Charlus wil weer eens van geen ophouden weten. [Archief]

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Charlus

02-06-09, 19:15

AdamRon

02-06-09, 19:43

Verdorie Charlus,
Je bent sneller als ik...
Ik zal maar geen nieuwe topic aanmaken maar deze in de gaten houden

Rourchid

04-06-09, 05:54

ARE MATHEMATICAL TRUTHS SYNTHETIC A PRIORI? *
The outlines of the partial answer that I can offer to this question have been argued for in my earlier papers.1 In the present one, I shall first summarize their relevant aspects.
*To be presented in an APA symposium on Mathematical Truth. December 29, 1968. Commentators will be Richard Montague and Charles D. Parsons.
1 See the following papers of mine: "Are Logical Truths Analytic?," Philosophical Review, LXXIV, 2 (April 1965): 178—203; "Kant’s ‘New Method of Thought’ and His Theory of Mathematics," Ajatus, XXVII (1965): 37—47; "An Analysis of Analyticity," in Deskription, Analytizität und Existenz, 3—4 Forschungsgespräch des internationalen Forschungszentrums Salzburg, ed. Paul Weingartner (Salzburg and Munich: Verlag Anton Pustet, 1966), pp. 193—214; "Are Logical Truths Tautologies?," ibid., pp. 215—233; "Kant Vindicated," ibid., pp. 234—253; "Kant and the Tradition of Analysis." ibid., pp. 254—272; "Kant on the Mathematical Method," The Monist, LI, 3 (July 1967): 352—375; "On Kant’s Notion of Intuition (Anschauung)," forthcoming in a collection of papers on Kant’s Critique of Pure Reason, eds. Terence Penelhum and J. H. MacIntosh, in the series Wadsworth Studies in Philosophical Criticism (Belmont, Calif.: Wadsworth).　
The question was initially posed by Kant, and most existing discussions of it refer in so many words to Kant. On the pain of gross historical distortion, one cannot therefore help discussing the question in Kantian terms. Now the examples of mathematical reasoning that Kant mentions and discusses are typically formalizable in first-order logic. Hence any historically accurate reading of the question turns it into a problem concerning the status of logical as much as mathematical truths. Again, by ‘synthetic truths’ Kant did not mean truths that do not turn solely on the meanings of the terms they contain, as a contemporary philosopher is likely to mean. I have argued that the best explication we can offer of Kant’s notion of an analytic truth (in first-order logic) is what I have called a surface tautology. Interpreted in this way, Kant’s doctrine of the existence of synthetic a priori truths in what he took to be mathematics turns out to be correct in an almost trivial fashion, for there are easily any number of valid (and provable) sentences of first-order logic that are not surface tautologies.
Instead of offering yet another exposition of these points, I shall in this paper comment on one particular aspect of the situation which I have not elaborated elsewhere and which seems to possess a great potential interest from a general philosophical point of view. This aspect is the nature of the kind of information (surface information) that goes together with the notion of surface tautology. An examination of this concept seems to open wide philosophical perspectives which are highly relevant to the traditional discussion of the possibility of synthetic a priori truths and to its background in idealistic philosophy.
For the purpose, let me first recapitulate how the concept of surface information can be defined and how it behaves.2 Let us assume that we are dealing with a given fixed first-order language with a finite number of predicates but (for simplicity) without individual constants. Define the depth of a sentence s as the length of the longest chain of nested and connected quantifiers in s. (Two quantifiers which contain the bindable variables x and y and of which the latter occurs within the scope of the former, are connected if there are quantifiers which occur within the scope of the former and which contain the variables z1, z2, . . . , zk such that x and z1, zi and zi+1 (i = 1, 2, . . . k — 1), zk, and y occur in the same atomic formula in s.) Each closed sentence of depth d can be effectively transformed into a disjunction of pairwise exclusive sentences of an especially simple structure, called (closed) constituents of the same depth. Likewise, each open sentence of depth d (with certain individual variables z1, . . . , zk) can be transformed into a similar distributive normal form (i.e., into a disjunction of constituents with the same depth and with the same variables). Some of these are effectively recognized as being, in a specifiable sense, trivially inconsistent. Roughly speaking, this means that two parts (not necessarily consecutive) of such a constituent contradict each other propositionally. Since there is no decision procedure for the whole of first-order logic, there must exist nontrivially inconsistent constituents, too, which cannot be effectively recognized.
2 A background for the following discussion is given by the following papers (in addition to those mentioned in the preceding footnote): "Distributive Normal Forms in First-order Logic," in J. N. Crossley and M. A. E. Dummett, eds., Formal Systems and Recursive Functions: Proceedings of the Eighth Logic Colloquium, Oxford, July 1963 (Amsterdam: North-Holland, 1965), pp. 47—90; and "Distributive Normal Forms and Deductive Interpolation," Zeitschrift für mathematische Logik und Grundlagen der Mathematik, x (1964): 185—191.
There exists, however, a systematic procedure for weeding out more and more inconsistent but not trivially inconsistent constituents. All we have to do is to keep on adding to the depth of our constituents (while preserving of course the same predicates and the same individual variables). At each addition to the depth of a constituent, it is usually split into a disjunction of a number of deeper constituents, which are said to be subordinate to the given one. These can be tested for trivial inconsistency, and it may happen that they are all trivially inconsistent although the original, shallower constituent was not. Moreover, it can be shown that at a sufficiently great depth the inconsistency of each inconsistent constituent and, hence, the inconsistency of each inconsistent sentence, is eventually betrayed in this way. This result, which I have proved in detail elsewhere, constitutes a completeness theorem for our method of enumerating inconsistencies.
If a probability-like measure (system of weights) is defined on the set of all consistent sentences, the weight of each consistent Constituent is split up between all its consistent subordinate constituents (of a fixed depth). Such weights will be called measures of inductive probability, and by their means one can define in the usual way measures of information, called depth information.3 One especially simple way is to put contdepth (s)= 1 — pind (s)= pind(~s), where ‘cont’ means "informative content" and ‘p’ "inductive probability."
3 For the different kinds of information, cf. my paper "The Varieties of Information and Scientific Explanation," in B. van Rootselaar, ed., Logic, Methodology, and Philosophy of Science, Proceedings of the 1967 International Congress in Amsterdam (Amsterdam: North-Holland, 1968), pp. 151—171.
It is remarkable that all natural-looking principles of assigning measures of inductive probability and depth information are non- recursive. For instance, if the weight w of each constituent of depth d is always divided evenly between all the consistent subordinate constituents of depth d + 1, one can tell the weight of one of the latter constituents (as a function of w) if and only if one knows the number of these consistent subordinate constituents. However, being able to tell this number is easily seen to be tantamount to being able to tell which of the constituents in question are inconsistent and, hence, tantamount to having a decision procedure for first-order logic.4 And this, of course, we cannot accomplish recursively. For this reason, measures of depth information cannot in general be effectively calculated. Hence they cannot in any realistic sense be operated with directly. They do not reflect faithfully the realities one has to deal with in logic and in mathematics.
This becomes especially striking if one recalls the close relationship between the concept of information and the idea of the elimination of uncertainty. Part of the uncertainty we inevitably have to face is the uncertainty as to which constituents (and other sentences) are inconsistent and which of them are consistent. In order to take into account the elimination of this kind of uncertainty in our measures of information, we have to use other systems of weights than those given to us by measures of inductive probability.
A much better candidate for a genuinely realistic measure of informative content is obtained by assigning a nonzero weight to each constituent that is not trivially inconsistent. It may be stipulated that, whenever a constituent of depth d is split up into a disjunction of a number of constituents (none of which is trivially inconsistent) of depth d + 1, its weight is divided between these (each of them receiving a nonzero weight) by some definite principle. When the sum of weights is normalized to 1, we again obtain a probability- like measure psurf, which will be called surface probability or prelogical probability. This may be thought of as the degree of belief it is rational to associate with a sentence before one has done to it any of the many things that logic enables us to do in order to spell out its implications more and more fully. (Hence the half-serious term ‘prelogical probability’.) In terms of such probability-like measures, we can in the usual way define measures of surface information. One such measure is contsurf (s) =1 — psurf (s).
4 Assuming that we know the number of consistent constituents (and therefore also the number of inconsistent ones) of a given depth, a simple method of deciding which constituents of this depth are Consistent is to list all valid sentences in order until the right number of constituents are among their negations. Since we know this number, we know that the remaining constituents are all consistent. In the same way, one can see more generally that the decision problem of the axiom system whose only nonlogical axiom is a constituent C0(d)(of depth d, say) is of the same degree of unsolvability as the function (of e) that indicates how many of the constituents subordinate to C0(d)and of depth d + e are inconsistent.

