WITTGENSTEIN: PHILOSOPHICAL ENGINEER
"When these painful contradictions are removed, the question as to the nature
of force will not have been answered; but our minds, no longer
vexed, will cease to ask illegitimate questions."
- Heinrich Hertz, Principles of Mechanics
Ludwig Wittgenstein, the youngest of eight children born of the wealthy steel industrialist Karl Wittgenstein, did not seem to exhibit the extraordinary artistic talents that possessed his siblings. Ludwig instead pursued the practical skills and technical interests that would gain the approval of his father. Although Ludwig felt he had "neither taste nor talent for engineering", he seemed to be adept in working with his hands, and was sent to the technical school in Linz whose educational objective his parents believed "would suit his interests better." Although he allowed people to believe that he was interested in technical pursuits, his real fascination seemed to lie with the philosophy of science. In his teenage years, Ludwig Wittgenstein was inclined to read books dealing with philosophy of science such as Heinrich Hertzs Principles of Mechanics and Ludwig Boltzmanns Populare Schriften. Despite his interest in philosophical pursuits, Ludwig was unwilling to forfeit his fathers approval and left to study mechanical engineering at the Technische Hochshule (now the Technical University) in Charlottenburg, Berlin.
Following three semesters of study in Berlin, Wittgenstein obtained his certificate in 1908, at the age of nineteen, and went to Manchester to further his studies in aeronautics. He experimented with the design of kites by trial and error in hopes of someday constructing and flying his own airplane. Wittgenstein registered as a research student in the Engineering Department at Manchester University where he began to develop an interest in pure mathematics. As Wittgenstein pursed research in the logical foundations of mathematics, he became disinterested in engineering but was torn between the two fields and did not give up aeronautics entirely. Wittgenstein investigated the design aircraft engines and studied discharge nozzles in combustion chambers, eventually designing and patenting a propeller for a jet engine. His engineering endeavors could no longer compete, however, with his desire to explore philosophical issues and in the summer of 1911 he ended his study in the field of aeronautics.
Wittgensteins literary pursuits as a teenager and his formal education in engineering seemed to influence the style of his later work in philosophy. In his teenage years, Wittgenstein read Principles of Mechanics, a book by Heinrich Hertz, and committed to memory a passage from Hertzs discussion of force:
When these painful contradictions are removed, the question as to the nature of force will not have been answered; but our minds, no longer vexed, will cease to ask illegitimate questions.
This passage significantly influenced Wittgensteins conception of the solution to philosophical problems. He took Hertzs approach to the solution of mechanical questions and applied it to the realm of philosophy. This construct could have been the impetus for the philosophical language problems addressed in the Tractatus and the Philosophical Investigations.
Wittgensteins formal training as an engineer also seemed to significantly affect his philosophical style. There are at least five parallels that can be drawn between engineering and the writings of Wittgenstein. The examples he used, the format of his propositions, and his use of repetition with variation, are three of the tools Wittgenstein uses to get his point across that are common to engineering. The last two parallels, correspond to the strategy behind the engineering curriculum in general, and implement a problem solving technique found in engineering design. Although in some respects Wittgensteins philosophical style may resemble a scientific investigation, these parallels to engineering stand out as remnants of his formal education.
SCIENTIST OR ENGINEER?
"The scientist seeks to understand what is;
the engineer seeks to create what never was."
- Theodore von Karman
John Prados used this quotation in an article explaining the basic differences between engineering and science. The quotation is ascribed to the great aerodynamicist, Theodore von Karman, who excelled both as a scientist and as an engineer. Prados explains that in general, a scientist seeks to understand the physical world in which we live. Scientists perform certain calculations in order to gain an understanding of underlying principles of the universe. An engineer, on the other hand, uses acquired scientific knowledge to determine the calculations required to create a device that will satisfy a need. Both scientists and engineers conduct experiments, yet typically with different objectives. Whereas a scientist may use an experiment to increase scientific understanding, an engineer might use a similar experiment to test the performance of a device. The ethical constraints placed on scientists and engineers are also different. While both are concerned with intellectual honesty and accuracy, an engineer must also consider the implications of a device on the environment in which it will perform its intended task. Although both scientists and engineers take satisfaction in discovery, the way they arrive at this discovery is also markedly different. Furthermore, while scientists are often individually responsible for their invention or discovery, an engineers accomplishment is rarely individual. The contribution of a team of engineers is usually required to effectively design a mechanism to solve a given problem.
Its interesting to note Wittgensteins apparent disassociation with science. Many derogatory comments about science are found in Wittgensteins notes published as Culture and Value. In one instance he remarks:
Man has to awake to wonder Science is a way of sending him to sleep again [Culture and Value, 5e].
