889April 29, 1951) was an Austrian philosopher who contributed several groundbreaking works to modern philosophy, primarily on the foundations of logic and the philosophy of language. He is widely regarded as one of the most influential philosophers of the 20th century. [1]

Although numerous collections from Wittgenstein's notebooks, papers, and lectures have been published since his death, he published only one philosophical book in his own lifetime — the Tractatus Logico-Philosophicus in 1921, while studying at Trinity College, Cambridge, under the supervision of the philosopher Bertrand Russell. With the completion of the Tractatus (1921), for which he was awarded a Ph.D. (1929), Wittgenstein believed he had solved all the problems of philosophy, and he abandoned his studies, working as a schoolteacher (1920), a gardener at a monastery (1926), and an architect on his sister's new house in Vienna (1927). However, in 1929, he returned to Cambridge and took a teaching position there, subsequently revising some of his earlier work. His development of a new philosophical method and a new understanding of language culminated in his second magnum opus, the Philosophical Investigations, which was published posthumously (1953).

Wittgenstein's early work was deeply influenced by Russell's work on logic, by his earlier brief study with the German logician Gottlob Frege, and by Arthur Schopenhauer. When the Tractatus was published, it was taken up as a major influence by the Vienna Circle positivists. However, Wittgenstein did not consider himself part of that school and alleged that logical positivism involved grave misunderstandings of the Tractatus.

Both his early and later work have been major influences in the development of analytic philosophy, especially in the philosophy of language, the philosophy of mind, and action theory. Former students and colleagues who carried on Wittgenstein's methods included Gilbert Ryle, Friedrich Waismann, Norman Malcolm, G. E. M. Anscombe, Rush Rhees, Georg Henrik von Wright and Peter Geach. Contemporary philosophers heavily influenced by Wittgenstein include James Conant, Michael Dummett, Peter Hacker, Stanley Cavell, and Saul Kripke.

## Life

He was born as Ludwig Joseph Johann Wittgenstein in Vienna. His paternal grandparents, after they had converted from Judaism to Protestantism, moved from Saxony in Germany to Vienna in Austria-Hungary. Here is where Ludwig's father, Karl Wittgenstein, gained wealth and esteem as one of the leading businessmen in the iron and steel industry. Ludwig's mother Leopoldine (née Kalmus) was a Catholic, but her father was also of Jewish descent. Thus by Jewish law, Ludwig was not Jewish. Ludwig was baptized in a Catholic church and was given a Catholic burial by his friends when he died. Although he was not a practicing Catholic, religious writing such as Tolstoy's work on the Gospels sustained him during World War I.

### Early life

Ludwig grew up as the youngest of eight children in a household that provided an intensely stimulating environment. Ludwig's parents were both very musical and all their children were artistically and intellectually gifted. Karl Wittgenstein was a leading patron of the arts, and the Wittgenstein house hosted many figures of high culture — above all, musicians. The family was often visited by artists such as Johannes Brahms and Gustav Mahler. Ludwig's brother Paul Wittgenstein went on to become a world-famous concert pianist, even after losing his right arm in World War I. Ludwig himself did not have prodigious musical talent, but his devotion to music remained vitally important to him throughout his life — he made frequent use of musical examples and metaphors in his philosophical writings, and was said to be unusually adept at whistling lengthy and detailed musical passages. A less fortunate family trait was a tendency to intense self-criticism, to the point of depression and suicidal tendencies. Three of his four brothers committed suicide.

Until 1903, Ludwig was educated at home; after that, he began three years of schooling at the Realschule in Linz, a school emphasizing technical topics. Adolf Hitler was a student there at the same time, and the two (both 14) can be seen near each other in a school photograph of all the students. (It is a matter of controversy whether Hitler and Wittgenstein knew each other at all, and if so whether either had any memory of the other. See below.)

In 1906, Wittgenstein took up studying mechanical engineering in Berlin, and in 1908 he went to the University of Manchester to study for his doctorate in engineering. For this purpose he registered as a research student in an engineering laboratory. There he did research on the behavior of kites in the upper atmosphere. From that, he moved to aeronautical research on the design of a propeller with small jet engines on the end of its blades. He successfully designed and tested a prototype of this design.

During his research Wittgenstein became interested in the foundations of mathematics, particularly after reading Bertrand Russell's Principles of Mathematics (1903).