Rourchid

04-06-09, 05:55

What has been said does not yet suffice to explain fully how these measures are obtained, for so far we have not said anything about what happens to the weight of a constituent C0(d) of depth d which is not trivially inconsistent but whose subordinate constituents of depth d + 1 are all trivially inconsistent. It turns out unnatural to let the weight of C0(d) simply get lost. The natural procedure seems to be to reassign the weight of C0(d) to its several "next of kin." By this I mean the following: Constituents that are not trivially inconsistent form a tree. When we have a situation of the kind just discussed, a branch comes to an end with the constituent C0(d) in question. When this happens, we trace the branch in question back till we come to the most recent branching point—say, to the constituent C0(d) (c < d)—from which at least two such branches emerge as reach down to depth d + 1. The weight of C0(d) is then divided among all the constituents Ci(c+1) subordinate to C0(c) which have at least one such branch going through them. This division follows of course some specified principles. For instance, if we otherwise follow even distribution of weights to subordinate constituents of the next greater depth, we can follow even distribution here, too.
This suffices to define measures of surface probability and surface information. By a surface tautology of depth d we can now mean the disjunction of all the constituents of depth d (with the given predicates and variables, of course) which are not trivially inconsistent, and, more generally, any sentence of depth d that has this disjunction as its distributive normal form. So defined, surface tautologies are precisely those sentences whose surface information is zero. This preserves the important systematic connection between the notion of informativeness and the notions of tautology and analyticity which was already relied on by Kant when he called analytic judgments merely "explicative" (Erlduterungsurteile).
An arbitrary surface tautology of depth d will be called in the sequel t(d).
Among sentences s of depth d or less, the conditional probability psurf(s|t(d)) (defined in the usual way) satisfies the customary Kolmogorov axioms of probability calculus (with the exception of countable additivity). In view of the familiar betting-theoretical motivation of these axioms,5 our observations imply that these conditional probabilities can be thought of as possible betting ratios for a rational agent who thinks of all those events as possible which are described by such constituents of depth d as are not trivially inconsistent. (Rationality may here be taken to mean simply an ability to avoid Dutch Books made against oneself.) This throws some light on the nature of our notions of surface probability and surface information. Notice, incidentally, that psurf(s|t(d+e)) is simply the surface probability of the distributive normal form of s at depth d + e.
Further light is thrown on our notions by an examination of what happens to consurf (s|t(d+e))=1 — psurf (s|t(d+e)) when e grows. The direction of change depends on the particular sentence in question. We do not always have contsurf (s|t(d+e))≤ contsurf (s|t(d+e+1)). This inequality nevertheless holds, even as a strict inequality, whenever one of the constituents in the distributive normal form of s (at the original depth d) becomes trivially inconsistent for the first time at depth d + e + 1 while the same happens to no constituent of the same depth that does not occur in the normal form of s. (This is very much in keeping with the idea of information as elimination of uncertainty. The information s conveys to us—relative to t(d+e) —grows whenever we can omit one of the possibilities s seemed to allow to begin with and among which we had to be uncertain, while no competing possibility is likewise omitted.) Moreover, from the completeness theorem mentioned earlier it follows that the limit lime→∞ contsurf(s|t(d+e)) is a measure of depth content. What is more, the distribution principle that gives us this depth information is related in a simple way to the distribution principles used in assigning the surface information in question. For instance, if psurf (s) is based on the principle of even distribution of weights where we move from a given depth to the next greater depth, then so is the pind (s)which we obtain as lime→∞ psurf(s|t(d+e)). More generally, one can easily see that ratios between weights are in a certain natural sense preserved when one thus moves from psurf (s)to the corresponding pind (s). In the sense that appears from these remarks, we can then say that depth content of a sentence s is the limit to which surface content converges when we gradually draw out from s all its more or less hidden implications. In short, depth information is the limit of surface information.
5 For the original works by Ramsey and De Finetti, see the handy anthology, H. E. Kyburg and H. E. Smokier, ed&, Studies in Subjective Probability (New York: John Wiley, 1964). For a more recent treatment, see the papers by John G. Kemeny, Abner Shimony, and R. Sherman Lehman in Journal of Symbolic Logic, xx (1955); 8 (September): 268—278; 1 (March): 1—28; and 3 (September): 251—262, respectively.
These observations perhaps help to illustrate the naturalness of our measures of surface information as a measure of the kind of information we actually (and not just "implicitly") have. In view of the obvious need of realistic measures of this kind, it is not surprising that some of the theoreticians of subjective probability have recently expressed interest in (not explicitly specified) probability-like measures which are supposed to resemble ours in not being invariant with respect to logical equivalence.6 Perhaps our measures of "prelogical" probability are answers to their prayers.
There is nothing subjective about our measures, however. Rather, they give us perfectly objective—and, I have suggested, fairly realistic—measures of information which show that there are senses of information in which logical and mathematical reasoning yields new information in a perfectly objective sense of ‘information’. This provides a definitive counterexample to the often-repeated neopositivistic thesis that the only sense in which logical or mathematical reasoning gives us new information is purely psychological or subjective, and thus also provides a partial answer to the Kantian question to which this symposium is dedicated. Elsewhere, I have explored the relation of my answer to the traditional philosophy of mathematics, especially to Kant.
All this leaves open a group of absolutely crucial questions, however, which have to be raised before we can hope to understand fully the notion of surface information. Speaking of information prompts the question: Information about what? How do the operations that increase our surface information enhance our grasp of some subject matter or other? In the last analysis, one would like to see how an increase in surface information enables us to deal more efficiently with the reality—the "external" nonconceptual world that we presumably are primarily interested in.
6 Leonard J. Savage, "Difficulties in the Theory of Personal Probability," Philosophy of Science, xxxiv, 4 (December 1967): 305—310, and Ian Hacking, "Slightly More Realistic Personal Probability," ibid.: 311—325