Speaking of scientific works, Wittgenstein writes:
The popular scientific books by our scientists arent the outcome of hard work, but are written when they are resting on their laurels [Culture and Value, 42e].
He seems to mock Eddingtons work on the "direction of time" and the law of entropy:
Of course you can call it that if you like; but then you should be clear in your mind that you have said no more than that people have changed the direction they walk in [Culture and Value, 18e].
Wittgenstein implies that science does not uncover the most important questions:
While still at school our children get taught that water consists of the gases hydrogen and oxygen, or sugar of carbon, hydrogen and oxygen. Anyone who doesnt understand is stupid. The most important questions are concealed [Culture and Value, 71e].
and apparently does not consider philosophy a science:
People sometimes say they cannot make any judgements about this or that because they have not studied philosophy. This is irritating nonsense, because the pretence is that philosophy is some sort of science [Culture and Value, 29e].
In addition, Wittgenstein doe seems to think that he can not influence a scientist or mathematician:
Nothing seems to me less likely than that a scientist or mathematician who reads me should be seriously influenced in the way he works [Culture and Value, 62e].
Wittgenstein possibly believed he could not influence them because his "way of thinking is different from theirs [Culture and Value, 7e]" and his Tractatus "will be understood only by someone who has himself already had the thoughts that are expressed in it [Tractatus, 3]" Finally, Wittgenstein concludes:
I my find scientific questions interesting, but they never really grip me. Only conceptual and aesthetic questions do that. At the bottom I am indifferent to the solution of scientific problems; but not the other sort [Culture and Value, 79e].
Considering the definition given by Theodore von Karman, Wittgenstein seems to be caught between playing the role of a scientist in one sense and desiring to perform like an engineer and "create what never was." In his investigation of language, Wittgenstein admits that others may not understand him. The notion of teamwork, which he most likely encountered as an engineer, did not enter into his philosophical work. Wittgenstein attempts to reveal the underlying principles of language in the same way a scientist might investigate the underlying principles of the natural world. He is involved in the very type of questioning that he speaks negatively of (Wittgenstein tells a former student [paraphrased] "you are wasting your time in philosophy go do something productive!").
From an engineering point of view, Wittgensteins sense of his own lack of originality could be troubling. These concerns are evident in Culture and Value:
Wittgensteins apparent concern with his lack of originality in philosophy parallels the apprehension that an engineer might have about his or her own designs. Drawing on my own experience, I believe that Wittgenstein leans more toward the role of an engineer in his philosophical writing style despite his scientific tendencies.
"For example, if you see the schematic drawing of a cube as a plane figure consisting of
a square on two rhombi you will, perhaps, carry out the order Bring me something like this
differently from someone who sees the picture three-dimensionally."
- Ludwig Wittgenstein, Culture and Value
Many of the examples Wittgenstein chooses to implement in communicating his philosophy of language directly parallel the engineering profession. For example, Wittgenstein continually refers to geometrical concepts to elucidate his ideas in the Tractatus, Culture and Value and in the Philosophical Investigations. Examples from science and chemistry are used to clarify philosophical notions in his works. Furthermore, examples that are directly connected to particular aspects of engineering appear in the Tractatus, in Culture and Value and once again in the Philosophical Investigations.
Engineering graphics rely heavily on a keen grasp of geometrical concepts. An understanding of symmetry and the perceptions of an object from various viewpoints are important in mechanical design.* Wittgenstein takes these geometrical concepts and effectively implements them in his theory of language. For example, Wittgenstein uses an arrow* * and a solid body to represent the sense of propositions in language:
Wittgenstein then goes on to represent language as an object with coordinates in space. He shows that there are separate domains in which language can have sense. Outside its domain, a word is typically nonsensical. In the same way that a geometrical figure (such as an arrow or a solid body) must obey the laws of space, Wittgenstein asserts that language must also obey the laws of logic:
To illustrate his ideas on "simple", "complex" and "composite" Wittgenstein chooses to use cubes, areas, and lengths of measurement. These objects are the building blocks of mechanical design. Using these examples, Wittgenstein builds, for the reader, a visual representation of language:
as a cube; and all similar phenomena. For we really see two different facts. (If I look in the first place at the corners marked a and only glance at the bs, then the as appear to be in front, and vice versa.) [Tractatus, 5.5423]
In addition, Wittgenstein uses geometrical shapes to comment on beauty, interpretation and invention:
can be seen as a triangular hole, as a solid, as a geometrical drawing; as standing on its base, as hanging from its apex; as a mountain, as a wedge, as an arrow, or pointer, as an overturned object which is meant to stand on the shorter side of the right angle, as a half parallelogram, and as various other things [Philosophical Investigations, 200e].
