Monday, June 16, 2008

Polska wobec wyzwań współczesności: prof. dr hab Jerzy Robert Nowak Prof. Wolniewicz

Polska wobec wyzwań współczesności: prof. dr hab Jerzy Robert Nowak Prof. Wolniewicz

Polska wobec wyzwań współczesności: prof. dr hab Jerzy Robert Nowak
(2008-06-15)
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Polska wobec wyzwań współczesności: prof.dr hab. Bogusław Wolniewicz (czyt. dr Kawęcki)
(2008-06-15)
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Polska wobec wyzwań współczesności: prof.dr hab. Andrzej Nowak
(2008-06-15)
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Polska wobec wyzwań współczesności: prof. dr hab. Rafał Broda
(2008-06-15)
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Saturday, June 7, 2008

Bogusław Wolniewicz (ur. w 1927 w Toruniu) - filozof i logik ...-


Prof। Wolniewicz

Zrozumieć rzeczywistość - wokół działań PO (2008-05-29)Rodzaj audycji: [Aktualności dnia]
Autor: prof. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=8123
Polski Punkt Widzenia: Ataki na Radio Maryja i Ojca Dyrektora (2008-05-27)Rodzaj audycji: [Inna audycja]
Autor: prof. dr hab. Bogusław Wolniewicz, red. Jan Maria Jackowski, red. Jacek Karczewski
Adres: http://www.radiomaryja.pl/audycje.php?id=8104
Wizyta premiera Tuska w Izraelu (2008-04-11)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab Bobusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=7681
Ważne sprawe dotyczące Polaków, analiza stu dni rządu Donalda Tuska (2008-02-23)Rodzaj audycji: [Rozmowy niedokończone]
Autor: prof. dr hab. Jerzy Robet Nowak, prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=7235
Polski Punkt Widzenia (2008-02-12)Rodzaj audycji: [Inna audycja]
Autor: prof. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=7154
Dyskusja nad "Strachem" (2008-01-21)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=6957
Polski Punkt Widzenia (2007-12-21)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=6656
Nagonka na Radio Maryja (2007-12-17)Rodzaj audycji: [Aktualności dnia]
Autor: prof.Boguslaw Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=6624
Komentarz powyborczy (2007-10-25)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=6153
Ostatnie debaty polityczne (2007-10-16)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=6085
"Minął miesiąc" (2007-10-07)Rodzaj audycji: [Rozmowy niedokończone]
Autor: prof. dr hab. Jerzy Robert Nowak, prof. dr hab. Bogusław Wolniewicz, Paweł Pasionek
Adres: http://www.radiomaryja.pl/audycje.php?id=6042
Echa wczorajszej debaty Jarosław Kaczyński - Aleksander Kwaśniewski (2007-10-02)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=6005
Prezydent Kwaśniewski kompromituje Polskę w świecie (2007-09-24)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=5962
Rewelacje "Wprost" na temat prof. Nowaka (2007-09-10)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=5898