Rourchid

04-06-09, 05:57

In order to answer these questions, let us assume that I receive an item of information from a source that I know to be absolutely reliable, and let us assume that this news item is expressed in the form of a first-order sentence s of depth d. What does that sentence "really" tell me about the aspect of reality of which itostensibly speaks? This can in principle be spelled out by seeing which possibilities concerning the world s admits and which possibilities it excludes, i.e., by transforming s into its distributive normal form of depth d. (This point can be greatly strengthened. One might say, for instance, that to specify what a sentence s "really" tells me about reality is to specify what kinds of individuals I can expect to find in the world when s is true and, after I have found one of them, how the further kinds of individuals are related to it which I may come across, etc. But what the distributive normal form of s does is just to answer all such questions as fully as one can do without going beyond the depth of s, i.e., going beyond the resources of expression already used in s.) However, this normal form does not yet give me everything I can extract from s without the benefit of further factual discoveries and without the benefit of further messages with a factual content. The reason for this is that some of the possibilities that s seems to admit at depth d may turn out to be only apparent.
I have tried to illustrate this state of affairs by comparing constituents not to pictures of reality, but to recipes for constructing such pictures.7 This analogy can in fact be profitably developed further in several directions. The main point relevant here is that some of these recipes may misfire in the sense that no picture can be constructed by their means. From the recipe alone one cannot see whether this is the case or not. Barring further information (surface information!), I therefore have to be prepared for the truth of any constituent in the normal form of s that is not trivially inconsistent. The reality and even urgency of this need merits some emphasis. For instance, in the normal form of s there may be some constituents asserting the existence of certain kinds of individuals (or n-tuples of individuals). Even though all these constituents are in the last analysis inconsistent, I cannot discount them as long as I have not actually ascertained their inconsistency. Before I have done that, I may even find myself making practical preparations for actually running into the kinds of individuals my (inconsistent) constituents assert to exist. (A rich stock of detailed illustrations of the phenomenon involved here, drawn from a slightly different department of first-order logic, are offered by the domino problems of Hao Wang and his collaborators.8 In the same way as one cannot see from a constituent whether it yields a consistent "picture" of the world or not, in the same way one cannot see from one of these domino problems whether it admits of a positive solution or not. For my purposes, the domino problems are illustrative in two different respects. First, a completed domino problem—i.e., an euclidean plane filled with domino chips of specifiable kinds—is closely reminiscent of a "picture of the world," especially of a completed jigsaw-puzzle picture. Second, the domino problems show how very far one sometimes has to carry out an attempted "picture construction" before one can see its impossibility, thus strikingly illustrating the kind of combinatorial information needed to rule out some merely apparent alternatives.
7 See my "Are Logical Truths Analytic?" (fn. 1).
8 See Hao Wang’s paper, "Remarks on Machines, Sets, and the Decision Problem," in Crossley and Dummett, op. cit., pp. 804—320.
The unavoidability of this predicament follows from the undecidability of first-order logic, which is thus seen to contain important morals for our concept of information.
Our description of the actual situation one faces when one receives a piece of information expressed in first-order language also shows what the practical (pragmatic) advantages are that accrue from an increase in surface information. It was pointed out above that, as far as s and its successively deeper and deeper normal forms are concerned, we obtain more surface information essentially insofar as we can eliminate some of the constituents in its normal form at the initial depth d as being inconsistent. The more such inconsistent constituents we can eliminate, the more narrowly we can restrict the range of eventualities we have to be prepared for when we know that s is the case. It is true that no new empirical observations and no further messages with a factual import are needed for the elimination. The fact nevertheless remains that this elimination is not automatic and that it is not a merely subjective process of getting rid of mental blocks that cloud our vision of what there already is in front of us. The elimination involves further work whose extent can be objectively measured.
Thus we can see a good reason for saying that the uncertainty we get rid of when our surface information grows is uncertainty concerning the reality our sentences speak of. The same is presumably true of the concept of information involved here. (This could also be construed as a reason for saying that nontrivial logical and mathematical knowledge is "synthetic" in a rather striking sense of the word.) At the same time, it is clear that the insights we obtain when we gain new surface information are in some important sense conceptual, almost linguistic. They pertain to the ways in which our language can or cannot represent reality. They are not comparable to having a look at a picture so as to see what that part of the world is like which the picture represents; they are, rather, like realizing that certain structures that might at first seem to be pictures do not really stand for anything. The information gained thus seems to be purely conceptual.
This double nature of surface information might seem very puzzling, almost paradoxical. Rightly viewed, it nevertheless points to a feature of the conceptual situation we are studying which seems to mehighly interesting. The paradoxical double nature of surface information illustrates the important fact that whatever we try tosay about reality is inextricably interwoven with the contributions of our own conceptual system. What we can directly and immediately express or grasp is a complex outcome which embodies both elements due to nonconceptual reality and elements due to the conceptual system we are relying on. The better we know the conceptual system, the more fully we know what is contributed to this complex outcome by our conceptual system. By discounting this we can therefore ipso facto know to the same extent what is contributed to it by the reality we in the first place want to describe (or want to have described to us). For this reason, the deeper understanding of our own conceptual system—in the case at hand, the wider mastery of first-order logic—which an increase in surface information amounts to can at the same time mean an elimination of uncertainty concerning the objective state of affairs "out there" in reality.
The metaphor that inevitably suggests itself here is the following:
We do not and cannot "touch" the reality directly, but only by means of a conceptual system. This system works like a highly complex instrument that connects our knowledge with the reality this knowledge is about. This instrument is so intricate that we do not know which of its registrations are due to the influence of the reality we are interested in and which of them merely reflect the mode of functioning of the instrument itself. The better we know the instrument, the more of the merely apparent registrations we can disregard. This also means that we can use the instrument more efficiently than before for the purpose of coming to know the reality its feelers touch.
Thus we can see how surface information may legitimately be thought of both as conceptual information and at the same time as information concerning objective reality. Strictly speaking, this is of course true only of that increase in surface information which takes place when a sentence is expanded into a disjunction of increasingly deeper constituents.
The most interesting feature of the situation is the inextricability of conceptual elements from those contributed by mind-independent reality. One reason why this is interesting is that it is closely related to a well-known thesis of certain traditional philosophers who are sometimes inaccurately referred to as idealists. These philosophers have claimed that all our knowledge—or at least all our "better" knowledge, which for Kant meant synthetic knowledge a priori—presupposes, and depends on, concepts that are of the nature of the mind’s own creations. As a corollary to this dependence of all our knowledge on our own concepts, it is maintained that "things in themselves," as they would be independent of all our concepts and therefore of our own activity, are unknowable and indescribable. At best, one school of thought avers, the concept of a Ding an sich is useful as an idealized limit that our knowledge can approximate but never fully reach. In brief, reality is for these philosophers inseparable from our concepts—and vice versa.
The simple but representative case of first order languages offers us a handy testing ground of these "idealistic" theses. In view of what has been said, these theses can in fact be understood so as to be in certain respects essentially correct. In terms of the metaphor, it is the case that (in general) we cannot effectively decide which registrations of the apparatus to which we are comparing our conceptual system are informative about "objective" reality and which registrations are, in contrast, merely due to the mode of operation of our registering apparatus. In a sense, whatever we may try to say of Dinge an sich in first-order terms is normally shot through with elements (apparent possibilities) which are entirely due to the specific way in which first-order sentences are related to the reality they strive to mirror. In this sense, reality and our concepts are inextricably interwoven with each other in all nontrivial use of first-order discourse. Furthermore, the central role of this discourse strongly suggests that my point can be generalized.
The inextricability of conceptual from objective factors in first- order languages is due to the undecidability of first-order logic. Looked upon from the point of view of the present paper, Church’s undecidability result thus turns out to have decidedly idealistic implications. Our modern version of a time-honored idealistic thesis undoubtedly appears undramatic as compared with the imagery that is usually associated with the original version or versions. For instance, the "things in themselves" that our version may perhaps be claimed to involve do not constitute a special class of unknowable but nevertheless in some strange way causally active entities. Speaking of one’s knowledge of "things in themselves" means for us merely a facon de parler—a counterfactual way of speaking—of one’s knowledge such as it would be if all elements contributed to it by our conceptual apparatus were eliminated. In short, it means for us speaking of depth information instead of surface information. There is nothing illegitimate about doing so, as long as we realize that there is no way of actually (i.e., effectively) dealing with the nonrecursive concept of depth information.
In spite of this undramatic appearance of our quasi-idealistic conclusions, it seems to me that they are in a deep sense connected with what is true and important in the original thesis. Among other things, I believe that thinking of Dinge an sich as a separate, unknowable class of entities has always been a case of fallacious hypostatization. If this connection really exists, it is not surprising that as a by-product we can also partially vindicate the old Kantian doctrine of the synthetic a priori character of nontrivial mathematical (and, for us, logical) truths.
JAAKKO HINTIKKA
University of Helsinki and Stanford University

Rourchid

04-06-09, 06:41

(enige herhalingen gingen vooraf)

Zeker wel, want waarom anders zie jij het als noodzakelijk om redenen te verzinnen waarom god wonderen laat gebeuren terwijl hij op andere momenten niet ingrijpt? Je maakt daarmee god tot een immorele knoeier.

