Postmodern Metaphysics and Evolution

Christos Yannaras is a fascinating Greek philosopher of whom I know too little to say anything more than that what I have read has been mind-expanding, explanatory, and beyond my grasp.

In his book Postmodern Metaphysics, he includes what he calls two “parentheses,” the first on “the logical place of chance” and the second on “the logical place of evolution.”

Under the second parenthesis, he lists 35 points, which I’ll call propositions, each of which is intended to explore “the place of evolution” with great precision. Before beginning, he footnotes Wittgenstein from his Tractatus, where the great mystical philosopher said this:

Darwin’s theory has no more to do with philosophy than any other hypothesis in natural science.”

And:

“Philosophy sets limits to the much disputed sphere of natural science.”

I agree with his second point, but I don’t see how the first can be true. I don’t mean to say that Darwin’s theory controls philosophy or overthrows it. That can’t be done for the simple reason that humans will always think about what is and what is knowable and the natural sciences will never be able to answer either of those questions.

However, I don’t see how either 1. every hypothesis of natural science can have nothing to say about philosophy and yet philosophy can set limits to the sphere of natural science or 2. all the hypotheses of natural science can be equally related to philosophy.

Regarding the first option, I understand philosophy to be a different activity to natural science; a more inclusive activity, but one that certainly includes the discoveries of the natural sciences and is informed by them. That is why, until the 18th century, the natural sciences were called “natural philosophy.”

Does philosophy have nothing to learn from the natural sciences?

Regarding the second option, if any hypotheses of the natural sciences have any impact at all on philosophy, it’s hard for me to see how all of these hypotheses would have the same impact on philosophy.

For example, Newton’s theories about gravity and all that had an unbelievable impact on the historical development of philosophy (and education) in England. Is Wittgenstein suggesting that the very fact that Newton’s theories impacted the development of philosophy demonstrates that the philosophers were in error (pardon the long subject)? Should philosophy remain impervious to what the natural sciences develop?

Or might the fact that Newton’s theories impacted philosophy prove that his theories were wrong?

Is Wittgenstein placing philosophy outside the reach of natural science? Then how can philosophy set limits for the natural sciences? Doesn’t something have to step down from its glory to limit something below it?

I don’t mean to speculate idly. If Wittgenstein is right and I am understanding him correctly, then we have built a society on the natural sciences, unlimited by philosophy, and it can’t work because it won’t correspond to reality.

Furthermore, if he is right, then Darwin’s theory is just a play thing. But it’s hard to imagine that. Everywhere I look I see evidence of Darwinism’s reach into ethics, politics, theology, ontology, pedagogy, etc.

Is this because the people in those fields are perfectly wrong in their application of Darwinism?

So we begin this “parenthesis” on the logical place of evolution by noting how confusing it is to try to find a logical place in the first place. I don’t know if Yannaras is referring to Wittgenstein as the starting point and foundation for his argument, to illustrate something, or to challenge him. We’ll see.

As I said, there are 35 propositions described by Yannaras, and I’m not going to copy them all here. But I hope to think through them with you over the next little while (along with I Corinthians and maybe even Julius Caesar and Pelikan’s Christianity and Classical Culture and maybe even Pagan Christianity).

The point of this post is, first, to let you know I’m going to be discussing this text and the idea of evolution vis postmodern philosophy, and second, to give some hints about the difficulties that we’re going to be confronted by.

Please note that my immediate experiment is philosophical, not strictly theological. I believe that theology settles a lot of these questions, but I still want to look at them from the philosophical perspective to see what it has to show us.

So here’s the first proposition, which I’ll discuss in a later post:

Parenthesis 2
The “logical place” of the theory of Evolution

If the sense of the world exists it must lie “outside” the world. If the world has no sense, then even the question concerning the existence or nonexistence of meaning must make its appearance under severely endocosmic presuppositions. The theory of evolution is a proposition that interprets these presuppositions. 