Polski punkt widzenia: Reakcje po decyzji prokuratury toruńskiej (2007-08-22)Rodzaj audycji: [Inna audycja]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=5797
Dalsze manipulacje medialne wokół Radia Maryja (2007-08-08)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=5682
Co to jest lobbing? (2007-07-30)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=5650
Wypowiedź w obronie o. Tadeusza Rydzyka CSsR (2007-07-16) Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=5673
Interes mediów w sprawie wypowiedzi o. Tadeusza Rydzyka (2007-03-16)Rodzaj audycji: [Aktualności dnia]
Autor: prof.dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=4576
Roszczenia względem Polski w sprawie mienia żydowskiego cz.III (2007-03-11)Rodzaj audycji: [Rozmowy niedokończone]
Autor: prof.dr hab. Bogusław Wolniewicz; prof.dr hab. Jerzy Robert Nowak
Adres: http://www.radiomaryja.pl/audycje.php?id=4516
Roszczenia względem Polski w sprawie mienia żydowskiego cz.II (2007-03-11)Rodzaj audycji: [Rozmowy niedokończone]
Autor: prof.dr hab. Bogusław Wolniewicz; prof.dr hab. Jerzy Robert Nowak
Adres: http://www.radiomaryja.pl/audycje.php?id=4515
Roszczenia względem Polski w sprawie mienia żydowskiego cz.I (2007-03-11)Rodzaj audycji: [Rozmowy niedokończone]
Autor: prof.dr hab. Bogusław Wolniewicz; prof.dr hab. Jerzy Robert Nowak
Adres: http://www.radiomaryja.pl/audycje.php?id=4514
"Rzetelność" dziennikarska... (2006-12-09) Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=3671
Opieszałość polskich sądów (2006-11-30)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=3561
Debata o wychowaniu młodzieży (2006-11-04)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=3325
Czy koalicja jest możliwa? (2006-10-10)Rodzaj audycji: [Aktualności dnia]
Autor: prof. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=3097
Zmowa z posłanką! Oświadczenie Niezależnego Zespołu ds. Etyki Mediów (2006-09-30)Rodzaj audycji: [Aktualności dnia]
Autor: prof. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=3008
Książka J.T. Grossa (2006-08-12)Rodzaj audycji: [Aktualności dnia]
Autor: prof. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=2640
Tajemniczy atak na Radio Maryja (2006-04-25) Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=1850
Artykuł Gazety Wyborczej dotyczący wypowiedzi prof. dra hab. Bogusława Wolniewicza z 11.04.2006 (2006-04-12)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=1763
Społeczny Niezależny Zespół ds. Etyki Mediów (2006-04-11) Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: http://www.radiomaryja.pl/audycje.php?id=1756
Rada Etyki Mediów oskarżyła Radio Maryja i red. Stanisława Michalkiewicza o antysemityzm (2006-04-04)Rodzaj audycji: [Aktualności dnia]
Autor: prof. dr hab. Bogusław Wolniewicz
Adres: १७०३" href="http://www.radiomaryja.pl/audycje.php?id=http://www.radiomaryja.pl/audycje.php?id=१७०३