Lijkt goed, maar die wonderen zijn ermee in tegenspraak. Jouw verklaring:

In die tijd was voor god zijn hoge moraal van niet ingrijpen dus ondergeschikt aan platte zieltjeswinnerij. Hij dacht in te kunnen spelen op de behoeften van de mensen, but boy was he wrong...

Van een vrije wil noch van geloven kan sprake zijn indien god zijn aanwezigheid ondubbelzinnig kenbaar maakt.

God rommelt ad hoc maar wat aan. Volgens jou dan. Hij zondigt tegen zijn zelfopgelegde verbod van niet rechtstreeks ingrijpen middels een onbeholpen en grotendeels niet succesvolle poging om mensen te bekeren.
Cirkelredeneringen als retorische vragen!

Rourchid

04-06-09, 08:41

Ik zal maar geen nieuwe topic aanmaken maar deze in de gaten houden
In de op één na laatste alinea van zijn uiteenzetting (hiervoor) schrijft Jaakko Hintikka: "Church’s undecidability result thus turns out to have decidedly idealistic implications."

M.a.w. als de institutie die jouw je normen en waarden verschaft besluiteloos is dan neem je zelf het iniatief.
Deze tekst van Jaakko Hintikka is overigens uit 1968 en is representatief voor een periode waarin leden van Lutheraanse Kerken zelf gingen bepalen wat de inhoud van geloven is.

De meest recente publicatie van Jaakko Hintikka 'Socratic Epistemic' (2007) - een boek dat als uiterst controversieel wordt beschouwd, beschrijft het gedwongen worden bij discussies over Gdsdienst partij te kiezen in het eeuwige duel tussen Aristoteles en Plato.