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4 Responses

  1. Andrew–

    I need to add to my first full paragraph of my latest response, which was as follows:

    I agree with your main point about W.’s statement in 4.116. Sometimes natural human language (as opposed to formal language, such as the notations used in math, logic, chemical and physical formulas, etc.) just can’t express an idea/thought as clearly as we’d like. As proof, consider the hard work of translating a piece of writing accuratey from one natural language into another: the saying is true that “something is always lost in translation” (well, not ALWAYS, but frequently).

    What needs to be added is this: It is generally held that there is a “later W.” and an “early W.” In his later writings, he practically turns his back on his earlier logical positivist, logical atomist, mathematical logic, formal language, and even mystical approach. He is all about natural, “ordinary” language and its vagaries in his later writings, the Blue and Brown Books, etc. Which is to say that he likely ended up agreeing with you and me that language (i.e., natural, ordinary language) cannot clearly express every thought, and that he gave up hope of equating science with “all the true propositions” there could ever be.

  2. Andrew–

    Glad it was helpful.

    I agree with your main point about W.’s statement in 4.116. Sometimes natural human language (as opposed to formal language, such as the notations used in math, logic, chemical and physical formulas, etc.) just can’t express an idea/thought as clearly as we’d like. As proof, consider the hard work of translating a piece of writing accuratey from one natural language into another: the saying is true that “something is always lost in translation” (well, not ALWAYS, but frequently).

    However, I disagree with your statement that it’s possible that NOTHING that is thought can be expressed clearly. For one thing, if this were true, it would mean that it might be the case that nothing in Scripture is clear, which would violate the clearly true Reformational doctrine of the perspicuity of the Scriptures. For another, think how often we all look at something we’ve written and say to ourselves, “What I have here written expresses clearly, accurately, and beautifully that which I intended to convey.”

    I’ve not yet had the pleasure of reading Gilson’s The Unity of Philosophical Experience. Can you give me a brief summary?

    Shalom,

    Tim

  3. Andrew–

    Dr. Tim Deibler here, Head of School at Covenant Academy in Houston (Cypress), TX.

    I ran across your fascinating blog on Christos Yannaras and Wittgenstein some weeks ago, but have only now found the time to comment. (Anytime someone mentions words such as ‘postmodern’, ‘metaphysics’, and ‘evolution’ in the same breath, you’ve got me hooked. Throw in ‘Wittgenstein’ as well, and I’m a goner.)

    I well remember studying Wittgenstein during my philosophy Ph.D. work at Rice University. Following my required phil. and logic courses and seminars, I focused primarily on the phil. of language in the analytic tradition, and of course W. looms large in that realm. The early W. of the Tractatus is indeed somewhat mystical, as you characterize him, but in a very unusual way, because he is all the while dealing with highly technical concepts, specifically, the philosophy of modern symbolic logic. He frequently alludes to Frege and Russell. He is really seeking to establish the relation between language, logic, and the world around us. And he finds he has to get pretty metaphysical (in the phil. sense of course, not the occult) to do that. In the process he makes certain remarks about how science, language, and logic are related.

    I have pasted below quite a long section from the Tractatus because it gives the context for his remarks about Darwin’s theory and how phil. sets the limits of natural science. You can readily see how the discussion arises in the context of his remarks about propositions, thoughts, the logical space they mark out, and the symbolic logic terms that must be used to describe and refer to (“picture”) them.

    W.’s remark about Darwin’s theory constitutes point #4.1122 in the Tractatus. The immediate context runs as follows:

    4.1 Propositions represent the existence and non-existence of states of affairs.
    4.11 The totality of true propositions is the whole of natural science (or the whole corpus of the natural sciences).
    4.111 Philosophy is not one of the natural sciences. (The word ‘philosophy’ must mean something whose place is above or below the natural sciences, not beside them.)
    4.112 Philosophy aims at the logical clarification of thoughts. Philosophy is not a body of doctrine but an activity. A philosophical work consists essentially of elucidations. Philosophy does not result in ‘philosophical propositions’, but rather in the clarification of propositions. Without philosophy thoughts are, as it were, cloudy and indistinct: its task is to make them clear and to give them sharp boundaries.
    4.1121 Psychology is no more closely related to philosophy than any other natural science. Theory of knowledge is the philosophy of psychology. Does not my study of sign-language correspond to the study of thought-processes, which philosophers used to consider so essential to the philosophy of logic? Only in most cases they got entangled in unessential psychological investigations, and with my method too there is an analogous risk.
    4.1122 Darwin’s theory has no more to do with philosophy than any other hypothesis in natural science.
    4.113 Philosophy sets limits to the much disputed sphere of natural science.
    4.114 It must set limits to what can be thought; and, in doing so, to what cannot be thought. It must set limits to what cannot be thought by working outwards through what can be thought.
    4.115 It will signify what cannot be said, by presenting clearly what can be said.

    You can see that W. defines natural science as the totality of all true propositions. And he specifically says that philosophy is not one of the natural sciences and must stand either above or below natural science. Thus, since W. thinks of science as all the true propositions that there could ever be (a very idealized notion of science), he is limiting ‘proposition’ to having a very specialized content, while also claiming, wittingly or unwittingly, that philosophy does not contain propositions at all, at least, not in his sense.

    But W. clearly does not want to say that all philosophy is nonsensical–which would be the case if it contained no propositions, unless there can be thoughts that are not expressed in propositions, something he seems to deny early on in the long section I’ve included below–since he of course knows that he himself is writing a philosophical work. (Interestingly, he does claim that much earlier philosophical work is indeed nonsensical, because “[M]ost of the propositions and questions of philosophers arise from our failure to understand the logic of our language.” See point #4.003.)

    Thus, W. seems to think of philosophy as an enterprise somehow “above” science that, among other things, is capable of setting limits to science. He implies that this capability is due to philosophy’s main role of “clarifying” propositions. (By the way, W. here paves the way for the notion that the main job of 20th C. analytic phil., epitomized by the phil.of language, far from the aims of previous philosophy to establish truths in metaphysics, ethics, political thought, etc., is mere “conceptual analysis”.)

    This would mean that natural science, including Darwin’s theory, has nothing to do with philosophy. You can see that W. is thinking of philosophy in a very special and contemporary way. He is thinking of it as highly specialized and normative (in the sense of providing clarification), but as incapable of discovering/establishing any real structures or truths within the world (including metaphysical and ethical truths), other than mathematical, logical and linguistic structures, all of which would be mere analytic (tautological) truths in Kant’s sense, rather than synthetic . He could care less whether IN FACT Darwin’s theory affected the philosophy of the 19th C. in any particular way or not, or Newton’s science the philosophy of HIS day, because those philosophies weren’t doing the REAL job philosophy is supposed to do.

    Now, I don’t know what use Christos Yannaras wants to make of W., since I have never read Y. All I’m commenting on here is your inquiry into W.’s own meaning in his remarks about natural science, Darwin, philosophy, and how philosophy sets limits to natural science. I hope some of this proves useful to you.