Bogusław Wolniewicz (ur. 22 września 1927 w Toruniu) - filozof i logik.
Studiował w latach 1947-1951 na Uniwersytecie Mikołaja Kopernika pod kierunkiem Tadeusza Czeżowskiego. Do 1953 r. był asystentem w Katedrze Logiki UMK, a od 1956 r. wykładowcą na WSP w Gdańsku. W 1963 r. został przeniesiony do Katedry Filozofii Uniwersytetu Warszawskiego z inicjatywy Adama Schaffa. Do 1998 r. był profesorem w Instytucie Filozofii UW, kiedy to odszedł na emeryturę. W latach 1956 - 1981 członek PZPR.
Bogusław Wolniewicz specjalizuje się w filozofii religii i filozofii współczesnej। Dystansuje się od głównych nurtów filozofii XX wieku i przyjmuje tezy wielkich myślicieli, m.in.: Arystotelesa, Leibniza, Hume'a, Kanta i szczególnie Wittgensteina. Krytyczny wobec freudyzmu, fenomenologii, postmodernizmu i fundamentalizmu religijnego, a od lat 90. XX wieku także marksizmu, reprezentuje postawę analityczną i metafizyczną. Główne założenia jego myśli to aksjologiczny absolutyzm w wersji racjonalistycznej i metafizyczny pesymizm w spojrzeniu na człowieka oraz społeczeństwo.
Boguslaw Wolniewicz and the Formal Ontology of Situations

INTRODUCTION
"The theory presented below was developed in an effort to clarify the metaphysics of Wittgenstein's Tractatus. The result obtained, however, is not strictly the formal twin of his variant of Logical Atomism. but something more, general, of which the latter is lust a special case. One might call it an ontology of situations. Some basic ideas of that ontology stern from Stenius Wittgenstein's Tractatus, Oxford, 1968 and Suszko Ontology in the Tractatus of L. Wittgenstein - Notre Dame Journal of Formal Logic, 1968.
Let L be a classic propositional language. Propositions of L are supposed to have their semantic counterparts in the realm of possibility, or as Wittgenstein put it: in logical space. These counterparts are situations, and S is to be the totality of them. The situation described by a proposition a is S(a). With Meinong we call it the objective of a."
From: Boguslaw Wolniewicz - A formal ontology of situations - Studia Logica 41: 381-413 (1982). pp. 381-382.

