"PHILOSOPHY OF SCIENCE"
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The content of No 3, 1997
Michal Heller
Cosmological singularities and noncommutative geometry
In the previous paper (Filozofia Nauki No 3-4, 1994, pp. 7-17)
we have shown how the initial and final singularities in the closed Friedman
world model can be analysed in terms of the structured spaces in spite
of the fact that these singularities constitute the single point
in the b-boundary of space-time. In the present paper we generalize
our approach by using methods of noncommutative geometry. We construct
a noncommutative algebra in terms of which geometry of space-time
with singularities can be developed. This algebra admits a representation
in the space of operators on a Hilbert space, and the initial and final singularities in the closed Friedman
model are given by its two distinct representations. The striking
feature of this approach is its analogy with the mathematical formalism
of quantum mechanics.
Jerzy Golosz
Some arguments in favor of substantivalism
In the article I subject to criticism Field's argument, according to
which field theory takes space-time to be a substance, since it ascribes
field properties to space-time points. The fundamental flaw of this argument,
I suggest, is the incompatibility of Field's interpretation of field
theory with the way this theory is understood and utilized
by its users, namely scientists. My criticism is based on the assumption
that one cannot propose an ontology of a given scientific theory and at the
same time imposing on it an interpretation which clashes with the interpretation current
among its users. I also suggest that in order to establish the ontology
of a scientific theory one should take into account not only the way it functions but also the way
it has been constructed. According to this criterion, field theory
does indeed take space-time to be a substance.
Leon Koj
Scientific theories as dynamic systems
In the first part of the paper three concepts of system are introduced.
The first is the following ordered set: S = <C, R1, ..., Rk,
Rk+1, ..., Rk+m, U>,
where S is a given system, C is the set of its parts,
R1, ..., Rk are relations between these parts,
Rk+1, ..., Rk+m are relations between parts of
S and its environment U. This concept does not
take into account the fact that real things change. Thus it is the
concept of abstract system.
The second concept takes changes of systems for granted. At every period
i the system is slightly different. At the periods i Si
is a set of sections of a real system: Si = <{C}i,
{R1, ..., Rk}i,
{Rk+1, ..., Rk+m}i, {U}i>,
where {C}i is the set of sets of parts of S,
{R1, ..., Rk}i and
{Rk+1, ..., Rk+m}i
are sets of relations.
Different sections of a system are similar; the same holds for the relations
and the subsequent environments. To describe the evolution of systems
these similarity-relations have to be considered. Let the relations between
the C's, the parts of the system, be symbolized as X,
the similarity relations between the
{R1, ..., Rk} pointed to by T, and the
relations between the other sets of relations marked by Z.
Let W be asigned to the relations between the succesive environments.
SI is a system which lasts during the period I and changes in this time.
The period I is in fact identical with i. The symbol
SI was introduced to point to the relations S,
T, Z, W, which were absent in the definition of Si.
Now we have the following third concept of system: SI =
<{C}i, X,
{R1, ..., Rk}i,
T,
{Rk+1, ..., Rk+m}i,
Z, {U}i, W>.
In the second part of the paper the relation X is analysed, when
C consists of statements and S is a theory. The relation is to the
effect that statements of later stages of a theory refer to n-tuples
which exhibit more arguments that the relation spoken of at earlier stages
of the theory.
Renata Zieminska
Intensionalism and foundationalism in epistemology
Contemporary philosophy (at least in English-speaking world) is dominated by discussions between
foundationalism and externalism on the other hand. R. Chisholm defends foundationalistic and internalistic position.
Epistemological foundationalism is the thesis that there are basic beliefs which are the foundation for the
justificaction of others. According to Chisholm such basic beliefs are some simple
truths of reason and some beliefs about the self-presenting states like thinking,
seeming or sensing. There are some problems with such basic beliefs, but Chisholm's main
important argument is that here is no alternative to foundationalism in epistemology, because
its opponent, the coherence theory, presupposes some form of foundationalism.