He studied in Germany briefly under Gottlob Frege who, in the preceding decades, had laid the foundations of modern mathematical logic. Frege urged him to read the work of Bertrand Russell, who had discovered certain crucial contradictions in Frege's own theories.

In 1912, Wittgenstein went to the University of Cambridge and studied with Russell at Trinity College. He made a great impression on Russell and G. E. Moore and started to work on the foundations of logic and mathematical logic. During this period, his three major interests were philosophy, music and travelling. He was also invited to join the elite secret society, the Cambridge Apostles, which Russell and Moore had both belonged to as students.

In 1913, Wittgenstein inherited a great fortune when his father died. He donated some of it, initially anonymously, to Austrian artists and writers including Rainer Maria Rilke and Georg Trakl. In 1914 he would go to see Trakl when the latter wanted to meet his benefactor, but Trakl killed himself days before Wittgenstein arrived.

Although he was invigorated by his study in Cambridge and his conversations with Russell, Wittgenstein came to feel that he could not get to the heart of his most fundamental questions while surrounded by other academics. In 1913, he retreated to the solitude of a remote mountain cabin in Skjolden, Norway, which could only be reached on horseback. The isolation allowed him to devote himself entirely to his work, and he later saw this period as one of the most passionate and productive times of his life. While there, he wrote a ground-breaking work in the foundations of logic, a book entitled Logik, which was the immediate predecessor and source of much of the Tractatus Logico-Philosophicus.

### World War I

The outbreak of World War I in the next year took him completely by surprise, as he was living a secluded life at the time. He volunteered for the Austro-Hungarian army as a soldier in the ranks, first serving on a ship and then in an artillery workshop. In 1916, he was sent as a member of a howitzer regiment to the Russian front where he won several medals for bravery. The diary entries of this time reflect his contempt for the baseness, as he saw it, of his fellow soldiers. He was later promoted from the ranks to become an officer.

Throughout the war, Wittgenstein kept notebooks in which he frequently wrote philosophical and religious reflections alongside personal remarks. At the beginning of his tour of duty, Wittgenstein devoured Tolstoy's commentary on the Gospels, and became a devoted, if troubled and doubting, Catholic. Wittgenstein's work on Logik began to take on an ethical and religious significance. With this new concern with the ethical, combined with his earlier interest in logical analysis, and with key insights developed during the war (such as the so-called "picture theory" of propositions), Wittgenstein's work from Cambridge and Norway was transfigured into the material that eventually became the Tractatus. In 1918, toward the end of the war, Wittgenstein was promoted to reserve officer (Lieutenant) and sent to north Italy as part of an artillery regiment where he was captured by the Italians. When he was taken prisoner, the Italians found a German manuscript entitled the Logische-Philosophische Abhandlung (Logical-Philosophical Treatise) in his rucksack. This manuscript would eventually become the Tractatus. Through the intervention of his Cambridge friends, Wittgenstein managed to get access to books, prepare his manuscript, and send it back to England. Russell recognized it as a work of supreme philosophical importance, and after Wittgenstein's release in 1919, he worked with Wittgenstein to get it published. An English translation was prepared, first by Frank Ramsey and then by C. K. Ogden, with Wittgenstein's involvement. After some discussion of how best to translate the title, G. E. Moore suggested Tractatus Logico-Philosophicus, in an allusion to Baruch Spinoza's Tractatus Theologico-Politicus. Russell wrote an introduction, lending the book his reputation as one of the foremost philosophers in the world.

However, difficulties remained. Wittgenstein had become personally disaffected with Russell, and he was displeased with Russell's introduction, which he thought evinced fundamental misunderstandings of the Tractatus. Wittgenstein grew frustrated as interested publishers proved difficult to find. To add insult to injury, those publishers who were interested proved to be mainly interested in the book because of Russell's introduction. At last, Wittgenstein found a publisher in Wilhelm Ostwald's journal Annalen der Naturphilosophie, which printed a German edition in 1921, and in Routledge Kegan Paul, which printed a bilingual edition with Russell's introduction and the Ramsey-Ogden translation in 1922.