"Different ontologies adopt different notions of existence as basic. Aristotle's paradigm of existence is given by the equivalence:
(A) to be = to be a substance.
On the other hand, the paradigm of existence adopted in Wittgenstein's Tractatus is given by the parallel equivalence:
(W) to be = to be a fact.
Now, an Aristotelian substance is the denotation of an individual name, whereas a Wittgensteinian fact is the denotation of a true proposition. It seems therefore that the notions of existence derived from these two paradigms should be quite different, and one might readily expect that the metaphysical systems erected upon them will display wide structural discrepancies.
It turns out, however, that in spite of this basic difference there runs between these two systems a deep and striking parallelism. This parallelism is so close indeed that it makes possible the construction of a vocabulary which would transform characteristic propositions of Wittgenstein's ontology into Aristotelian ones, and conversely. To show in some detail the workings of that transformation will be the subject of this paper.
The vocabulary mentioned is based on the following four fundamental correlations:

Aristotle
Wittgenstein
1) primary substances (substantiae primae)
atomic facts
2) prime matter (materia prima)
objects
3) form (forma)
configuration
4) self-subsistence of primary substances (esse per se)
independence of atomic facts

Aristotle's ontology is an ontology of substances, Wittgenstein's ontology is an ontology of facts. But concerning the respective items of each of the pairs (1)-(4) both ontologies lay down conditions which in view of our vocabulary appear to be identical. To show this let us confront, to begin with, the items of pair (1): substances and facts.
(The interpretation of Aristotle adopted in this paper is the standard one, to be found in any competent textbook of the history of philosophy. Therefore, with but one exception, no references to Aristotle's works will be given here.)Relatively to the system involved substances and facts are of the same ontological status. Aristotle's world is the totality of substances (summa rerum), Wittgenstein's world is the totality of facts (die Gesamtheit der Tatsachen). For Aristotle whatever exists in the basic sense of the word is a primary substance, for Wittgenstein - an atomic fact. Moreover, both ontologies are MODAL ones, allowing for different modes of being (modi essendi); and both take as basic the notion of `contingent being' (esse contingens), opposed to necessary being on the one hand, and to the possibility of being on the other. Both substances and facts are entities which actually exist, but might have not existed. The equality of ontological status between substances and facts is corroborated by the circumstance that both are PARTICULARS, there being - as the saying goes - no multiplicity of entities which FALL UNDER them.
Substances and facts stand also in the same relation to the ontological categories of pairs (2) and (3). Both are always COMPOUND entities, a substance consisting of matter and form, and a fact consisting of objects and the way of their configuration. But in neither of the two systems is this compoundness to be understood literally as composition of physically separable parts or pieces. The compoundness (compositio) of a substance consists in its being formed stuff (materia informata), and the compoundness of a fact in its being a configuration of objects.
In view of correlation (4) we have also an equality of relation which a substance bears to other substances, and a fact to other facts. Self-subsistence is the characteristic attribute of primary substances: substantia prima = ens per se. If we take this to mean that each substance exists independently of the existence or non-existence of any other substance we get immediately the exact counterpart of Wittgenstein's principle of logical atomism stating the mutual independence of atomic facts. It should be noted that thus understood the attribute of self-subsistence or independence is a relative one, belonging to a substance - or to a fact - only in virtue of its relation to other substances - or facts.
From a Wittgensteinian point of view Aristotle's substances are not things, but hypostases of facts, and thus their names are not logically proper names, but name-like equivalents of propositions. (By that term we mean roughly either a noun clause of the form `that p', or any symbol which might be regarded as a definitional abbreviation of such clause.) Surely, from the Aristotelian point of view it might be easily retorted here that just the opposite is the case: substances are not `reified' facts, but on the contrary - facts are 'dereified' substances. Without passing judgement on these mutual objections let us note in passing that their symmetric character seems to be itself an additional manifestation of the parallelism discussed."
From: Boguslaw Wolniewicz - A parallelism between Wittgensteinian and Aristotelian ontologies. In Boston studies in the philosophy of science. Vol. IV. Edited by Cohen Robert S. and Wartofsky Marx W. Dordrecht: Reidel Publishing Company 1969. pp. 208-२१०
Wittgensteinian Foundations of Non‑Fregean Logic
Boguslaw Wolniewicz
The term "Non‑Fregean Logic" has been introduced in 1968 by the well‑known Polish logician Professor Roman Suszko to mark the distinction between two kinds of logical systems. A logical system is called by him "Fregean", if for its propositional calculus the following formula holds as a theorem:
(F) P ≡ q → P = q
He calls this formula "the axiom of Frege”, and it is not difficult to see why. (According to Frege's theory of meaning all true propositions denote the same, and similarly—all false ones. Thus if two propositions are materially equivalent, their denotations have to be identical; and exactly this is stated by the formula F.) The foremost example of a Fregean logic is the classical prepositional calculus, but—as we shall see—the three‑valued logic of Łukasiewicz is Fregean too. On the other hand, a logical system is called "Non‑Fregean" if the formula F is rejected in it as a theorem.