    Many blessings, and Soli Deo Gloria,

    Tim

    __________________________________

    4 A thought is a proposition with a sense.
    4.001 The totality of propositions is language.
    4.022 Man possesses the ability to construct languages capable of expressing every sense, without having any idea how each word has meaning or what its meaning is–just as people speak without knowing how the individual sounds are produced. Everyday language is a part of the human organism and is no less complicated than it. It is not humanly possible to gather immediately from it what the logic of language is. Language disguises thought. So much so, that from the outward form of the clothing it is impossible to infer the form of the thought beneath it, because the outward form of the clothing is not designed to reveal the form of the body, but for entirely different purposes. The tacit conventions on which the understanding of everyday language depends are enormously complicated.
    4.003 Most of the propositions and questions to be found in philosophical works are not false but nonsensical. Consequently we cannot give any answer to questions of this kind, but can only point out that they are nonsensical. Most of the propositions and questions of philosophers arise from our failure to understand the logic of our language. (They belong to the same class as the question whether the good is more or less identical than the beautiful.) And it is not surprising that the deepest problems are in fact not problems at all.
    4.0031 All philosophy is a ‘critique of language’ (though not in Mauthner’s sense). It was Russell who performed the service of showing that the apparent logical form of a proposition need not be its real one.
    4.01 A proposition is a picture of reality. A proposition is a model of reality as we imagine it.
    4.011 At first sight a proposition–one set out on the printed page, for example–does not seem to be a picture of the reality with which it is concerned. But neither do written notes seem at first sight to be a picture of a piece of music, nor our phonetic notation (the alphabet) to be a picture of our speech. And yet these sign-languages prove to be pictures, even in the ordinary sense, of what they represent.
    4.012 It is obvious that a proposition of the form ‘aRb’ strikes us as a picture. In this case the sign is obviously a likeness of what is signified.
    4.013 And if we penetrate to the essence of this pictorial character, we see that it is not impaired by apparent irregularities (such as the use [sharp] of and [flat] in musical notation). For even these irregularities depict what they are intended to express; only they do it in a different way.
    4.014 A gramophone record, the musical idea, the written notes, and the sound-waves, all stand to one another in the same internal relation of depicting that holds between language and the world. They are all constructed according to a common logical pattern. (Like the two youths in the fairy-tale, their two horses, and their lilies. They are all in a certain sense one.)
    4.0141 There is a general rule by means of which the musician can obtain the symphony from the score, and which makes it possible to derive the symphony from the groove on the gramophone record, and, using the first rule, to derive the score again. That is what constitutes the inner similarity between these things which seem to be constructed in such entirely different ways. And that rule is the law of projection which projects the symphony into the language of musical notation. It is the rule for translating this language into the language of gramophone records.
    4.015 The possibility of all imagery, of all our pictorial modes of expression, is contained in the logic of depiction.
    4.016 In order to understand the essential nature of a proposition, we should consider hieroglyphic script, which depicts the facts that it describes. And alphabetic script developed out of it without losing what was essential to depiction.
    4.02 We can see this from the fact that we understand the sense of a propositional sign without its having been explained to us.
    4.021 A proposition is a picture of reality: for if I understand a proposition, I know the situation that it represents. And I understand the proposition without having had its sense explained to me.
    4.022 Man possesses the ability to construct languages capable of expressing every sense, without having any idea how each word has meaning or what its meaning is–just as people speak without knowing how the individual sounds are produced. Everyday language is a part of the human organism and is no less complicated than it. It is not humanly possible to gather immediately from it what the logic of language is. Language disguises thought. So much so, that from the outward form of the clothing it is impossible to infer the form of the thought beneath it, because the outward form of the clothing is not designed to reveal the form of the body, but for entirely different purposes. The tacit conventions on which the understanding of everyday language depends are enormously complicated.
    4.003 Most of the propositions and questions to be found in philosophical works are not false but nonsensical. Consequently we cannot give any answer to questions of this kind, but can only point out that they are nonsensical. Most of the propositions and questions of philosophers arise from our failure to understand the logic of our language. (They belong to the same class as the question whether the good is more or less identical than the beautiful.) And it is not surprising that the deepest problems are in fact not problems at all.