### The "lost years": life after the Tractatus

At the same time, Wittgenstein was a profoundly changed man: he became a passionate Christian, faced harrowing combat in World War I, and succeeded in crystallizing the upheavals in his intellectual and emotional life with the exhausting composition of the Tractatus. It was a work which transfigured all of his past work on logic into a radically new framework that he believed offered a definitive solution to all the problems of philosophy. These changes in Wittgenstein's inner and outer life left him both haunted and yet invigorated to follow a new, ascetic life. One of the most dramatic expressions of this change was his decision to give away his portion of the family fortune that he had inherited when his father had died. Some of the main beneficiaries were avant-garde German and Austrian artists (among them Rainer Maria Rilke). He also gave much of it to his siblings, insisting that they promise never to give it back. He felt that giving money to the poor could only corrupt them further; the rich would not be harmed by it.

Since Wittgenstein thought that the Tractatus had solved all the problems of philosophy, he left philosophy and returned to Austria to train as a primary school teacher (1920). He was educated in the methods of the Austrian School Reform Movement which advocated the stimulation of the natural curiosity of children and their development as independent thinkers, instead of just letting them memorize facts. Wittgenstein was enthusiastic about these ideas but ran into problems when he was appointed as an elementary teacher in the rural Austrian villages of Trattenbach, Puchberg-am-Schneeberg, and Otterthal. During his time as a schoolteacher, Wittgenstein wrote a pronunciation and spelling dictionary for his use in teaching students; it was published and well-received by his colleagues. This would be the only book besides the Tractatus that Wittgenstein published in his lifetime.

Wittgenstein's teaching methods were intense and exacting, and his students enjoyed a level of education very rarely available in impoverished rural schools. However, Wittgenstein had very little patience for his slower students, and his severe disciplinary methods (often involving corporal punishment) — as well as a general suspicion amongst the villagers that he was somewhat mad — led to a long series of bitter disagreements with some of his students' parents. During this period, Wittgenstein was prone to bouts of depression. In April 1926, he resigned his position and returned to Vienna, feeling that he had failed as a school teacher.

After that, he worked as a gardener's assistant in a monastery near Vienna. He considered becoming a monk, and went so far as to enquire about the requirements for joining an order. However, at the interview he was advised that he could not find in monastic life what he sought.

Two major developments helped to save Wittgenstein from this despairing state. The first was an invitation from his sister Margaret ("Gretl") Stoneborough to work on the design and construction of her new house. He worked with the architect, Paul Engelmann (who became a close friend of Wittgenstein's during the war), and the two designed a spare modernist house after the style of Adolf Loos (whom they both greatly admired). Wittgenstein found the work intellectually absorbing, and exhausting — he poured himself into the design in painstaking detail, including even small aspects such as doorknobs and radiators (which had to be exactly positioned to maintain the symmetry of the rooms). As a work of modernist architecture the house evoked some high praise; G. H. von Wright said that it possessed the same "static beauty" as the Tractatus. The effort of totally involving himself in intellectual work once again did much to restore Wittgenstein's spirits.

Secondly, toward the end of his work on the house, Wittgenstein was contacted by Moritz Schlick, one of the leading figures of the newly-formed Vienna Circle. The Tractatus had been tremendously influential to the development of the Vienna positivism, and although Schlick never succeeded in drawing Wittgenstein into the discussions of the Vienna Circle itself, he and some of his fellow circle members (especially Friedrich Waismann) met occasionally with Wittgenstein to discuss philosophical topics. Wittgenstein was frequently frustrated by these meetings — he believed that Schlick and his colleagues had fundamentally misunderstood the Tractatus, and at times would refuse to talk about it at all. (Much of the disagreements concerned the importance of religious life and the mystical; Wittgenstein considered these matters of a sort of wordless faith, whereas the positivists disdained them as useless. In one meeting, Wittgenstein refused to discuss the Tractatus at all, and sat with his back to his guests while he read aloud from the poetry of Rabindranath Tagore.) Nevertheless, the contact with the Vienna Circle stimulated Wittgenstein intellectually and revived his interest in philosophy. He also met with Frank P. Ramsey, a young philosopher of mathematics who travelled several times from Cambridge to Austria to meet with Wittgenstein and the Vienna Circle. In the course of his conversations with the Vienna Circle and with Ramsey, Wittgenstein began to think that there might be some "grave mistakes" in his work as presented in the Tractatus — marking the beginning of a second career of ground-breaking philosophical work, which would occupy him for the rest of his life.

### Returning to Cambridge

In 1929 he decided, at the urging of Ramsey and others, to return to Cambridge. He was met at the train station by a crowd of England's greatest intellectuals, discovering rather to his horror that he was one of the most famed philosophers in the world. In a letter to Lydia Lopokova, Lord Keynes wrote: "Well, God has arrived. I met him on the 5.15 train."