Charlus

04-06-09, 09:38

Rourchid

05-06-09, 11:07

The history of epistemology
Ancient philosophy
The pre-Socratics
The central focus of ancient Greek philosophy was the problem of motion. Many pre-Socratic philosophers thought that no logically coherent account of motion and change could be given. Although this problem was primarily a concern of metaphysics, not epistemology, it had the consequence that all major Greek philosophers held that knowledge must not itself change or be changeable in any respect. This requirement motivated Parmenides (fl. 5th century BC), for example, to hold that thinking is identical with "being" (i.e., all objects of thought exist and are unchanging) and that it is impossible to think of "nonbeing" or "becoming" in any way.
Plato
Plato accepted the Parmenidean constraint that knowledge must be unchanging. One consequence of this view, as Plato pointed out in the Theaetetus, is that sense experience cannot be a source of knowledge, because the objects apprehended through it are subject to change. To the extent that humans have knowledge, they attain it by transcending sense experience in order to discover unchanging objects through the exercise of reason.
The Platonic theory of knowledge thus contains two parts: first, an investigation into the nature of unchanging objects and, second, a discussion of how these objects can be known through reason. Of the many literary devices Plato used to illustrate his theory, the best known is the allegory of the cave, which appears in Book VII of the Republic. The allegory depicts people living in a cave, which represents the world of sense-experience. In the cave people see only unreal objects, shadows, or images. Through a painful intellectual process, which involves the rejection and overcoming of the familiar sensible world, they begin an ascent out of the cave into reality. This process is the analogue of the exercise of reason, which allows one to apprehend unchanging objects and thus to acquire knowledge. The upward journey, which few people are able to complete, culminates in the direct vision of the Sun, which represents the source of knowledge.
Plato's investigation of unchanging objects begins with the observation that every faculty of the mind apprehends a unique set of objects: hearing apprehends sounds, sight apprehends visual images, smell apprehends odours, and so on. Knowing also is a mental faculty, according to Plato, and therefore there must be a unique set of objects that it apprehends. Roughly speaking, these objects are the entities denoted by terms that can be used as predicates—e.g., "good," "white," and "triangle." To say "This is a triangle," for example, is to attribute a certain property, that of being a triangle, to a certain spatiotemporal object, such as a figure drawn in the sand. Plato is here distinguishing between specific triangles that are drawn, sketched, or painted and the common property they share, that of being triangular. Objects of the former kind, which he calls "particulars," are always located somewhere in space and time—i.e., in the world of appearance. The property they share is a "form" or "idea" (though the latter term is not used in any psychological sense). Unlike particulars, forms do not exist in space and time; moreover, they do not change. They are thus the objects that one apprehends when one has knowledge.
Reason is used to discover unchanging forms through the method of dialectic, which Plato inherited from his teacher Socrates. The method involves a process of question and answer designed to elicit a "real definition." By a real definition Plato means a set of necessary and sufficient conditions that exactly determine the entities to which a given concept applies. The entities to which the concept "being a brother" applies, for example, are determined by the concepts "being male" and "being a sibling": it is both necessary and sufficient for a person to be a brother that he be male and a sibling. Anyone who grasps these conditions understands precisely what being a brother is.
In the Republic, Plato applies the dialectical method to the concept of justice. In response to a proposal by Cephalus that "justice" means the same as "honesty in word and deed," Socrates points out that, under some conditions, it is just not to tell the truth or to repay debts. Suppose one borrows a weapon from a person who later loses his sanity. If the person then demands his weapon back in order to kill someone who is innocent, it would be just to lie to him, stating that one no longer had the weapon. Therefore, "justice" cannot mean the same as "honesty in word and deed." By this technique of proposing one definition after another and subjecting each to possible counterexamples, Socrates attempts to discover a definition that cannot be refuted. In doing so he apprehends the form of justice, the common feature that all just things share.
Plato's search for definitions and, thereby, forms is a search for knowledge. But how should knowledge in general be defined? In the Theaetetus Plato argues that, at a minimum, knowledge involves true belief. No one can know what is false. A person may believe that he knows something, which is in fact false, but in that case he does not really know, he only thinks he knows. But knowledge is more than simply true belief. Suppose that someone has a dream in April that there will be an earthquake in September, and on the basis of his dream he forms the belief that there will be an earthquake in September. Suppose also that in fact there is an earthquake in September. The person has a true belief about the earthquake, but not knowledge of it. What he lacks is a good reason to support his true belief. In a word, he lacks justification. Using arguments such as these, Plato contends that knowledge is justified true belief.
Although there has been much disagreement about the nature of justification, the Platonic definition of knowledge was widely accepted until the mid-20th century, when the American philosopher Edmund L. Gettier produced a startling counterexample. Suppose that Kathy knows Oscar very well. Kathy is walking across the mall, and Oscar is walking behind her, out of sight. In front of her, Kathy sees someone walking toward her who looks exactly like Oscar. Unbeknownst to her, however, it is Oscar's twin brother. Kathy forms the belief that Oscar is walking across the mall. Her belief is true, because Oscar is in fact walking across the mall (though she does not see him doing it). And her true belief seems to be justified, because the evidence she has for it is the same as the evidence she would have had if the person she had seen were really Oscar and not Oscar's twin. In other words, if her belief that Oscar is walking across the mall is justified when the person she sees is Oscar, then it also must be justified when the person she sees is Oscar's twin, because in both cases the evidence—the sight of an Oscar-like figure walking across the mall—is the same. Nonetheless, Kathy does not know that Oscar is walking across the mall. According to Gettier, the problem is that Kathy's belief is not causally connected to its object (Oscar) in the right way.
Aristotle
In the Posterior Analytics, Aristotle (384–322 BC) claims that each science consists of a set of first principles, which are necessarily true and knowable directly, and a set of truths, which are both logically derivable from and causally explained by the first principles. The demonstration of a scientific truth is accomplished by means of a series of syllogisms—a form of argument invented by Aristotle—in which the premises of each syllogism in the series are justified as the conclusions of earlier syllogisms. In each syllogism, the premises not only logically necessitate the conclusion (i.e., the truth of the premises makes it logically impossible for the conclusion to be false) but causally explain it as well. Thus, in the syllogism
All stars are distant objects.
All distant objects twinkle.
Therefore, all stars twinkle.
