Induction From The Observations Of Singular Events example essay topic

Introduction After presenting an outline of Carnap's article, I want to proceed to critique his position. Firstly, I will offer a critique of Carnap's proposition that "science begins with direct observations of single facts". Secondly, I will try to point out the peculiarities and contradictions, that Carnap will necessarily have to fall into by taking on a logical positivistic and empiricist position. Thirdly, I will try to point out the weaknesses of induction and the impossibility of arriving at "theoretical laws" as well as the principle of induction using only the method of induction. At last, I will discuss Carnap's understanding of probability and weather or not his use of it is justified. As a critique I will use Edith Steins "Einf " uhrung in die Philosophie", especially in showing that the observation of single facts, cannot be the starting point in science.

Fritz Wenisch's "Untersuchung zum Methodenproblem in der Philosophie" will be useful in showing the contradiction of Carnap's assumption that we only arrive at knowledge through induction. Chalmers "What is this thing called Science" I will discuss in so far as it is helpful to clarify the difference between the meaning of Carnap's "theoretical laws", Chalmers concept of "theory" and Hildebrand's demonstration of the a priori. Hildebrand's " Introduction to Philosophy" will be used throughout this essay, in order to elucidate the importance of acknowledging a priori propositions as a foundation of science. Before I proceed with an outline and criticism of Carnap's article, I would like to say a few general things about logical positivism, of which Carnap is a major representative. I. Logical positivism and the claim that all knowledge is achieved through induction Logical positivism was first introduced in 1931 by Blumen berg and Herbert Feign.

It is often referred to as "consistent empiricism", "logical empiricism", and "scientific empiricism". In a wider context, the term is also used to include the "analytic" or "ordinary language" philosophy developed at Cambridge and Oxford. The latter is a direct consequence of the first. We will see why. The logical positivistic position can be seen as the attempt, to account for the general principles of mathematics, logic and theoretical physics, without abandoning the doctrine, that science is the description of experience and the only source of knowledge. The defense of this doctrine of naturalism, which leaves no room for the knowledge gained through insight, must also evidently have an effect on the way language is used.

For the logical positivists, the only method of arrived at knowledge is induction: the inductive statements can never be necessary, at most only highly probable. Terms like "truth" and "necessity" have a conventional use, but essentially no meaning. We are not so much concern in this essay with the ills of "analytic" language philosophy. I just wanted to point out, that analytic language philosophy is in many ways a direct outcome of the empiricists initial claim "That all science starts with observable events" What I am concerned with, is the initial claim and doctrine, which is implicitly present in Carnap's article. It is not always easy, to realize, that at the basis of all his assumptions lies a faulty epistemology.

Nevertheless, it is very important, when reading Carnap, that we keep in mind, that he is making claims, that he as an inductivist cannot adhere to, without falling into contradiction. II. Carnap's confirmation of laws and theories and the method of induction The starting point of all science, so Carnap, is the observation of singular events, which he calls facts. "Of course" so Carnap "all our knowledge has its origin in singular statements - the particular observation of particular individuals... science begins with direct observation of single facts. Nothing else is observable". Facts are distinct from universal statements, they are called laws.

The statement "this woman is blond" corresponds to the observation of a singular event. To say that "all women are blond" is a "universal" statement. If we are not hallucinating, dreaming or severely projecting something into a fact, we can assume that "this women is really blond". We have to keep in mind, that fact that this specific women is blond, is a contingent one, she could also have red hair; But also the "universal" statement derived from this singular fact is never absolutely true. On the one hand, when we make a "particular statement" about a particular event, we are making nothing more than a statement about a fact that could be otherwise. On the other hand, when we generalize, that all women are blond, we are making a "universal" statement, that can never be absolutely certain.