And had said that one day it would be the shape of an instrument of locomotion
[Culture and Value, 43e]
Wittgenstein uses shapes to illustrate philosophical concepts just as an engineer might use geometry to create a model of a device in the real world.
Mathematics, science and chemistry are important fields of study within the engineering discipline. These fields help to explain the behavior of matter in the natural world. An engineer depends on this knowledge to create a device to solve a particular problem. Wittgenstein appeals to the realms of mathematics, science and chemistry to depict his philosophical ideas. The logic of the Tractatus, for example, is mathematical by nature. In his discussion of "simple" and "composite", Wittgenstein employs the scientific notion of "composition of forces" and the mathematical concept of "division of a line by a point outside it" [Philosophical Investigations, #48]. Wittgenstein refers to hyperbolic functions to describe a particular type of sentence [Philosophical Investigations, #19] and even refers to the use of language as a "calculus" [Philosophical Investigations, 14e]. Moreover, Wittgenstein uses the concepts of force and friction to describe society in the absence of culture and uses chemical analysis to describe logical possibility:
Wittgenstein does not only take examples from the realms of math and science, however. Wittgenstein references specific engineering situations in his notes in Culture and Value and in the Philosophical Investigations. His previous work in the field of aeronautics is seen in his comments on perceptions of the future and on large-scale thinking:
References to Wittgensteins work in mechanical engineering appear in some of his other illustrations. For example, Wittgenstein depicts tools in a toolbox [Philosophical Investigations, #11] and handles in a locomotive [Philosophical Investigations, #12] to illustrate the diverse functions of words. These specific examples Wittgenstein chose to implement within his philosophy of language seemed to arise in part from his formal engineering education.
Not only are engineers involved in the creation of systems such as machines and engines, but they are also involved with the design and fabrication of structures such as bridges and buildings. Wittgenstein notes peculiar uses of language through an illustration dealing with the building of a bridge:
From Simplicissimus: Riddles of technology. (A picture of two professors in front of a bridge under construction.) Voice from above: "Fotch it dahn coom on fotch it dahn A tell tha well turn it tother rooad sooin." "It really is quite incomprehensible, my dear colleague, how anyone can carry out such complicated and precise work in such language." [Culture and Value, 15e]
and compares the dangers of philosophical work to the construction of a building:
I believe Bacon got bogged down in his philosophical work, and this is a danger that threatens me too. He had a vivid image of a huge building which, however, faded when he really wanted to get down to details. It was as through his contemporaries had begun to erect a great building, from the foundations up; and as though he, in his imagination, had seen something similar, a vision of such a building, an even more imposing vision perhaps than that of those doing the building work. For this he needed to have an inkling of the method of construction, but no talent whatever for building. But the bad thing about it was that he launched polemical attacks on the real builders and did not recognize his own limitations, or else did not want to [Culture and Value, 68e]
Wittgenstein also uses construction-oriented examples in the first part of the Philosophical Investigations. Throughout his discussion on primitive language, Wittgenstein presents the picture of a builder and his assistant:
The language is meant to serve for communication between a builder A and an assistant B. A is building with building-stones: there are locks, pillars, slabs and beams. B has to pass the stones, and that in the order in which a needs them. For this purpose they use a language consisting of the words "block", "pillar", "slab", "beam" [Philosophical Investigations, #2]
He continues to use this example when discussing language used as numbers [Philosophical Investigations, #9] and in explaining the attachment of a label to an object [Philosophical Investigations, #20].
There are at least three other examples that stand out as direct parallels to engineering. Within his discussion on primitive language, Wittgenstein indirectly alludes to one of these - the engineering educational technique of laboratory learning:
Are "there" and "this" also taught ostensively? - Imagine how one might perhaps teach their use. One will point to places and things but in this case the pointing occurs in the use of the word too and not merely in learning the use [Philosophical Investigations, #9].
Engineering students often have the opportunity to apply what they have learned in lecture through a series of laboratory assignments. It is the hands-on application of theory that is often the most effective method of teaching. This concept parallels Wittgensteins assertion that learning the use of words is partly in the actual use of the words themselves.
Secondly, in engineering graphics, the sides of a three-dimensional object are often projected into various "planes of view". This projection simplifies the perception of the object and provides a clear two-dimensional picture from which accurate information can be obtained. Wittgenstein uses this same geometrical concept to explain the repetition with variation found in his works:
Each of the sentences I write is trying to say the whole thing, i.e. the same thing over and over again; it is though they were all simply views of one object seen from different angles [Culture and Value, 7e].