    4.0031 All philosophy is a ‘critique of language’ (though not in Mauthner’s sense). It was Russell who performed the service of showing that the apparent logical form of a proposition need not be its real one.
    4.01 A proposition is a picture of reality. A proposition is a model of reality as we imagine it.
    4.011 At first sight a proposition–one set out on the printed page, for example–does not seem to be a picture of the reality with which it is concerned. But neither do written notes seem at first sight to be a picture of a piece of music, nor our phonetic notation (the alphabet) to be a picture of our speech. And yet these sign-languages prove to be pictures, even in the ordinary sense, of what they represent.
    4.012 It is obvious that a proposition of the form ‘aRb’ strikes us as a picture. In this case the sign is obviously a likeness of what is signified.
    4.013 And if we penetrate to the essence of this pictorial character, we see that it is not impaired by apparent irregularities (such as the use [sharp] of and [flat] in musical notation). For even these irregularities depict what they are intended to express; only they do it in a different way.
    4.014 A gramophone record, the musical idea, the written notes, and the sound-waves, all stand to one another in the same internal relation of depicting that holds between language and the world. They are all constructed according to a common logical pattern. (Like the two youths in the fairy-tale, their two horses, and their lilies. They are all in a certain sense one.)
    4.0141 There is a general rule by means of which the musician can obtain the symphony from the score, and which makes it possible to derive the symphony from the groove on the gramophone record, and, using the first rule, to derive the score again. That is what constitutes the inner similarity between these things which seem to be constructed in such entirely different ways. And that rule is the law of projection which projects the symphony into the language of musical notation. It is the rule for translating this language into the language of gramophone records.
    4.015 The possibility of all imagery, of all our pictorial modes of expression, is contained in the logic of depiction.
    4.016 In order to understand the essential nature of a proposition, we should consider hieroglyphic script, which depicts the facts that it describes. And alphabetic script developed out of it without losing what was essential to depiction.
    4.02 We can see this from the fact that we understand the sense of a propositional sign without its having been explained to us.
    4.021 A proposition is a picture of reality: for if I understand a proposition, I know the situation that it represents. And I understand the proposition without having had its sense explained to me.
    4.022 A proposition shows its sense. A proposition shows how things stand if it is true. And it says that they do so stand.
    4.023 A proposition must restrict reality to two alternatives: yes or no. In order to do that, it must describe reality completely. A proposition is a description of a state of affairs. Just as a description of an object describes it by giving its external properties, so a proposition describes reality by its internal properties. A proposition constructs a world with the help of a logical scaffolding, so that one can actually see from the proposition how everything stands logically if it is true. One can draw inferences from a false proposition.
    4.024 To understand a proposition means to know what is the case if it is true. (One can understand it, therefore, without knowing whether it is true.) It is understood by anyone who understands its constituents.
    4.025 When translating one language into another, we do not proceed by translating each proposition of the one into a proposition of the other, but merely by translating the constituents of propositions. (And the dictionary translates not only substantives, but also verbs, adjectives, and conjunctions, etc.; and it treats them all in the same way.)
    4.026 The meanings of simple signs (words) must be explained to us if we are to understand them. With propositions, however, we make ourselves understood.
    4.027 It belongs to the essence of a proposition that it should be able to communicate a new sense to us.
    4.03 A proposition must use old expressions to communicate a new sense. A proposition communicates a situation to us, and so it must be essentially connected with the situation. And the connexion is precisely that it is its logical picture. A proposition states something only in so far as it is a picture.
    4.031 In a proposition a situation is, as it were, constructed by way of experiment. Instead of, ‘This proposition has such and such a sense, we can simply say, ‘This proposition represents such and such a situation’.
    4.0311 One name stands for one thing, another for another thing, and they are combined with one another. In this way the whole group–like a tableau vivant–presents a state of affairs.