Since by the observation of one singular event we do not see any necessity why all women should be blond, we have to observe many instances, many women, to be able to formulate a highly probable statement, one that we can call a "universal law"; a law that expresses certain regularities in nature, that have occurred so many times, "that we can have complete confidence in its truth" However, since there can be an infinity of instances as long as the world does not cease to exist tomorrow, we can never arrive at necessity, because we can never be absolutely certain to the degree, that we can say that all women are necessarily blond, even if all we see are blond women. Since tomorrow, or in ten years etc. can observe a red haired woman. If this is the case, how can we be justified in making universal claims about all, infinite possibilities, when we have only observed a finite amount of instances. This is what Carnap calls the problem of induction. Personally, I do not see much of a problem in the method of induction, if we treat it as the only source of knowledge.

That is, if we accept, what Wenisch calls a chreontic method in philosophy, one that accounts for necessary states of affairs as a fundamental foundation of the inductivist method. We can live with the fact that there are unnecessary and necessary states of affairs, chaotic and random, real-type and necessary entities, as Hildebrand classifies all real and unreal things. If, however, we adopt a naive empiricist epistemology, and Carnap has done just that, then I admit that we run into problems. It will be a major purpose of this essay, to point out the problems that have to arise. Before continue, I want to point out, that Carnap's use of terms like "truth" etc. would seem to be inconsistent with his persuasion that only observable facts exist. It is obvious that we can only have an "insight" into to truth, never empirically observe it.

How then is he justified to use the term. Let me just say, that Carnap was aware of this problem, and he spent quite some time of his academic career to figure out, how to rationalize such a "conventional" use of language. For now, we will just accept, that Carnap is using these terms for our sake. Carnap himself will make use of these "senseless" terms, because they are useful, not, however, because they are necessary. I do not want to offer this problem of Carnap as a major criticism, but I do believe that it, nevertheless, demonstrates the difficulties that arise if one refuses to accept a chreontic position, one that will enable us to reach outside of the merely probable. There are two apparent problems that I see, besides the contradictions that arise: Firstly, the positivist should ask themselves whether it is really worth it, to stick to a position that poses so many problems.

When Wittgenstein realized that his position would make ontological assertions senseless, Carnap went on to suggest, that they were not senseless, but meaningful assertion about language, not statements about a world beyond language. For me, this is just a way of shifting the problem. How can Carnap justify the fact, that the love for his wife (assuming he was married and loved his wife) to show only one example, was only meaningful insofar as it was an assertion about language. Secondly, I find it hard to belief, that Carnap's doctrines will not eventually lead to a denial of the real word all together. Because a more radical skepticism, (logical positivism is already a kind of skepticism, because it denies insight into essential necessities) is the only alternative to a chreontic position, if he is to avoid serious contradictions. Not to say, that even radical skepticism, as St. Augustine has shown in his Si fallow, sum - Argument, at least presupposes ones own existence. (if I doubt, I am).

Lets resume in presenting some plain arguments against the most basic assertion of logical positivism. Lets look at it again: Carnap states, that "all our knowledge has its origin in singular statements - the particular observation of particular individuals... science begins with direct observation of single facts. Carnap actually asserts three things: First, we can only arrive at knowledge through observation. Second, the only thing we can observe, are singular facts in the physical world. Hence, it is clear, i.e. that also our conscious acts are nothing more than an epiphenomenon of physical events. To this I will come back later.

Third, since we can only observe singular facts of the physical world, facts which are contingent by nature, (and "universal laws" about frequently observed contingent facts can themselves only be probable) necessary states of affairs are useless. Edith Stein has dealt with the problem of naturalism in her book "Einf " uhrung in die Philosophie", and there is one argument which is useful to point out the non-sensical starting point of Carnap. Edith Stein at first explicates two major motifs for having a naive attitude of cognition, which proclaims nature as the only reality. First, our experience and all our conscious activity is in some way intertwined with nature. We are persons that have bodies, and our consciousness is also confronted with things in nature that have bodily form. It is for this reason, that our conscious activity is seen, solely as an epiphenomenon of physical events, such as the events in our body.