Finally, in the Tractatus, Wittgenstein uses truth tables to illustrate the existence and non-existence of states of affairs. Truth tables are often used in by engineers to design circuitry. The terms and, not, and or are used to define a set of conditions for which an event will or will not occur. These "gates", as they are more commonly known, typically allow current to pass or not pass through certain wires. They are similar to mechanical switches that are either open or closed, on or off.
In his philosophy of language, Wittgenstein asserts that "A proposition is an expression of agreement and disagreement with truth-possibilities of elementary propositions" [Tractatus, 4.4]. He chooses to express these truth-possibilities in the form of truth tables similar to those used by engineers:
We can represent truth-possibilities by schemata of the following kind (T means true, F means false; the rows of Ts and Fs under the row of elementary propositions symbolize their truth-possibilities in a way that can
be easily understood) [Tractatus, 4.31]
Wittgenstein would have been exposed to these concepts in his training as an engineer. His use of truth tables to explain the logic of language stands out as another direct parallel to the design of circuitry in the engineering profession.
Wittgenstein draws from the realms of geometry and mathematics, chemistry and mechanics to illustrate his philosophy of language. The examples he uses in the Tractatus, his Philosophical Investigations and throughout his notes in Culture and Value parallel his formal education and experiences as an engineer.
"Thinking is essentially the activity of operating with signs."
- Ludwig Wittgenstein, 1933
Most students encounter basic geometrical proofs in their second or third year of high school education. Although most students may never see them again, engineering students are exposed to similar proofs throughout their college education. Engineering students are continually exposed to propositions that explain and provide conditions for determining the truth or falsity of scientific and mathematical assertions. These propositions, or more commonly called theorems and corollaries, consist of particular phases that are consistent over engineering courses and disciplines. Phrases such as "let X equal ", "if B exists then " and "define C as " are typical within the proof of a theorem. This precise delineation of terms is required in the fields of engineering, science and mathematics. In the same way, when laying out a scenario before the reader, Wittgenstein uses these types of phrases and definitions to explain his philosophy.
The Tractatus was written in such a way as to show the logic of language. In many cases, Wittgenstein represents the form of a sentence with letters just as an engineer or mathematician might express a physical system by its empirical formula. In describing the spatial arrangement of written signs, Wittgenstein suggests that:
Instead of, The complex sign "aRb" says that a stands to b in the relation R, we ought to put, That "a" stands to "b" in a certain relation says that aRb. [Tractatus, 3.1432]
He goes on to describe actual sentences as functions of variables:
For let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition F(F(fx)), in which the outer function F and the inner function F must have different meanings, since the inner one has the formf(fx) and the outer one has the form y(f(fx)) This immediately becomes clear if instead of F(Fu) we write ($ f):F(fu). fu = Fu. [Tractatus, 3.333]
In Wittgensteins mind this functional format clears up a paradox using a numerical language that is typically common to a mathematician or an engineer. Wittgenstein continues to convert language into mathematical logic using infinite series notation:
For n states of affairs, there are Kn = å ( ) possibilities of existence or non-existence. Of these states of affairs any combination can exist and the remainder not exist. [Tractatus, 4.27]
In addition, Wittgenstein uses if-then statements similar to the one below:
If we are given a proposition, then with it we are also given the results of all truth-operations that have it as their base. [Tractatus, 5.442]
Wittgensteins use of truth tables (4.31-5.1) and probability functions (5.15-5.156) is another example of engineering and mathematical concepts at work in the format of his presentation. Another use of this type of language is seen in the following two propositions:
In the Philosophical Investigations the use of mathematical statements is not as prevalent as in the Tractatus. Wittgenstein does use this technique, however, in at least two cases. In a portion of his discussion on primitive language, Wittgenstein again uses language familiar to the engineer. Proposition #8 begins much like a mathematical proof:
let it contain a series of words let there be two words
Wittgenstein did not simply state the facts; rather he presented them in this proof type format. Again in proposition #64, Wittgenstein uses a similar phrase:
Let such a rectangle be called "U"
In proposition #51:
In order to see more clearly, here as in countless similar cases, we must focus on the details of what goes on; must look at them from close to."
Looking at something "from close to", more commonly called "taking the limit of" in engineering, is a technique used to approximate a curve as it approaches zero or some other fixed value. Wittgenstein alludes to this mathematical concept of a limit to describe focusing on details of an event. From my experience, only someone with a background in mathematics and engineering would use this presentation format to explain the subject of language.