    4.0312 The possibility of propositions is based on the principle that objects have signs as their representatives. My fundamental idea is that the ‘logical constants’ are not representatives; that there can be no representatives of the logic of facts.
    4.032 It is only in so far as a proposition is logically articulated that it is a picture of a situation. (Even the proposition, ‘Ambulo’, is composite: for its stem with a different ending yields a different sense, and so does its ending with a different stem.)
    4.04 In a proposition there must be exactly as many distinguishable parts as in the situation that it represents. The two must possess the same logical (mathematical) multiplicity. (Compare Hertz’s Mechanics on dynamical models.)
    4.041 This mathematical multiplicity, of course, cannot itself be the subject of depiction. One cannot get away from it when depicting.
    4.0411 If, for example, we wanted to express what we now write as ‘(x) . fx’ by putting an affix in front of ‘fx’–for instance by writing ‘Gen. fx’–it would not be adequate: we should not know what was being generalized. If we wanted to signalize it with an affix ‘g’–for instance by writing ‘f(xg)’–that would not be adequate either: we should not know the scope of the generality-sign. If we were to try to do it by introducing a mark into the argument-places–for instance by writing ‘(G,G) . F(G,G)’ –it would not be adequate: we should not be able to establish the identity of the variables. And so on. All these modes of signifying are inadequate because they lack the necessary mathematical multiplicity.
    4.0412 For the same reason the idealist’s appeal to ‘spatial spectacles’ is inadequate to explain the seeing of spatial relations, because it cannot explain the multiplicity of these relations.
    4.05 Reality is compared with propositions.
    4.06 A proposition can be true or false only in virtue of being a picture of reality.
    4.061 It must not be overlooked that a proposition has a sense that is independent of the facts: otherwise one can easily suppose that true and false are relations of equal status between signs and what they signify. In that case one could say, for example, that ‘p’ signified in the true way what ‘Pp’ signified in the false way, etc.
    4.062 Can we not make ourselves understood with false propositions just as we have done up till now with true ones?–So long as it is known that they are meant to be false.–No! For a proposition is true if we use it to say that things stand in a certain way, and they do; and if by ‘p’ we mean Pp and things stand as we mean that they do, then, construed in the new way, ‘p’ is true and not false.
    4.0621 But it is important that the signs ‘p’ and ‘Pp’ can say the same thing. For it shows that nothing in reality corresponds to the sign ‘P’. The occurrence of negation in a proposition is not enough to characterize its sense (PPp = p). The propositions ‘p’ and ‘Pp’ have opposite sense, but there corresponds to them one and the same reality.
    4.063 An analogy to illustrate the concept of truth: imagine a black spot on white paper: you can describe the shape of the spot by saying, for each point on the sheet, whether it is black or white. To the fact that a point is black there corresponds a positive fact, and to the fact that a point is white (not black), a negative fact. If I designate a point on the sheet (a truth-value according to Frege), then this corresponds to the supposition that is put forward for judgement, etc. etc. But in order to be able to say that a point is black or white, I must first know when a point is called black, and when white: in order to be able to say,'”p” is true (or false)’, I must have determined in what circumstances I call ‘p’ true, and in so doing I determine the sense of the proposition. Now the point where the simile breaks down is this: we can indicate a point on the paper even if we do not know what black and white are, but if a proposition has no sense, nothing corresponds to it, since it does not designate a thing (a truth-value) which might have properties called ‘false’ or ‘true’. The verb of a proposition is not ‘is true’ or ‘is false’, as Frege thought: rather, that which ‘is true’ must already contain the verb.
    4.064 Every proposition must already have a sense: it cannot be given a sense by affirmation. Indeed its sense is just what is affirmed. And the same applies to negation, etc.
    4.0641 One could say that negation must be related to the logical place determined by the negated proposition. The negating proposition determines a logical place different from that of the negated proposition. The negating proposition determines a logical place with the help of the logical place of the negated proposition. For it describes it as lying outside the latter’s logical place. The negated proposition can be negated again, and this in itself shows that what is negated is already a proposition, and not merely something that is prelimary to a proposition.
    4.1 Propositions represent the existence and non-existence of states of affairs.
    4.11 The totality of true propositions is the whole of natural science (or the whole corpus of the natural sciences).
    4.111 Philosophy is not one of the natural sciences. (The word ‘philosophy’ must mean something whose place is above or below the natural sciences, not beside them.)