The second motif of naturalism, and all its relatives (including all forms of empiricism) comes from the ideal that is put into science. Science has to be an exact science, a mathematical science; outside of nature guided by exact mathematical laws, there is no being. We have to keep in mind, that logical positivism is considered to be an exact science, and that the problem starts with their exclusion of one part of reality, that of essential necessities. Stein writes "If the exact mathematical science is not capable of accounting for the whole of reality, it can not yet be concluded, that whatever does not allow for an exact mathematical treatment, does not posses real being". If we look more closely at the assertion, that consciousness is an epi-phenomenon of physical events, we will be able to understand, that Carnap's claim, that all science starts with observable facts, is untenable. If we speak of consciousness as an epi-phenomenon, we speak of it as a side effect or secondary result of physical events.

By stating, that it is a side-effect or secondary result, we also state, that consciousness is not the same as the physical events which it is a result of. If we assume that the link between physical events and consciousness is a factual one, we have not yet said that it is a necessary one. "What do you mean, necessary", Carnap could of course reply "there is nothing aside from experience, and experience can never show necessary states of affairs". With this, he falls into a trap, into which all skeptics fall (we have already shown, that logical positivism is only another appearance of skepticism): Carnap's answer denies in content, what he logically presupposes. If he says that there is nothing outside of experience, then he states that "there is something at all" (namely, in experience); and the fact that there is at all, has to be necessarily presupposed.

This of course cannot be experience, but only understood by having an insight into the necessity "that there is". Stein concludes, that the mode of experience of facts in nature, that could be or not be, or could be of such a nature or another nature, is not applicable to the mode of pure cognition of our consciousness. "consciousness by its essence, cannot be grounded on nature" Such being the case, we can see, that not the observable facts are the starting point for science, rather it is the "insight" into essential necessary states of affairs, by which our thinking is governed, and which must fundamentally underlie all experience. Let me conclude Steins argument with a passage from Hildebrand's " Introduction to Philosophy": "Empirical observations are not the starting point for induction (author's note: consequently, for science. ).

Rather, with the beginning interpretation of empirical observations, a specifically philosophical (author's note: chreontic) cognition sets in, an interpretation, that builds on a priori insights and which proceeds with a definite philosophical method". A more fundamental criticism of the assertion that "all science starts with experienced facts" is offered by Fritz Wenisch in his book "Untersuchungen zum Methodenproblem in der Philosophie" (Invesitgations into the Problem of Method in Philosophy). There, Wenisch shows, that the denial of "insight" as a method in philosophy which that can lead to universal propositions, will inevitably result in a contradiction. Wenisch writes "The thesis, that there is a method of cognition based on insight, is not at all universally accepted today.

There are two ways, in which it can be denied: First, by making the assertion, that only universal propositions exist, which we arrive at through the principle of induction; second, by denying all together that we can know anything. The former is the thesis of logical empiricism, the latter seems to go into the direction of Poppers thesis... ". In this essay, we will not be concerned with the second assertion, instead we will turn our attention exclusively to the verification of the empiricist statement which Carnap himself formulates, and which for him serves as the starting point of science. Before we turn to, what I consider a very strong criticism by Wenisch, I will point to another bizarre fact that logical positivism has to face. As Carnap points out at the beginning of his article, a universal law of science can never be a necessary one.

If we want to confirm the law of thermal expansion, we cannot do so by insight, but we have to test many instances, without limiting our testing to metals and solid substances. No matter how many instances we test, we will always be confronted with a finite number. Hence, our assertion can never be absolute ones in the sense that we can say that a "universal law" must necessarily hold for all instances tested in the future. Although we can never be absolutely sure, we can nevertheless arrive at a certain "degree of confirmation".

Instead of saying, that a law is "well-founded" or "not well-founded", we can express this degree of confirmation numerically in what Carnap calls logical probability, as opposed to statistical probability. When we role a six sided die, then the statistical probability of number 5 and 6 appearing on the top is expressed in the ratio 2: 6 or 1: 3. Statistical probability is the measurement of absolute frequency. In the example of the die, we are confronted with an absolute number, which is six. In logical probability we are not confronted with absolute numbers. We are confronted with a finite numbers of instances, where actually there are infinite possibilities.