REPETITION WITH VARIATION
"The repeat is necessary. In what respect is it necessary?
Well, sing it and you will see that only the repeat gives it its tremendous power."
- Ludwig Wittgenstein, Culture and Value
Wittgenstein uses many different scenarios to expresses the same idea. This method of repetition with variation is prevalent throughout the Philosophical Investigations. Take Wittgensteins discussion of reading, for example. He uses various situations to reveal our alleged misinterpretations of what it means to be able to read. Wittgenstein begins (much like an engineer would) by defining terms:
First I need to remark that I am not counting the understanding of what it means to read as part of reading for purposes of this investigation: reading is here the activity of rendering out loud what is written or printed; and also of writing from dictation, writing out something printed, playing from a score, and so on [Philosophical Investigations, #156].
His then introduces the notion of an Englishman who is able to read. Wittgenstein suggests that the Englishman reads the words by "taking in their printed shapes as wholes [or] first syllables [or] syllable by syllable [and occasionally] perhaps letter by letter" [Philosophical Investigations, #156]. This Englishman can either attend to his reading (he is able to repeat the sentence word for word after he has read it) or function as a reading-machine (when questioned immediately after reading, is unable to relate what he was reading about). Next, Wittgenstein introduces the beginning reader. A teacher may say that the beginning reader is not really "reading" or is only pretending to read since the beginning reader may only be "laboriously spelling [each word] out" or partly knows the passage by heart.
Wittgenstein then goes on to suggest that there may be no difference in what goes on in an experienced reader or a beginning reader. He does this by presenting various cases corresponding to features found in experienced and beginning readers. Wittgenstein introduces creatures used as "reading-machines" [Philosophical Investigations, #157]. In one case, these machines know how to read by translating marks into spoken words in a particular way (experienced reader). In another case, the machine translates marks into sounds in the same fashion as a player piano (beginning reader). Next Wittgenstein uses symbols, "Suppose A and B " to describe "memorization reading" where A attempts to make B believe A is reading [Philosophical Investigations, #159]. In this case, A has more of a sensation of cheating than reading (beginning reader). Wittgenstein then introduces the scenario of a person on drugs who utters sounds and has the "sensation" of reading much like an experienced reader [Philosophical Investigations, #160]. Wittgenstein questions additional conceptions of reading by bringing up common situations such as words simply coming to mind [Philosophical Investigations, #165] or the inability to recollect what has been read. Once a solution seems to be at hand, Wittgenstein raises another question leading to a subsequent contradiction.
Wittgenstein uses the technique of repetition with variation to illustrate other concepts as well. One such example is found in his discussion of being guided:
You are in a playing field ready for the tug of [the leaders] hand
someone leads you by the hand by force.
you are guided by a partner in a dance
someone takes you for a walk
you walk along a field-track, simply following it.
[Philosophical Investigations, #172]
Wittgenstein goes on to discuss the similarities and differences between these situations and call their commonality into question. In using repetition with variation, Wittgenstein was able to refute many different views of language. He attacked misconceptions not from merely one, but from many different and significant angles. Wittgenstein was able to target many different schools of thought, connecting with individuals by delving into their own realm of thinking [class notes, 1998].
Much like the philosophy of Wittgenstein, engineering material is taught in many different ways to accommodate the vast range of individual student learning styles. Professors lecture at the blackboard, engage students in problem solving and often form student teams to tackle design problems. The instructor incorporates many different teaching methods designed to make connections with as many students as possible. Just as Wittgenstein has many philosophical constructs at his disposal, engineering professors have at least five problem-solving activities in which to engage their students.
Henry Lester Plants, professor emeritus in the department of mechanical engineering at West Virginia University, has identified these problem-solving activities as 1) routine, 2) diagnosis, 3) strategy, 4) interpretation, and 5) generation [Schwartz, 1996]. Some problems are routine, requiring students to simply perform a sequence of given steps in order to find a solution to the problem. When these steps are not given, however, students must engage in diagnosis. They must chose between various correct and incorrect routines in order to select the one or ones most appropriate for the solution of the problem. When several correct routines are possible, the students must have a strategy for determining which is best for use in the situation at hand. Once selected, the routine is typically applied to a set of real-world data. In forming an interpretation of the real world, students gather this set of data by making appropriate assumptions about the particular situation. Another form of interpretation addresses the implications of the problem solution in the real world. The final problem solving technique is the invention or generation of new problem solving routines. Within a design team students have the opportunity to participate in all or some of these activities. A student is able to see the problem from various points of view, mathematical, theoretical and/or applied, and is able to gain a better understanding than if the student were exposed to only one problem solving technique.