    4.112 Philosophy aims at the logical clarification of thoughts. Philosophy is not a body of doctrine but an activity. A philosophical work consists essentially of elucidations. Philosophy does not result in ‘philosophical propositions’, but rather in the clarification of propositions. Without philosophy thoughts are, as it were, cloudy and indistinct: its task is to make them clear and to give them sharp boundaries.
    4.1121 Psychology is no more closely related to philosophy than any other natural science. Theory of knowledge is the philosophy of psychology. Does not my study of sign-language correspond to the study of thought-processes, which philosophers used to consider so essential to the philosophy of logic? Only in most cases they got entangled in unessential psychological investigations, and with my method too there is an analogous risk.
    4.1122 Darwin’s theory has no more to do with philosophy than any other hypothesis in natural science.
    4.113 Philosophy sets limits to the much disputed sphere of natural science.
    4.114 It must set limits to what can be thought; and, in doing so, to what cannot be thought. It must set limits to what cannot be thought by working outwards through what can be thought.
    4.115 It will signify what cannot be said, by presenting clearly what can be said.
    4.116 Everything that can be thought at all can be thought clearly. Everything that can be put into words can be put clearly. 4.12 Propositions can represent the whole of reality, but they cannot represent what they must have in common with reality in order to be able to represent it–logical form. In order to be able to represent logical form, we should have to be able to station ourselves with propositions somewhere outside logic, that is to say outside the world.
    4.121 Propositions cannot represent logical form: it is mirrored in them. What finds its reflection in language, language cannot represent. What expresses itself in language, we cannot express by means of language. Propositions show the logical form of reality. They display it.
    4.1211 Thus one proposition ‘fa’ shows that the object a occurs in its sense, two propositions ‘fa’ and ‘ga’ show that the same object is mentioned in both of them. If two propositions contradict one another, then their structure shows it; the same is true if one of them follows from the other. And so on.
    4.1212 What can be shown, cannot be said.
    4.1213 Now, too, we understand our feeling that once we have a sign-language in which everything is all right, we already have a correct logical point of view.
    4.122 In a certain sense we can talk about formal properties of objects and states of affairs, or, in the case of facts, about structural properties: and in the same sense about formal relations and structural relations. (Instead of ‘structural property’ I also say ‘internal property’; instead of ‘structural relation’, ‘internal relation’. I introduce these expressions in order to indicate the source of the confusion between internal relations and relations proper (external relations), which is very widespread among philosophers.) It is impossible, however, to assert by means of propositions that such internal properties and relations obtain: rather, this makes itself manifest in the propositions that represent the relevant states of affairs and are concerned with the relevant objects.
    4.1221 An internal property of a fact can also be bed a feature of that fact (in the sense in which we speak of facial features, for example).
    4.123 A property is internal if it is unthinkable that its object should not possess it. (This shade of blue and that one stand, eo ipso, in the internal relation of lighter to darker. It is unthinkable that these two objects should not stand in this relation.) (Here the shifting use of the word ‘object’ corresponds to the shifting use of the words ‘property’ and ‘relation’.)
    4.124 The existence of an internal property of a possible situation is not expressed by means of a proposition: rather, it expresses itself in the proposition representing the situation, by means of an internal property of that proposition. It would be just as nonsensical to assert that a proposition had a formal property as to deny it.
    4.1241 It is impossible to distinguish forms from one another by saying that one has this property and another that property: for this presupposes that it makes sense to ascribe either property to either form.
    4.125 The existence of an internal relation between possible situations expresses itself in language by means of an internal relation between the propositions representing them.
    4.1251 Here we have the answer to the vexed question ‘whether all relations are internal or external’.
    4.1252 I call a series that is ordered by an internal relation a series of forms. The order of the number-series is not governed by an external relation but by an internal relation. The same is true of the series of propositions ‘aRb’, ‘(d : c) : aRx . xRb’, ‘(d x,y) : aRx . xRy . yRb’, and so forth. (If b stands in one of these relations to a, I call b a successor of a.)