Despite this fame, he could not initially work at Cambridge, as he did not have a degree, so he applied as an advanced undergraduate. Russell noted that his previous residency was in fact sufficient for a doctoral degree, and urged him to offer the Tractatus as a doctoral thesis, which he did in 1929. It was examined by Russell and Moore; at the end of the thesis defense, Wittgenstein clapped the two examiners on the shoulder and said, "Don't worry, I know you'll never understand it." Moore commented in the examiner's report to the effect that: "In my opinion this is a work of genius; it is, in any case, up to the standards of a degree from Cambridge." Wittgenstein was appointed as a lecturer and was made a fellow of Trinity College.

Wittgenstein's political sympathies lay on the left, and while he was opposed to Marxist theory, he described himself as a "communist at heart" and romanticized the life of labourers. In 1934, attracted by Keynes' description of Soviet life in Short View of Russia, he conceived the idea of emigrating to the Soviet Union with his close friend (or lover) Francis Skinner. They took lessons in Russian and in 1935 Wittgenstein traveled to Leningrad and Moscow in an attempt to secure employment. He was offered teaching positions but preferred manual work and returned three weeks later.

From 1936 to 1937, Wittgenstein lived again in Norway, leaving Skinner behind. He worked on the Philosophical Investigations. In the winter of 1936/37, he delivered a series of "confessions" to close friends, most of them about minor infractions, in an effort to cleanse himself.

After G. E. Moore's resignation in 1939, Wittgenstein, who was by then considered a philosophical genius, was appointed to the chair in Philosophy at Cambridge. He acquired British citizenship soon afterwards.

After exhausting philosophical work, Wittgenstein would often relax by watching an American western or reading detective stories. These tastes are in stark contrast to his preferences in music, where he rejected anything after Brahms as a symptom of the decay of society.

By then, Wittgenstein's view on the foundations of mathematics had changed considerably. Earlier, he had thought that logic could provide a solid foundation, and he had even considered updating Russell and Whitehead's Principia Mathematica. Now he denied that there were any mathematical facts to be discovered and he denied that mathematical statements were "true" in any real sense: they simply expressed the conventional established meanings of certain symbols. He also denied that a contradiction should count as a fatal flaw of a mathematical system. He gave a series of lectures which were attended by Alan Turing and in which the two argued vigorously about these matters.

During a period in World War II he left Cambridge and volunteered as a hospital porter in Guy's Hospital in London and as a laboratory assistant in Newcastle upon Tyne's Royal Victoria Infirmary. This was arranged by his friend John Ryle, a brother of the philosopher Gilbert Ryle, who was working at the hospital then. Wittgenstein taught at Cambridge until 1947 when he resigned to concentrate on his writing. He never liked the intellectual's life at Cambridge, and in fact he encouraged several of his students to pursue non-academic careers. There are stories, perhaps apocryphal, that if any of his philosophy students expressed an interest in pursing the subject, he would ban them from attending any more of his classes.

Wittgenstein communicated with the Finnish philosopher Georg Henrik von Wright, who succeeded Wittgenstein as professor at the University of Cambridge.

Although Wittgenstein was involved in a relationship with Marguerite Respinger (a young Swiss woman whom he had met as a friend of the family), his plans to marry Marguerite were broken off in 1931, and Wittgenstein never married. Most of his romantic attachments were to young men. There is considerable debate over how active Wittgenstein's homosexual life was--inspired by W. W. Bartley's claim to have found evidence of several casual liaisons during Wittgenstein's time in Vienna. What is clear, in any case, is that Wittgenstein had several long-term homosexual attachments, including an infatuation with his friend David Pinsent and long-term, active affairs with Francis Skinner and Ben Richardson.

Wittgenstein's grave lies in the chapel for Ascension Parish Burial Ground in Cambridge.

Much of Wittgenstein's later work was done in the rural isolation that he preferred, on the west coast of Ireland. By 1949, when he was diagnosed as having prostate cancer, he had written most of the material that would be published after his death as Philosophische Untersuchungen (Philosophical Investigations), which arguably contains his most important work. He spent the last two years of his life working in Vienna, the United States, Oxford, and Cambridge. He worked continuously on new material, inspired by the conversations that he had had with his friend and former student Norman Malcolm, during a long vacation at the Malcolms' house in the United States. Malcolm had been wrestling with G.E. Moore's commonsense response to external world skepticism ("Here is one hand, and here is another; therefore I know at least two external things exist"). Wittgenstein began to work on another series of remarks inspired by his conversations, which he continued to work on until two days before his death; the remarks would be collected and published posthumously as On Certainty.