When we observe 100 cases of women that are blond, we do not actually have an absolute number of cases past, present and future. Here we are dealing with what Carnap calls relative frequency. Relative frequency expresses the ratio of 100 women to the total possible infinite number of women. What is important, however, is that Keynes, who first came up with the notion of logical probability, insisted that we can only intuit what logical probability is. If, like Carnap, we deny intuition as a means of arriving at knowledge of what logical probability is, then we could only arrive at what logical probability is through induction. But as we have already seen, inductive statements are never necessary, but only probable.

In other words, our knowledge of probability will in this case itself only be probable. To make things even more absurd, we can ask ourselves this question "how probable is probability? It is typical from the standpoint of a consistent logical positivist that he refuses, although he acknowledges these problem, to recognize "insight" as a valid method of philosophy, and in so doing end their dilemma instantly. We are therefor not surprised, when Carnap has the following to say about Keynes: "His book... gave a few axioms and definitions... but they are not very sound from a modern point of view.

Some of Keynes' axioms were actually definitions. Some of his definitions were really axioms. But his book is interesting from a philosophical standpoint... ". I for myself, understand Keynes position quite well. For if Carnap thinks that ontological statements are senseless, we might well be inclined to ask, how sensible it is, to make, what Carnap calls "meta-scientific" statements that are expressed numerically in the form of probable logical probabilities?

The following quote is from Carnap's article and will not be further commented by me: .".. we need logical probability. It is especially useful in metascientific statements, that is, statements about science. We say to a scientist, 'You tell me that I can rely on this law in making a certain prediction. How well established is the law? How trustworthy is the prediction? The scientist today may not be willing to answer a metascientific question of this kind in quantitative terms.

But I believe that, once inductive logic is sufficiently developed, he could reply, 'This hypothesis is confirmed to a degree. 8 on the basis of the available evidence. ' " (authors comment: maybe one day we could even say: "My love for you is confirmed to a degree. 8 on the basis of the available physical evidence) It is not my intention to engage into polemics; I only wanted to give an example of how far away logical positivism takes us from reality, by denying the essential necessities. Logical positivism cannot really deny essential necessity; they would have to admit that the existence of essential necessities are at least to some degree probable. This points to another peculiarity that we are confronted with in logical positivism. This is an argument that Wenisch gives; It is not as strong an argument, but it useful in pointing out another non-sensical position.

Lets look at the statement Carnap makes on page 124 of his article. There Carnap says: "The truth of an inductive conclusion is never certain". If Carnap only recognizes inductive-universal conclusions, then the assertion "The truth of an inductive conclusion is never certain" must have been found through inductive reasoning. He could not give apodictic character to this assertion. The fact, that "the truth of an inductive conclusion is never certain" would itself be uncertain.

Carnap would therefor be forced to leave open the possibility, that one day, he could come across an example of an induction, that did not have an uncertain conclusion. In other words, he would have to admit, that he could one day have an "insight" that there are necessary "universal" statements. It is, of course, not possible to ever run across an induction, that could lead to subjective necessity; for this reason, Wenisch suggest, it would be more reasonable to admit apodictic certainty to the assertion, that "the truth of an inductive conclusion is never certain". The strongest arguments against logical positivism is the apparent contradiction that it involves itself in. Russell admitted to this contradiction. In his book on the "Problems of Philosophy" he writes: "We have already seen, that the answer of the pure empiricists - that our mathematical knowledge is derived through induction from the observations of singular events - is untenable for two reasons: First, the principle of Induction cannot itself be validated through induction and second, it is evident, that we can recognize the validity of propositions like 2 x 2 = 4, by looking at one single example".

In order to clarify this contradiction, we will again look at the principle that governs inductions. According to this principle, we are justified to grant probability to a "universal" claim about the whole of instances, if the observation of a certain amount of instances will always be the same. If we observe a hundred cases of smart IAP students, then we are justified to grant probability to the "universal" claim, that all IAP students are smart. This principle of induction must have already existed, before any concrete induction was performed. If, however, as Carnap states, we can only arrive at universal knowledge through induction, than the principle of induction must have existed before it existed. This is the apparent contradiction into which the logical positivists fall.