    4.126 We can now talk about formal concepts, in the same sense that we speak of formal properties. (I introduce this expression in order to exhibit the source of the confusion between formal concepts and concepts proper, which pervades the whole of traditional logic.) When something falls under a formal concept as one of its objects, this cannot be expressed by means of a proposition. Instead it is shown in the very sign for this object. (A name shows that it signifies an object, a sign for a number that it signifies a number, etc.) Formal concepts cannot, in fact, be represented by means of a function, as concepts proper can. For their characteristics, formal properties, are not expressed by means of functions. The expression for a formal property is a feature of certain symbols. So the sign for the characteristics of a formal concept is a distinctive feature of all symbols whose meanings fall under the concept. So the expression for a formal concept is a propositional variable in which this distinctive feature alone is constant.
    4.127 The propositional variable signifies the formal concept, and its values signify the objects that fall under the concept.
    4.1271 Every variable is the sign for a formal concept. For every variable represents a constant form that all its values possess, and this can be regarded as a formal property of those values.
    4.1272 Thus the variable name ‘x’ is the proper sign for the pseudo-concept object. Wherever the word ‘object’ (‘thing’, etc.) is correctly used, it is expressed in conceptual notation by a variable name. For example, in the proposition, ‘There are 2 objects which. . .’, it is expressed by ‘ (dx,y) … ‘. Wherever it is used in a different way, that is as a proper concept-word, nonsensical pseudo-propositions are the result. So one cannot say, for example, ‘There are objects’, as one might say, ‘There are books’. And it is just as impossible to say, ‘There are 100 objects’, or, ‘There are !0 objects’. And it is nonsensical to speak of the total number of objects. The same applies to the words ‘complex’, ‘fact’, ‘function’, ‘number’, etc. They all signify formal concepts, and are represented in conceptual notation by variables, not by functions or classes (as Frege and Russell believed). ‘1 is a number’, ‘There is only one zero’, and all similar expressions are nonsensical. (It is just as nonsensical to say, ‘There is only one 1’, as it would be to say, ‘2 + 2 at 3 o’clock equals 4’.)
    4.12721 A formal concept is given immediately any object falling under it is given. It is not possible, therefore, to introduce as primitive ideas objects belonging to a formal concept and the formal concept itself. So it is impossible, for example, to introduce as primitive ideas both the concept of a function and specific functions, as Russell does; or the concept of a number and particular numbers.
    4.1273 If we want to express in conceptual notation the general proposition, ‘b is a successor of a’, then we require an expression for the general term of the series of forms ‘aRb’, ‘(d : c) : aRx . xRb’, ‘(d x,y) : aRx . xRy . yRb’, … , In order to express the general term of a series of forms, we must use a variable, because the concept ‘term of that series of forms’ is a formal concept. (This is what Frege and Russell overlooked: consequently the way in which they want to express general propositions like the one above is incorrect; it contains a vicious circle.) We can determine the general term of a series of forms by giving its first term and the general form of the operation that produces the next term out of the proposition that precedes it.
    4.1274 To ask whether a formal concept exists is nonsensical. For no proposition can be the answer to such a question. (So, for example, the question, ‘Are there unanalysable subject-predicate propositions?’ cannot be asked.)
    4.128 Logical forms are without number. Hence there are no preeminent numbers in logic, and hence there is no possibility of philosophical monism or dualism, etc.
    4.2 The sense of a proposition is its agreement and disagreement with possibilities of existence and non-existence of states of affairs. 4.21 The simplest kind of proposition, an elementary proposition, asserts the existence of a state of affairs.
    4.211 It is a sign of a proposition’s being elementary that there can be no elementary proposition contradicting it.

    • Dr. Deibler,

      It certainly does prove useful, as per your final paragraph. I have to go through W more slowly as time permits, but your summary and your explanation of W’s very precise definition of philosophy helps a lot. I hate to be simplistic about a gigantic intellect like W’s, but he clearly has either created or is functioning in a thought world that arises from philosophers and not from nature. He has radically redefined natural science in opposition to the philosophical tradition at least up to Bacon/Descartes, but even, practically speaking, well beyond them.

      By making natural science all truth, he expands its reach beyond its power or else defines its meaning beyond usefulness.

      Thus, of course, he is among the multitude of 19th and 20th century intellectuals who attempt to destroy philosophy by redefining it, thus denying its existence.

      At 4.116 I believe he reveals another error. I could just as easily contend that nothing that is thought can be expressed clearly. Thrasymachus and Descartes were also terribly distracted by this standard of excessive clarity. It puts a burden on language that language can’t bear – and thus on thought.

      Dr. D. have you read Gilson’s The Unity of Philosophical Experience? I’d be very interested in your response to that work.

      Thanks for you help!

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