the fact that stars twinkle is explained by the fact that all distant objects twinkle and the fact that stars are distant objects. The premises of the first syllogism in the series are first principles, which do not require demonstration, and the conclusion of the final syllogism is the scientific truth in question.
Much of what Aristotle says about knowledge is part of his doctrine about the nature of the soul, and in particular the human soul. As he uses the term, the soul (psyche) of a thing is what makes it alive; thus, every living thing, including plant life, has a soul. The mind or intellect (nous) can be described variously as a power, faculty, part, or aspect of the human soul. It should be noted that for Aristotle "soul" and "intellect" are scientific terms.
In an enigmatic passage, Aristotle claims that "actual knowledge is identical with its object." By this he seems to mean something like the following. When a person learns something, he "acquires" it in some sense. What he acquires must be either different from the thing he knows or identical with it. If it is different, then there is a discrepancy between what he has in mind and the object of his knowledge. But such a discrepancy seems to be incompatible with the existence of knowledge. For knowledge, which must be true and accurate, cannot deviate from its object in any way. One cannot know that blue is a colour, for example, if the object of that knowledge is something other than that blue is a colour. This idea, that knowledge is identical with its object, is dimly reflected in the modern formula for expressing one of the necessary conditions of knowledge: A knows that p only if it is true that p.
To assert that knowledge and its object must be identical raises a question: In what way is knowledge "in" a person? Suppose that Smith knows what dogs are—i.e., he knows what it is to be a dog. Then, in some sense, dogs, or being a dog, must be in the mind of Smith. But how can this be? Aristotle derives his answer from his general theory of reality. According to him, all (terrestrial) substances are composed of two principles: form and matter. All dogs, for example, consist of a form—the form of being a dog—and matter, which is the stuff out of which they are made. The form of an object makes it the kind of thing it is. Matter, on the other hand, is literally unintelligible. Consequently, what is in the knower when he knows what dogs are is just the form of being a dog.
In his sketchy account of the process of thinking in De anima (On the Soul), Aristotle says that the intellect, like everything else, must have two parts: something analogous to matter and something analogous to form. The first of these is the passive intellect; the second is active intellect, of which Aristotle speaks tersely. "Intellect in this sense is separable, impassible, unmixed, since it is in its essential nature activity. …When intellect is set free from its present conditions it appears as just what it is and nothing more: it alone is immortal and eternal…and without it nothing thinks."
This part of Aristotle's views about knowledge is an extension of what he says about sensation. According to him, sensation occurs when the sense organ is stimulated by the sense object, typically through some medium, such as light for vision and air for hearing. This stimulation causes a "sensible species" to be generated in the sense organ itself. This "species" is some sort of representation of the object sensed. As Aristotle describes the process, the sense organ receives "the form of sensible objects without the matter, just as the wax receives the impression of the signet-ring without the iron or the gold."
Ancient Skepticism
After the death of Aristotle the next significant development in the history of epistemology was the rise of Skepticism, of which there were at least two kinds. The first, Academic Skepticism, arose in the Academy (the school founded by Plato) in the 3rd century BC and was propounded by the Greek philosopher Arcesilaus (c. 315–c. 240 BC), about whom Cicero (106–43 BC), Sextus Empiricus (fl. 3rd century AD), and Diogenes Laërtius (fl. 3rd century AD) provide information. The Academic Skeptics, who are sometimes called "dogmatic" Skeptics, argued that nothing could be known with certainty. This form of Skepticism seems susceptible to the objection, raised by the Stoic Antipater (fl. c. 135 BC) and others, that the view is self-contradictory. To know that knowledge is impossible is to know something; hence, dogmatic Skepticism must be false.
Carneades (c. 213–129 BC), also a member of the Academy, developed a subtle reply to this charge. Academic Skepticism, he insisted, is not a theory about knowledge or the world but rather a kind of argumentative strategy. According to this strategy, the skeptic does not try to prove that he knows nothing. Instead, he simply assumes that he knows nothing and defends that assumption against attack. The burden of proof, in other words, is on those who believe that knowledge is possible.
Carneades' interpretation of Academic Skepticism renders it very similar to the other major kind, Pyrrhonism, which takes its name from Pyrrho of Elis (c. 365–275 BC). Pyrrhonists, while not asserting or denying anything, attempted to show that one ought to suspend judgment and avoid making any knowledge claims at all, even the negative claim that nothing is known. The Pyrrhonist's strategy was to show that, for every proposition supported by some evidence, there is an opposite proposition supported by evidence that is equally good. Arguments like these, which are designed to refute both sides of an issue, are known as "tropes." The judgment that a tower is round when seen at a distance, for example, is contradicted by the judgment that the tower is square when seen up close. The judgment that Providence cares for all things, which is supported by the orderliness of the heavenly bodies, is contradicted by the judgment that many good people suffer misery and many bad people enjoy happiness. The judgment that apples have many properties—shape, colour, taste, and aroma—each of which affects a sense organ, is contradicted by the equally good possibility that apples have only one property that affects each sense organ differently.
What is at stake in these arguments is "the problem of the criterion"—i.e., the problem of determining a justifiable standard against which to measure the worth or validity of judgments, or claims to knowledge. According to the Pyrrhonists, every possible criterion is either groundless or inconclusive. Thus, suppose that something is offered as a criterion. The Pyrrhonist will ask what justification there is for it. If no justification is offered, then the criterion is groundless. If, on the other hand, a justification is produced, then the justification itself is either justified or it is not. If it is not justified, then again the criterion is groundless. If it is justified, then there must be some criterion that justifies it. But this is just what the dogmatist was supposed to have provided in the first place.
If the Pyrrhonist needed to make judgments in order to survive, he would be in trouble. In fact, however, there is a way of living that bypasses judgment. He can live quite nicely, according to Sextus, by following custom and accepting things as they appear to him. In doing so, he does not judge the correctness of anything but merely accepts appearances for what they are. If the Pyrrhonist needed to make judgments in order to survive, he would be in trouble. In fact, however, there is a way of living that bypasses judgment. He can live quite nicely, according to Sextus, by following custom and accepting things as they appear to him. In doing so, he does not judge the correctness of anything but merely accepts appearances for what they are.
Ancient Pyrrhonism is not strictly an epistemology, since it has no theory of knowledge and is content to undermine the dogmatic epistemologies of others, especially Stoicism and Epicureanism. Pyrrho himself was said to have had ethical motives for attacking dogmatists: being reconciled to not knowing anything, Pyrrho thought, induced serenity (ataraxia).
Epistemology, Encyclopaedy Britannica Article: http://www.speedyshare.com/953827320.html (http://www.speedyshare.com/953827320.html)