It must be admitted that at least the principle of induction is expressed in an non-inductive argument. This being the case, logical positivism is refuted, alongside with Carnap and his rejections of all philosophical question. In light of this evident contradiction it is hard to understand, apart from the two motifs we have already mentioned above, how Carnap can reject synthetic a priori propositions and the necessary states of affairs to which they relate (see p. 133 of Carnap's article). Chalmers' criticism of Carnap and the position of "naive inductionism". Chalmers' book "What is this thing called Science?" offers some good criticism of what he calls "naive inductionism". And according to his definition of it, we can assume that Carnap is included in this criticism.

Chalmer writes: "According to the naive inductivist, science starts with observation". Carnap writes. ".. science begins with direct observation of single facts". (p. 123) We have already criticized Carnap's assertion, that all science "begins with direct observation of single facts". We have also seen, that Carnap presupposes necessary states of affairs, although he denies them. Furthermore we have seen, that the denial of a valid philosophical method based on "insight" must necessarily lead to contradiction. In addition to the circular ities involved in attempts to justify the principle of induction, there are other deficiencies involved.

For instance, how many observations have to be made, Chalmers poses the following question: Should a metal bar be heated ten times, a hundred times or one thousand times, before we can conclude that this metal will always expand when we heat it. Well if the answer is, that we have to observe a large number of facts and not one singular event, what about the explosion of the atomic bomb in Hiroshima. Is it really necessary to repeat this event many times, before we can conclude that it causes a great deal of harm? How many times do I have to stick my hand into the fire, before I can conclude that fire burns and what are the criteria for determining how many times we have to experience events, before we can reach any certain conclusion? Do we arrive at these criteria by method of induction? The answer is clear, that we have to appeal to our theoretical knowledge of things, in order to understand what is significant and what is not.

Carnap does not yet disagree. He recognizes that we have to separate "empirical laws" from "theoretical laws"; and that we need theory to discover new empirical laws. But Carnap could never admit "that theory plays a vital role prior to (all) observation. The naive inductivist, cannot afford to make such an admission". In order to go around this problem, Carnap has attempted to show, how "theoretical laws" are only further derivatives of "empirical laws".

All science starts with the observation of events that are directly observable. From these observables we arrive at general "empirical laws" which in turn make possible "theoretical laws", such as the theory an the atomic structure of solid substances. We cannot observe the atoms in the substance (they are non-observables), but with the help of other observations and in relying on the probability of "empirical laws", we can make further assumptions. In the case of the law of thermal expansion, which we can directly verify in heating the substance, we can then make further assumptions about inner structure of the substance, and see if these assumption can hold in the light of direct observable facts. Carnap refines his initial starting point, adding that science actually starts with, what he know calls direct observables.

Observables are easily explained. If we can directly sense an event, for instance when we sense the voice of our friend, we speak of observables. In the case of atomic particles, which we cannot directly sense, we are confronted with non-observables. For Carnap, this distinction is important to demonstrate, that theoretical laws are not presupposed in the observation of the direct observable color red, for example. It is clear that in the case of the atomic particles, we cannot observe anything directly. Without the help of "theoretical laws" universal laws making predictions about atomic particles could not be formulated in any way.

Carnap does not deny that theoretical knowledge is necessary in more complicated in-direct observation. But he claims, that theoretical knowledge is again derived only from directly observable facts: "Theoretical laws are related to empirical laws in a way somewhat analogous to the way empirical laws are related to single facts. An empirical law helps to explain a fact that has been observed and to predict a fact not yet observed. In similar fashion, the theoretical law helps to explain empirical laws already formulated and to permit the derivation of new empirical laws". This assertion of Carnap is directly opposed by Chalmers, who grants priority of theory over observation. Chalmers says: "Theories may be, and usually are, conceived of prior to the making of those observations necessary to test them".