The only known fragment of music composed by Wittgenstein was premiered in November 2003. It is a powerful passage of music that lasts less than half a minute. Wittgenstein died in Cambridge in 1951, just a few days before his friends arrived to pay their last respects. His last words were "Tell them I've had a wonderful life."

## Work

### The Tractatus

Main article: Tractatus Logico-Philosophicus

In rough order, the first half of the book sets forth the following theses: the world consists of independent atomic facts — existing states of affairs — out of which larger facts are built. Language consists of atomic, and then larger-scale propositions that correspond to these facts by sharing the same "logical form." Thought, expressed in language, "pictures" these facts. We can analyse our thoughts and sentences to express ('express' as in show, not say) their true logical form. Those we cannot so analyse cannot be meaningfully discussed. Philosophy consists of no more than this form of analysis: "Wovon man nicht sprechen kann, darüber muss man schweigen" — whereof one cannot speak, thereof one must be silent.

Some commentators believe that, although no other type of discourse is, properly speaking, philosophy, Wittgenstein does imply that those things to be passed over "in silence" may be important or useful, according to some of his more cryptic propositions in the last sections of the Tractatus: indeed, may be the most important and most useful. Other commentators point out that the sentences of the Tractatus would not qualify as meaningful according to its own rigid criteria, and that Wittgenstein's method in the book does not follow its own demands regarding the only strictly correct philosophical method. These commentators believe that the book is deeply ironical, and that it demonstrates the ultimate nonsensicality of any sentence attempting to say something philosophical, something about those fixations of philosophers, about those things that must be passed over in silence, and about logic.

### Intermediary works

Wittgenstein wrote copiously after his return to Cambridge, and arranged much of his writing into an array of incomplete manuscripts. Some thirty thousand pages existed at the time of his death. Much, but by no means all, of this has been sorted and released in several volumes. During his "middle work" in the 1920s and 1930s, much of his work involved attacks from various angles on the sort of philosophical perfectionism embodied in the Tractatus. Of this work, Wittgenstein published only a single paper, "Remarks on Logical Form," which was submitted to be read for the Aristotelian Society and published in their proceedings. By the time of the conference, however, Wittgenstein had repudiated the essay as worthless, and gave a talk on the concept of infinity instead. Wittgenstein was increasingly frustrated to find that, although he was not yet ready to publish his work, some other philosophers were beginning to publish essays containing inaccurate presentations of his own views based on their conversations with him. As a result, he published a very brief letter to the journal Mind, taking a recent article by R. B. Braithwaite as a case in point, and asked philosophers to hold off writing about his views until he was himself ready to publish them. Although unpublished, the Blue Book, a set of notes dictated to his class at Cambridge in 1933–1934 contains seeds of Wittgenstein's later thoughts on language (later developed in the Investigations), and is widely read today as a turning point in his philosophy of language.

### The Philosophical Investigations

Main article: Philosophical Investigations

Although the Tractatus is a major work of philosophy, it is for the Philosophical Investigations (PI) (known as Philosophische Untersuchungen in German) that Wittgenstein is best known today. Published posthumously in 1953, PI comprises two parts. Part I, consisting of 693 numbered paragraphs, which was ready for printing in 1946 but was withdrawn from the publisher by Wittgenstein, and Part II which was added on by the editors, trustees of his estate.

It is notoriously difficult to find consensus among interpreters of Wittgenstein's work, and this is particularly true concerning PI. What follows, then, is but one of many readings to be found. In PI, Wittgenstein presents an analysis of our use of language which he sees as crucial to the carrying out of philosophical research. In brief, Wittgenstein describes language as a set of language-games within which the words of our language function and receive their meaning. This view of meaning as use represents a break from the classical view, also presented by Wittgenstein in the Tractatus, of meaning as representation.