Wittgensteins method of repetition with variation is a common technique used to communicate the actual concepts in many engineering courses as well. Engineering concepts are multifaceted and are presented to students in a variety of ways. Many engineering courses, especially at the freshman/sophomore level and again at the graduate level, are interdisciplinary. Introductory physics courses contain all types of engineering students as well as chemists, biologists and computer scientists. Graduate level mechanical engineers almost always need to take a course in electrical and computer engineering and vice versa. It is often common for mechanical engineers to have difficulty in visualizing electrical engineering concepts. There is often an effort to provide a mechanical equivalent for circuit diagrams used in electrical engineering classes. In the same way, mechanical mechanisms are reduced to circuit diagrams to accommodate electrical engineering students. Furthermore, mechanical and electrical systems are often presented as systems in the human body in an attempt to make them clear to other groups of students.
With good reason, engineering research and design is subjected to harsh scrutiny. Therefore, repetition with variation is also used to analyze engineering proposals. When designing a new machine or introducing a new process, engineers must take into consideration much more than just the efficiency of the design. Ethical, environmental and financial aspects must be taken into consideration. By teaching an engineer to explore all aspects of a design, he or she will be able to determine where problems may occur. The engineer will then be prepared to defend a design from many different standpoints.
In his philosophy of language, Wittgenstein uses repetition with variation to target many different schools of thought. Similarly, engineering educators use repetition with variation to accommodate varying student learning styles. Wittgenstein is able to connect with unique individuals through repetition with variation in the same way that engineering educators attempt to speak in each disciplines own language. Just as engineers evaluate designs from various angles, Wittgenstein explored the many facets of language in his philosophical investigations.
LEVEL OF CLARITY OR ANALYSIS
Is it even always an advantage to replace an indistinct picture by a sharp one?
Isnt the indistinct on often exactly what we need?
- Ludwig Wittgenstein, Philosophical Investigations
An amusing article appeared in the September 1996 issue of the American Society for Engineering Education (ASEE) Prism magazine. A coach decides to take the engineering curriculum of a large university and turn it into a baseball training schedule. He starts out teaching the rules of the game and makes sure everyone is on the same footing when it comes to physical condition and technique. Games were left for the last two weeks of the season as a culmination to all they had learned in the first six weeks. The coach was not discouraged when many of the players found the training boring and resigned. He figured that if they could not handle the rigorous schedule they might as well get out early. Needless to say, the team had a terrible season and even though they improved when given experience on the field, they were so discouraged that the team was dissolved. However, although none became successful ball players, their knowledge of the game enabled many of them to obtain great jobs as broadcasters and sports columnists.
This analogy highlights a weakness in some engineering curricula. Students who express an interest in engineering are highly encouraged to pursue this ambition. Many lose interest, however, after being swamped with math and science courses that have hardly a hint of engineering content. Those students who are not discouraged and do well in these classes still have to labor through other courses designed to "weed" out students who "arent serious" about engineering. Those who make the cut are finally introduced to design projects that are required for graduation. Most students, however, are not ready for such a task since they have had no previous experience in practical design.
There is an ongoing debate as to whether or not first and second year engineering students should be exposed to design problems. Some argue that first and second year students should be concerned with learning the basics of engineering computational methods and measurement systems. Others argue that not exposing students to design on the onset of their education will foster disinterest in the field by sheltering the students from a real-world concept of engineering. They contend that students should begin to learn how to think like an engineer right from the start.
Introducing design in the initial stages of the engineering curriculum, however, must be done in a manner that gives students enough information to understand the basic concepts without being overwhelmed by an abundance of detailed information. This is what I see current engineering curricula trying to accomplish by providing a wide range of courses prior to allowing students substantive design experience. Engineering students first learn measurement techniques and calculus principles at a basic level. Physics and chemistry courses usually follow providing a basic understanding of the physical world. As students proceed in the engineering curriculum, they are exposed to higher levels of calculus and analysis of physical systems. Engineering educators provide a level of clarity or analysis only to the point where understanding occurs. However, we could ask in this case, "Is a blurred [engineering] concept a concept at all?"
Let us say that we want to teach students about the effects of gravity on a car sitting at the top of an inclined plane. A course in trigonometry will teach the student how to resolve the force vector due to gravity into components. In a first dynamics course, a student learns which component of gravity allows friction to hold the car on the ramp and which component causes the car to roll down the ramp. Many assumptions are made, however, to allow for ease in calculation of these forces. In a second dynamics course, allowances are made for events such as slipping of the tires. In a junior level gas dynamics course, other phenomena could be taken into consideration such as wind drag and sonic forces (depending on the speed of the vehicle). A first dynamics student, faced with the daunting task of considering all possible effects, would likely give upon the whole exercise. Sometimes the blurry concept is all that is really needed.