Some logicians have objected to drawing any such distinction, on the ground that in the classical propositional calculus there is no identity sign for propositions, and that consequently nothing like the "axiom of Frege" can be a theorem of this particular logical system. This objection, however, has a flavor of spurious innocence, being apparently based on the dubious principle that what is not spoken about doesn't exist. To see this let's note in the first place that the axiom of Frege is deductively equivalent to the following schematic formula:
(F' ) P ≡ q → / Φ (p) ≡ Φ (q) /
Certainly, in the ordinary propositional calculus there is no such schema either. (Though it is present in one of its variants, namely in Leśniewski's protothetics.) But we have there all its particular instances, known as "the laws of extensionality":
p ≡ q → ~p ≡ ~q
p ≡ q → p ∧ r=q ∧ r
and so on.
By these laws whatever holds good of one of two materially equivalent propositions, holds also of the other one. Thus from the point of view of classical propositional logic equivalent propositions are indistinguishable, and being indistinguishable they are by Leibniz's principle identical. This is, however, only another way of stating the axiom of Frege, so what is the point of objecting to it?
The idea of a Non‑Fregean logic goes back to Wittgenstein's Tractatus, where it is introduced right from the start in the thesis:
"1.13 Facts in logical space are the world."
The Tractatus is in the first place a work on the philosophy of logic, and the key to that philosophy is the concept of "logical space". Part of that concept is the idea of a Non‑Fregean logic.
Before going on, something has to be said here concerning Wittgenstein's general philosophical position. In our Marxist literature it is a firmly established opinion that Wittgenstein was a logical positivist, and that consequently his philosophical outlook is that of subjective idealism. This opinion, however, doesn't bear scrutiny. In fact it has been rashly taken over from the logical positivists of the Vienna Circle, whose early enthusiasm for the Tractatus was only a sad monument of misunderstanding and a rare specimen of philosophical blindness. Wittgenstein's doctrine is idealistic, no doubt about that. But its idealism is not of the subjectivist variety characteristic of positivism. The doctrine of the Tractatus is a peculiar and powerful variant of objective idealism, and it has much more in common with the doctrines of Plato or Leibniz, than with those of Berkeley and Mach. This again is most readily seen while investigating the philosophical import of the concept of "logical space".
The Tractatus starts from the assumption that the logic of language—its logical syntax—has been already, and in the main correctly, described by the systems of Frege and Russell. But there still remains the big question of a correct interpretation of that description, and it may be put as follows: the logical structure of language being such as described by Frege and Russell, what must be the ontological structure of a reality capable of being described by such a language?
Wittgenstein's answer to this question is embedded in the whole system of the Tractatus, and it may be useful to represent its framework schematically in a simple diagram (due to Suszko):
It is fairly easy to discern in the text of the book particular theses forming the three main parts of its system; e.g. thesis 4.22. "An elementary proposition consists of names" surely belongs to part (1), 3.203: "The name denotes an object", — to part (2), and 2.02: "The object is simple" — to part (3). Thesis 1.13 is obviously an ontological one too, as are, by the way, all the theses numbered “1 ‑ 2.0. . .”.
Now according to Wittgenstein's syntax, language is the totality of propositions, and according to his semantics the correspondence between language and reality has to be of the one‑to‑one type. What then, according to his ontology, is meant here by reality, the one‑to‑one counterpart of the totality of propositions? Reality cannot be identical with the world, for the world is the totality of facts, and to the totality of facts there corresponds in language only the totality of true propositions (= science, 4.11). Since language contains also false propositions, and these do not have counterparts in the totality of facts, it proves to be larger than the world; and the same holds good of reality too. If the overall semantical correspondence is to be preserved, something in reality must answer even to a false proposition. (And it has to be preserved, for if nothing in reality answered to false propositions they would have no relation to it; and being thus out of touch with reality they could not be false, but only meaningless.)
According to the Tractatus the ontological counterpart of a true proposition is a fact; and the ontological counterpart of a false proposition is the possibility of a fact, something that might be the case. (On the other hand, any fact is the actualization of some possibility.) And reality is the totality of all possibilities called by Wittgenstein "logical space". Thus we have the following identities:
Language = the totality of propositions,
Science = the totality of true propositions,
The world = the totality of facts,
Logical space = the totality of possibilities;
and to make their relations even more precise we may present them in the form of a diagram:
The meaning of Wittgenstein's pronouncement in 1.13 is sufficiently clear now: the world is, so to speak, an island of facts in the ocean of possibilities. But this simile is only a useful first approximation to Wittgenstein's idea of logical space. And we proceed now to the second one.
Logical space is the ontological counterpart of language taken as a whole, but what are the counterparts to its particular propositions? According to Wittgenstein to every proposition there corresponds a definite area of logical space, or—as he calls it—a logical place. Thus the logical place of a given proposition "p" may be visualized like this:

It is already apparent that Wittgenstein's idea aims at the construction of a geometrical representation for the logic of propositions, and that his "logical space" is an abstract space like the "phase‑space" of physics or the "sample‑space" of the theory of probability. And this leads immediately to the next and most essential question: what are to be the points of this abstract logical space?
The right answer: to this question has been already given by Stenius (Wittgenstein's 'Tractatus', 1960): every point in logical space is the representation of a possible world! (Stenius' answer is not the only one that has been suggested, but none of the others will do as an interpretation of Wittgenstein's position.) Let's call these worlds "logical points". We have thus:
Logical space = the totality of logical points,
The logical the set of logical points whichplace of “p" = would make the proposition "p" true.
One point in logical space is designated: it represents the actual world. (Since each possible world is incompatible with every other the designated point is unique.) Of course, we do not know its exact position; but if we know a proposition "p" to be true, we know the designated point to lie in that area of logical space which is the logical place of "p". Thus we have:
"p" is true = the designated point is contained in the logical place of "p".
According to Frege the denotation of a proposition is its truth‑value; according to Wittgenstein the denotation of a proposition is its logical place (= a set of possible worlds). And 'this makes clear, why formula (F) has to be rejected.
A material equivalence "p ≡ q" means that the propositions “p” and “q” have the same truth-value. Upon our interpretation this corresponds to the following situation in logical space:
A statement of material equivalence "p ≡ q" is true if, and only if. the designated point lies as a matter fact [sic] somewhere in the shaded area of logical space. And this may be the case, or it may not be. On the other hand, an identity statement "p = q” means that the logical places of "p" and "q" coincide; and this cannot be the case here by any means.
But how can formula (F) be a theorem of "Fregean" logic, if it is not valid? To solve this puzzle let us assume for the sake of intuitiveness that there are only three possible worlds, marked by the numbers (1), (2), (3) respectively. Under this assumption the relation between language and reality may be presented in the form of a matrix, with columns of the digits "1" and "0" representing the logical places of the corresponding propositions:
Language
p1 p2 p3 p4 p5 p6 p7 p8
(1) 1 1 1 1 0 0 0 0
Logical space (2) 1 1 0 0 1 1 0 0
(3) 1 0 1 0 1 0 1 0
In the logical space consisting of only 3 points there are only 8 logical places; and consequently there are in the corresponding language only 8 extensionally distinguishable propositions (i.e. propositions with different denotations).
However, our assumption was quite arbitrary, for there are as yet no obvious reasons against taking any other number—finite or infinite—to be the number of logical points. So let us assume now, that this number is one: There is only one possible world, namely the actual one. Under this assumption we get the following matrix of the relation between language and reality:
Language
p1 p2
Logical space { (1) 1 0
In this matrix there are only two logical places. And since these two logical places (columns) are correlated in a one‑to‑one manner with the two truth‑values (digits), there is neither the need nor the possibility of distinguishing the logical place of a proposition from its truth‑value, or the designated truth‑value from the designated logical point.
But this is exactly the import of the axiom of Frege. According to Frege true propositions are indistinguishable extensionally, for they all denote (bedeuten) one and the same, namely the real world or Being (das Wahre); and similarly with false propositions: they all denote Non‑Being (das Falsche). Therefore Being and Non‑Being are the two logical places of Frege's logic.
The number of logical places (m) depends obviously upon the number of truth‑values (v), and upon the number of logical points (n); and they are interrelated in a most simple way:
(I) m=vⁿ
If our logic is, as usual, a two‑valued one (v = 2), clearly the number of logical places will be: m = 2ⁿ. But to Fregean logic it is not essential to assume that there are only two truth‑values. What is essential to it, is to have the equality:
(II) m = v
which in view of (I) is equivalent to assuming that the number of logical points is one! i.e.:
(F'') n = 1
Formula (F) holds good if, and only if, condition (F'') is satisfied. In other words: the axiom of Frege is equivalent to the assumption that logical space consists of a single point. Obviously this single point is at the same time the designated one.
Frege's logic is a logic of two truth‑values and two logical places, and so it is Fregean. But the three‑valued logic of Łukasiewiez is Fregean too, for its matrix has the form:
Language
p1 p2 p3
logical space { (1) 1 ½ 0
with "½" marking the logical indeterminateness. (According to Łukasiewiez's philosophy this realm of indeterminateness was to be the Future, regarded as something intermediate between Being and Non‑Being; i.e. in our terminology as a third logical place.) But Wittgenstein’s logic is Non‑Fregean, for there are in it two truth values and many logical places, the number of logical points—and consequently also the number of logical places—being kept variable.
In this framework Frege's logic is just a special case of Non‑Fregean logic, but it is also a very peculiar one. This peculiarity consists in its extreme simplicity: to construct a still simpler logic seems out of question [sic]. Formal simplicity is thus the great and indisputable merit of Frege's system of logic, but it is not come free of charge [sic]. It has been based on the assumption that the real coincides with the possible, and both of them with the necessary, that modal distinctions are not concerned with reality, but only with our thoughts.
This assumption may be disputed, but that is not our point. What is to be insisted on here, is only the fact that in Fregean logic there is such an assumption present.
UNIVERSITY OF WARSAWPOLAND
SOURCE: Wolniewicz, Boguslaw. "Wittgensteinian Foundations of Non-Fregean Logic," in Contemporary East European Philosophy, Vol. 3, edited by Edward D'Angelo, David DeGrood, and Dale Riepe (Bridgeport, CT: Spartacus Books, 1971), pp. 231-243.