Rourchid

05-06-09, 11:10

Geen van beide. Het is toch zo simpel. Een gelovige die gaat rationaliseren (in dit geval zelfverzonnen beweegredenen aan god toeschrijven) waarom god wonderen eens liet plaatsvinden maar later niet meer, grijpt naar strohalmen. Zelfs ik als ongelovige zie dat.
Gelovige of ongelovige is niet relevant inzake deze.
Vaststellen dat een cirkel rond is onafhankelijk van levensbeschouwing.
Zo ook het feit dat na Mohammed (Gd's Heil en Vrede zij met hem) er geen Profeten meer zullen komen.
De Koran gezonden als herinnering aan Hem SWT vervangt eerder gezonden tekenen.

Wie stelt die bewijst en jij kan pas bewijzen dat DNA/Sallahhdin's historische beschrijving semantisch (en formeel) ongeldig is als jij een nieuwe Profeet en een nieuw Vers kunt aanleveren.
Rest in het rijtje 'formele geldigheid, semantische geldigheid en verborgen argument' jouw verborgen argument te categorisren als dat jij DNA/Sallahhdin ongeloofwaardig vindt omdat jij Islam ongeloofwaardig vindt.

Hiervoor heb ik als educatief interlude een citaat uit het artikel over epistemologie in de Encyclopaedy Britannica geplaatst:

<DIR><DIR>Epistemology is the study of the nature, origin, and limits of human knowledge. The term is derived from the Greek epistēmē ("knowledge") and logos ("reason"), and accordingly the field is sometimes referred to as the theory of knowledge.

</DIR></DIR>Misschien is het een idee om het voornoemde artikel te bestuderen opdat je een beter inzicht krijgt wat modern redeneren inhoudt.

Orakel

06-06-09, 13:16

DNA

06-06-09, 18:20

Interessanter is waarom een ongelovige allerlei vreemdsoortige theologische rekenkunst nodig heeft om halsstarrig een gelovige te blijven wijze op de vermeende inconsistenties en andere ongerijmdheden in diens religieuze zelfverstaan.

:lol:

nou, dat zijn achterlijk christelijke projecties , dwaas pretentieus zarathustra : :

maar ,wat betreft die religieuze zaken & ander het volgende :

de waarheid benaderen is een groot kunst die rekening zou moeten houden met de beperkt kennis, ervaring, ontwikkeling of "evolutie" ....van de mens :

in de zin van : hoe meer geloof , werk , kennis, praktijk, ervaring, constant zoektocht , hoe dichter bij God :

vandaar dat de waarheid , wat dat ook moge zijn, kan niet benaderd worden buiten het geloof in Islam althans :

Kijk's naar die achterlijk belachelijk tragi_hilarisch puinhoop & flauwekul van ideologisch materialisme sinds Descartes althans met betrekking tot de opvatting & benadering van de waarheid althans !