One of the most radical characteristics of "later" Wittgenstein is his view of the task of philosophy. The "conventional" view of philosophy, accepted by almost every Western philosopher since Plato, is that the philosopher's task was to solve a number of seemingly intractable problems using logical analysis (for example, the problem of "free will", the relationship between "mind" and "matter", what is "the good" or "the beautiful" and so on). However, Wittgenstein argued in PI that these "problems" were in fact pseudo-problems that arose from philosopher's misuse of language. Wittgenstein's new philosophical methodology was to continually remind the philosopher of the facts of linguistic usage that they had forgotten in their search for abstract "truths". It would then become obvious that the great questions posed by philosophers had arisen because they presupposed a mistaken view of language and its relation to reality. Philosophers in the Western tradition were not "wiser" than anyone else, as had been assumed — they were simply ordinary men and women more likely to entrap themselves in linguistic confusion. The task of the true philosopher (i.e. Wittgenstein) was to "show the fly out of the fly bottle": to show that the problems with which philosophers tormented themselves were in fact not really problems at all, but rather were examples of "language gone on holiday," as he put it. So the true philosopher becomes more like a therapist removing distress and confusion than someone who creates or discusses philosophical theories or positions.

### Later work

• "On Certainty" — A collection of aphorisms discussing the relation between knowledge and certainty, extremely influential in the philosophy of action.
• "Remarks on Colour"

### Important publications

• Logisch-Philosophische Abhandlung, Annalen der Naturphilosophie, 14 (1921)
• Tractatus Logico-Philosophicus, trans. by C.K. Ogden (1922)
• Philosophische Untersuchungen (1953)
• Philosophical Investigations, trans. by G.E.M. Anscombe (1953)
• Bemerkungen über die Grundlagen der Mathematik, ed. by G.H. von Wright, R. Rhees, and G.E.M. Anscombe (1956) (a selection from his writings on the philosophy of logic and mathematics between 1937 and 1944)
• Remarks on the Foundations of Mathematics, trans. by G.E.M. Anscombe, rev. ed. (1978)
• The Blue and Brown Books (1958) (Notes dictated in English to Cambridge students in 1933-35)
• Philosophische Bemerkungen, ed. by Rush Rhees (1964)
• Philosophical Remarks (1975)

## Quotations

• Proposition 6.54 from the Tractatus: "My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.) ... He must surmount these propositions; then he sees the world rightly." This conception is sometimes referred to as "Wittgenstein's Ladder".
• The final proposition from the Tractatus, numbered 7: "What we cannot speak about we must pass over in silence" An alternative translation sometimes quoted is: "whereof one cannot speak, thereof one must be silent."
• From the introduction to the Tractatus: "...the aim of this book is to draw a limit to thought, or rather — not to thought, but to the expression of thoughts: for in order to be able to draw a limit to thought, we should have to find both sides of the limit thinkable..."
• The later Wittgenstein: "Philosophy is a battle against the bewitchment of our intelligence by means of language."
• "Philosophy is not a theory but an activity."
• "If one tries to advance 'theses' (i.e. theories) in philosophy, it would never be possible to debate them, because everyone would agree to them."
• "The answer to every philosophical question is a truism."
• "Philosophy simply puts everything before us, and neither explains nor deduces anything."
• Philosophical Investigations § 281 "But doesn't what you say come to this: that there is no pain, for example, without pain-behaviour? It comes to this: only of a living human being and what resembles (behaves like) a living human being can one say: it has sensations; it sees; is blind; hears; is deaf; is conscious or unconscious."

• In The Jew of Linz, Kimberly Cornish attempted to show that not only did the young Wittgenstein and Adolf Hitler know each other, but also that they hated each other, that the "one Jewish boy" from his schooling days at Linz that Hitler refers to in Mein Kampf was in fact Wittgenstein, and even that key elements of Hitler's anti-Semitic writings were in fact projections of the young Wittgenstein's traits onto the whole Jewish people. Most biographers of Wittgenstein contend that Cornish's evidence is thin (most of the arguments adduced in favor of the claim are based on circumstantial associations and speculation), and hold that there is little evidence that Hitler and Wittgenstein knew each other, and none at all for the more sensational claims that there was a personal antagonism between them, or that Hitler's personal hatred of Wittgenstein shaped the course of Nazi anti-Semitism. E. L. Doctorow treats Wittgenstein and Hitler as classmates in sections of his novel City of God, in which he writes as Wittgenstein. Hitler was just six days older than Wittgenstein, however they were two grades apart at the Realschule — Hitler had been held back one year and Wittgenstein had been advanced one year.