This concept is prevalent in Wittgensteins Philosophical Investigations in opposition to the view of a precise, definitive language found in the Tractatus. Wittgenstein uses the example of a broom to suggest that understanding is not necessarily based on the level of clarity or analysis. He suggests that making a statement about the "position of the stick and the position of the brush" would be a further analyzed sentence than "My broom is in the corner" [Philosophical Investigations, #60]. Wittgenstein concludes, "This sentence achieves the same as the ordinary one, but in a more roundabout way." Wittgenstein also raises the question of the desire for exact and essential information:
If I tell someone "Stand roughly here" may not this explanation work perfectly? And cannot every other one fail too? [Philosophical Investigations, #88]
In speaking of the purpose of a lamp:
The essential thing is that this is a lamp, that it serves to give light; - that it is an ornament to the room, fills an empty space, etc., is not essential [Philosophical Investigations, #62].
Wittgenstein concludes that, " there is not always a sharp distinction between essential and inessential" information [Philosophical Investigations, #62].
Engineering concepts are typically analyzed in stages. Information is given that is not necessarily complete or exact but that is essential to a particular level of understanding. In the same way, the goal of Wittgensteins theory of language in the Philosophical Investigations is not "a state of complete exactness" [Philosophical Investigations, #91]. Engineers are exposed to deeper and deeper levels of analysis to clarify concepts as they advance in their education. Although there may arise the need for deeply analyzed propositions in language, Wittgenstein concludes with the statement, "Does it matter which we say, so long as we avoid misunderstandings in any particular case?" [Philosophical Investigations, #48].
IDEAL AND NON-IDEAL CHARACTERISTICS
"We want to walk so we need friction. Back to the rough ground!"
- Ludwig Wittgenstein, Philosophical Investigations
When engineers first attempt to implement a particular device within a system, assumptions are usually made about the components of the device. These assumptions are made in an attempt to eliminate some of the difficulties associated with the application of the device in the real world system. This is accomplished by stripping down some or all of its components to an "ideal" form. In practice, however, the performance of these components is far less than ideal. Often times, the engineer finds that the idealized characteristics of the components inadequately model its actual performance within the device. The engineer re-designs the device taking into consideration more and more non-ideal characteristics of its components, until the device functions properly within the system.
Electrical circuits, for example, are used to power and control various electrical and mechanical systems. In the medical field, an electrocardiogram (ECG or EKG) is one such system. An ECG monitors a patients heart by capturing the voltages induced on the surface of the body during each heart cycle and converting these voltages, or potentials, into graphical form that can be seen on a monitor. Since the potential on the surface of the body is so small, its electrical signal must be amplified and filtered using a circuit configuration known as an ECG amplifier.
The ECG amplifier is a device containing various electrical components such as resistors, capacitors, and operational amplifiers (op amp). The most complex component of an ECG amplifier is arguably the op amp. An op amp is a solid state device that has a very high resistance to incoming current. This characteristic is more commonly known as high input impedance. Using a high impedance op amp in an ECG minimizes the perturbation of the subject. In other words, less current is drawn from the body thereby protecting the patient and improving the quality of the signal that is obtained. Although the inner workings of the op amp are complicated, assumptions can be made about this component, making it as easy to work with as a resistor or a capacitor.
As a rule, certain ideal characteristics are attributed to an op amp. The characteristics of an ideal op amp are detailed in the figure below:
Ideal Operational Amplifier Characteristics
1. A = ¥ (Gain is infinite)
2.Vout = 0, when V1 = V2 (No current flows)
3.Rd = ¥ (Input impedance is infinite)
4.Ro = 0 (Output impedance is zero)
5. Bandwidth = ¥ (No frequency response limits)
For various reasons, these ideal characteristics make the op amp easy to implement within an ECG amplifier or any other device. In reality, however, a gain (1), impedance, (3) or a bandwidth (5) can never be infinite. The output resistance is not really zero (4) due in part to hardware limitations. Also, the voltages at the terminals (2) can not be exactly equal since some current must flow in order to provide a portion of the power required by the op amp.
In the initial stages of ECG amplifier design, the consideration of only the ideal characteristics of the op amp is sufficient. The circuit is examined to determine the influence of the non-ideal characteristics. If the non-ideal characteristics become important, a new design is created taking these characteristics into consideration. The circuit is checked once again, and the process of re-design continues until the amplifier performs according to the desired behavior. In the real world, discrepancies from the ideal exist. In fact, it is these non-ideal characteristics that, in many ways, support the proper function of the system.