Islam houdt ook rekening met het intellect, vrijheid, vrij wil, kennis, ontwikkeling ...van de mens & met diens menselijk natuur :

het vergaren van kennis in het algemeen, het gebruik van rede , ervaringnen opdoen , constant zoektocht naar de benadering van de waarheid ......worden niet alleen gestimuleerd &² hoog geprezen door Islam ,maar worden zelfs tot religieuze plichten verheven !

vandaar al die erder moslim prestaties op alle niveaus toen moslims de essentie , natuur , geest, dynamiek, beginselen van Islam hadden goed begrepen & verwezenlijkt, zo veel mogelijk althans :

vandaar dat moslims zelfs de modern wetenschap hadden "uitgevonden" ...juist dankzij die Islam's geest & essentie van experimentatie, ervaringnen op doen, praktijk, constant zoektocht ....

see how muslims had even contributed to building the very foundations of modern civilization :

the latter w'dn't have been possible without Islam_muslims !

those Islam _muslims who had helped medieval ignorant superstitious foolish Europe out of dark age :

This Islam that will help this west get out of its "scientific" , philosophical, ideological, moral ....backwardness , ignorance = Jahilia !

congratulations ! :cola:

Charlus

07-06-09, 00:24

<...>Islam houdt ook rekening met het intellect, vrijheid, vrij wil, kennis, ontwikkeling ...van de mens & met diens menselijk natuur<...>
Wonderen (al dan niet der profeten) zijn hiermee in tegenspraak. Van een vrije wil kan geen sprake zijn indien god zijn aanwezigheid ondubbelzinnig kenbaar maakt.

Charlus

07-06-09, 00:34

(enige herhalingen gingen vooraf)

<...>Onzeker in mijn geloof ??? zeker niet<...>
Zeker wel, want waarom anders zie jij het als noodzakelijk om redenen te verzinnen waarom god wonderen laat gebeuren terwijl hij op andere momenten niet ingrijpt? Je maakt daarmee god tot een immorele knoeier.

Bovendien , God grijpt niet in om de vrijheid, vrij wil , intellect, menselijk natuur, natuurwetten ....niet uit te schakelen
Lijkt goed, maar die wonderen zijn ermee in tegenspraak. Jouw verklaring:

<...>vroeger waren mensen niet zo ontwikkeld ,vandaar dat die tastbare bewijzen nodig hadden om in de profeten & God te geloven, vandaar die wonderen :
In die tijd was voor god zijn hoge moraal van niet ingrijpen dus ondergeschikt aan platte zieltjeswinnerij. Hij dacht in te kunnen spelen op de behoeften van de mensen, but boy was he wrong...

daarna mogen zij hun vrij wil inschakelen & al dan niet geloven in God met alle gevolgen van dien :
Van een vrije wil noch van geloven kan sprake zijn indien god zijn aanwezigheid ondubbelzinnig kenbaar maakt.

maar velen wilden toch niet geloven<...>
God rommelt ad hoc maar wat aan. Volgens jou dan. Hij zondigt tegen zijn zelfopgelegde verbod van niet rechtstreeks ingrijpen middels een onbeholpen en grotendeels niet succesvolle poging om mensen te bekeren.
Cirkelredeneringen als retorische vragen!
Geen van beide. Het is toch zo simpel. Een gelovige die gaat rationaliseren (in dit geval zelfverzonnen beweegredenen aan god toeschrijven) waarom god wonderen eens liet plaatsvinden maar later niet meer, grijpt naar strohalmen. Zelfs ik als ongelovige zie dat.
<...>Vaststellen dat een cirkel rond is onafhankelijk van levensbeschouwing.
Zo ook het feit dat na Mohammed (Gd's Heil en Vrede zij met hem) er geen Profeten meer zullen komen.
Dat laatste is geen feit, maar jouw geloof en niet vergelijkbaar met de vaststelling dat een cirkel rond is. Je begint de greep op de realiteit te verliezen.

De Koran gezonden als herinnering aan Hem SWT vervangt eerder gezonden tekenen.
Alweer jouw vrijheid van geloof.

Wie stelt die bewijst en jij kan pas bewijzen dat DNA/Sallahhdin's historische beschrijving semantisch (en formeel) ongeldig is als jij een nieuwe Profeet en een nieuw Vers kunt aanleveren.<...>
DNA stelt; hij verklaart te weten waarom god vroeger wonderen liet gebeuren en later niet meer. Aan hem dus om met een vers of desnoods overlevering te komen waarin god deze motivatie uiteenzet. Blijft hij in gebreke, dan is hij een fantast die mensen voorliegt over de woestijnreligies. Bovendien lijdt hij aan grootheidswaan omdat hij zogenaamd op de hoogte is van god zijn gedachtenprocessen.

Rourchid

07-06-09, 09:07

Interessanter is waarom een ongelovige allerlei vreemdsoortige theologische rekenkunst nodig heeft om halsstarrig een gelovige te blijven wijze op de vermeende inconsistenties en andere ongerijmdheden in diens religieuze zelfverstaan.
Je zou kunnen zeggen dat ongelovigen die zich in hun grot van Plato opgezadeld zien met een Gordiaanse knoop vaak de neiging hebben om hun ingebeelde tegenstrijdigheden in hun Gordiaanse knoop te vervlechten waardoor deze zo meta-Gordiaans wordt dat zij (ongelovigen) zelf worden doorgehakt?

Rourchid

07-06-09, 09:07

DNA stelt; hij verklaart te weten waarom god vroeger wonderen liet gebeuren en later niet meer. Aan hem dus om met een vers of desnoods overlevering te komen waarin god deze motivatie uiteenzet. Blijft hij in gebreke, dan is hij een fantast die mensen voorliegt over de woestijnreligies. Bovendien lijdt hij aan grootheidswaan omdat hij zogenaamd op de hoogte is van god zijn gedachtenprocessen.
Jij dient te bewijzen dat de formuleringen van DNA/Sallahhdin tegen de Islam in gaan.