This assertion of Chalmers is not the same position Hildebrand has: Hildebrand does not speak of a priority of theory over observation, but of a priori insights that underlie any interpretation of observation. Here we are referring to essential necessary links, that are presupposed in the evaluation of any observable fact. Hildebrand is pointing to the fact, that we could not even interpret observable events, and make sense of them, without relying on a priori insights. The meaning of "theory" in Chalmers is at times vague: "It will... become increasingly clear as this book progresses that it is essential to understand science as an historically evolving body of knowledge and that a theory can only be adequately appraised if due attention is paid to its historical context" Chalmers assumption does not yet refute Carnap's position. Since it is possible, that all historical scientific knowledge is initially derived from "empirical laws" that are in turn derivatives of directly observable events.

In another instance, Chalmers attempts to refute the inductivist position, in pointing out that we persons can have different experience although the sense-perception is the same. One and the same fact can be observed but experienced differently. He uses the example of a picture of a tree that contains the outline of a human face. In looking at the image, some people will recognize the face, others will only see the tree. "In this example", says Chalmers "what an observer sees is affected by his knowledge and experience...

". Although we see the same thing, it does not follow that we have "identical perceptual experience". Chalmers' example is important in showing, that sense perception and experience are not the same. In the light of this example, it will be difficult for the inductivist to arrive at universal laws dependent on experience that can vary given the same sense perception of an object. Chalmer points a very important problem, that an inductivist account of reality will have to face. The inductivist will argue, that the meaning of the simple concept "red", is acquired through observation.

There are two difficulties involved in that: first, as we have already seen, we have to assume that every sense-perception of the color red equally corresponds to the experience of the color red. Second, the inductivist assumes, that we arrive at the concept red, by isolating among an infinitude of sight perceptions all those, that have the common quality red. But what is the criterion, according to which we can isolate one set of sight-perception from another. The criterion, of course, is that only perceptions of red objects are isolated from the others. But this presupposes the very concept redness, the acquisition of which it is meant to explain.

The very fact that we can separate one quality from another, presupposes that quality. Although Chalmers has shown that we cannot experience the concepts "redness" the way the inductivist understand it, he does not answer the question why this is so. It will be helpful to introduce Hildebrand's elucidation of the term "experience". First, experience can refer to the observations of singular events and to induction. Second, experience can refer to the concrete acquisition of a "such being" that cannot be otherwise. (so-sein), as in the experience of the color "red". Yet we have to at least experience it in this way, for the first time.

A blind person, will never have a concept of red. But this dependency on experience of a thing the way it is (so-sein), does not imply an impairment of a-priori experiences of color. Having experienced colors, we have an insight into the a priori statement, that "orange lies between red and yellow". This distinction between the two types of meanings of experience is important for the following reasons: When Chalmer claims, that we presupposes the very concept redness in the inductivist account of experience, what really is the case, is that we presuppose the experience of a thing the way it is (Soseinserfahrung). The reason why I am pointing this out, is that, an inductionism could one day broaden his account of experience to include the experience of thing the way it is, without having to admit to the insight of a priori necessities. I think it is clear, that logical positivism and their claim "that all knowledge begins with experience" can only be refuted, when point to the existence of necessary entities such as the "principle of contradiction".

Only chreontic philosophy can justify knowledge apart from experience and can show that necessary states of affairs are presupposed by logical positivism. We can therefore, as Chalmers does, only speak of "theory" presupposed by experienced, when by "theory" we mean those necessary laws, that govern all being. Carnap, Rudolf: The Confirmation of Laws and Theories, in Kournay (ed) Carnap, Rudolf: Theories and Non observables, in Fetzer (ed) Stein, Edith: Einf " uhrung in die Philosophie, Herder: Wien, 1991. Von Hildebrand, Dietrich: What is Philosophy?

, Kohl hammer: Stuttgart 1976. Wenisch Fritz: Untersuchungen zum Methodenproblem in der Philosophie, Habilitation schrift, Universit " at Salzburg: 1971. Chalmers, A.F. : What is this thing called Science? , Hackett: Cambridge, Indianapolis, 1976.