Wittgenstein seems to apply a similar method of analysis to a system of thought. Within a system of thought there exists a device called philosophy. A component of this device is language. In the Tractatus, Wittgenstein attempts to strip language down to its ideal form so that it can be properly used in philosophical investigation. He breaks language into sets of "facts" and "atomic facts", in an effort to arrive at an ideal form of language. Wittgenstein wants to "draw a limit to the expression of thought" [Tractatus, pp. 3] with definite boundaries and rules:
(and did lead me) to think that if anyone utters a sentence and means or understands it here is operating a calculus according to definite rules [Philosophical Investigations, #81].
Once this was achieved, the logic of language would be shown. People would no longer be tempted to speak "nonsense" and the problems of philosophy would disappear.
Just as an ECG amplifier will not function on the basis of ideal op amp characteristics, Wittgenstein found that language does not function on the basis of pure logic. With a further examination of the tractarian model of language, Wittgenstein finds it to be inadequate to describe language in the real world. In his Philosophical Investigations, Wittgenstein takes into consideration the non-ideal characteristics of language. "For the crystalline purity of logic was, of course, not a result of investigation; it was a requirement" [Philosophical Investigations, #107]. Wittgenstein contends that the relationships between a group of words are important, rather than a common logical thread among them:
Wittgenstein urges the reader "dont think, but look!" [Philosophical Investigations, #66]. He asserts that there is not a concrete meaning for every word, but rather, "the meaning of a word is its use in the language" [Philosophical Investigations, #43]. He also refutes the idea that precise, unbounded definitions are necessary, since "any general definition can be misunderstood" [Philosophical Investigations, #71] and that exactness is not "the real goal of our investigation" [Philosophical Investigations, #91]. Instead of relying on an ideal form of language, Wittgenstein contends that "The sign-post [i.e. language] is in order if, under normal circumstances, it fulfils its purpose" [Philosophical Investigations, #87]. This non-ideal view of language is more practical, allowing for cultural and social differences within meanings of a word. To address the original issue of philosophical problems, Wittgenstein introduces the notion of "language-games" in which words have their context and meaning. He surmises that philosophical problems arise when words are incorrectly used within the context of a language game. By redesigning his view of language taking these non-ideal characteristics into account, Wittgenstein surmises that philosophy may now function properly.
Ideal component characteristics are used in engineering to avoid difficulties that arise when analyzing complicated subjects. Once the fundamental components are understood they can be modified and put back together in a way that makes the entire system more efficient. The relationships between components are often the very things that allow the system to have meaning. In language, a similar relationship can be seen between the Tractatus and the Philosophical Investigations. Even if Wittgenstein did not have this mode of analysis in mind at the onset of the Tractatus, the parallel to this method of engineering problem solving is found in his writing.
Wittgensteins training in engineering seemed to give him a methodical approach to problems of philosophy. The examples he used and the format in which he chose to write, are familiar to the engineering profession. Repetition with variation and analysis based on the level of understanding, are methods used throughout the engineering curriculum that are also found in Wittgensteins philosophical works. The application of ideal characteristics of language in the Tractatus, then modification to include non-ideal characteristics in the Philosophical Investigations, is typical of engineering analysis as a whole. This is only a sample of the parallels between engineering and Wittgensteins writing style. Whether or not Wittgensteins intentionally used his engineering background to model his philosophy will never really be known. Further research is required to determine the similarities and differences between engineering education of then and of now. However, one thing seems clear: even though Wittgenstein did not continue to pursue his formal education as a career, he was able to draw from his experiences in engineering to help elucidate his ideas on the philosophy of language.
Class notes, Discussions in EPS 408 with Burbules and Peters, Fall 1998.
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Monk, R., Ludwig Wittgenstein: The Duty of Genius. New York: Penguin, 1990.
Prados, J.P., Who we are: some musings on the nature of science and engineering,
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Safe Haven, Ludwig Wittgenstein,http://www.ultranet.com/~rsarkiss/WITTGEN.HTM
Schwartz, R.A., Five types of problem solving, ASEE Prism, 11, September 1996.
Wittgenstein, L., Culture and Value. Illinois: University of Chicago Press, 1980.
Wittgenstein, L., Philosophical Investigations. Massachusetts: Blackwell Publishers Ltd., 1953.
Wittgenstein, L., Tractatus Logico-Philosophicus. New York: Routlege & Kegan Paul, 1961.