The discussion between internalism and externalism is more recent. Externalism
claims that what makes our beliefs justified is something external to subject,
It may be truth, causal relations or counterfactual relations. According to Chisholm
all externalistic theories are either empty (they reduce justification to truth) or they
use some internalistic concepts. He gives some counterexamples to the theory by A. Goldman
(one of the most important proponents of externalism). Internalists claim that what can make our beliefs justified
must be something internal, accessible to subject.
Marek Lagosz
Frege'c category of unsaturatedness
Frege's category of unsaturatedness (incompleteness) is a central concept of his
ontology. By means of it Frege divides the realm of all entities into functions
and objects.
In this paper I try to show some fundamental difficultes relevant to the concept in hand.
First of all I am interested in difference between incompleteness of the propositional
functions (especially concepts) and incompleteness of the non-propositional functions
(particularly arithmetical functions).
I also discuss a few other problems closely conected with the above, namely:
1) distinction between unsaturatedness of expressions and unsaturatedness of entities
to which these expressions refer;
2) possibility of ontological and epistemological interpretation of incompleteness;
3) interpretation of Fregean semantical category of sense from Frege's dualistic
ontology point of view.
Andrzej Bilat
Remarks on the logic of properties
Tadeusz Skalski
Coloured patches and images or praise of Democritus
Witold Marciszewski
Lukasiewicz's syntactical formalism as a model for intelligent action
Stefan Snihur
On the existence and ontological status of the future
Two questions are the starting point for the discussion contained in this article:
(a) Does the future exist? (b) What is the future?
A preliminary analysis of these questions leads to the conclusion that their solution
needs to introduce three different principal modes of existence characterized for objects
belonging to the time sphere of being. They are: real (actual) existence (i.e. existence
of "now"), postreal existence (the past) and potential (prereal) existence. In accordance
with this differentiation the answer to point (a) is generally determined by the following
theses: (1) The future exists in potentiality, (2) The future exists neither in reality nor
in postreality.
The notion of potential existence includes two categories of objects. The first one -
objects which in fact will become real objects (present). They may be described as
potential objects sensu stricto. The second category constists of the
quasi-potential objects, that is the objects whose potentiality of becoming real
(actual) ones will never come into existence.
The differentiation of categories mentioned above makes possible to formulate three
definitions of the future: (D1) The future is the domain of potential, or quasi-potential
objects, (D2) The future is the domain of the potential objects, (D3) The future is the domain of quasi-potential
objects.
The definition (D3) is obviously inadequate, hence the solution of the problem, what is the future, may be
reduced to the choice between definitions (D1) and (D2). The arguments of the paper convince us that
the adequate definition of the future is the definition (D2). First - contrary to (D1) -
it describes the future as ontologically homogeneous domain containing only objects which
will become objects of the present and subsequently past objects. Second, when
the future is defined by the competitive definition (D1) it is doubtful whether the language
systems, referring to the time sphere of being, can fulfill the basic principles
of the classical logig: the principle of contradiction and the principle
of excluded middle.
Tomasz Bigaj
Philosophical remarks on three-valued logic (text downloadable)
As it is well known, Jan Lukasiewicz invented his three-valued logic as a result
of philosophical considerations concerning the problem of determinism and the status of
future contingent sentences. In the article I critically analyse the thesis that
the sentential calculus introduced by Lukasiewicz himself actually fulfills his
philosophical assumptions. I point out that there are some counterintuitive features
of Lukasiewicz three-valued logic. Firstly, there is no clear explanation
for adopting specific truth-tables for logical connectives, such as conjunction,
disjunction and first of all implication. Secondly, it is by no means clear,
why certain classical logical principles should be invalid for future contingents. And thirly,
I show that within Lukasiewicz logic it is possible to construct a "paradoxical" sentence,
namely a conditional which changes in time its logical value from truth to falsity.
This fact obviously contradicts Lukasiewicz's philosophical reading of his three truth values, according
to which true sentences are already positively determined, false sentences are negatively determined,
and possible sentences are neither positively, nor negatively determined.
Above-mentioned facts justify in my opinion the thesis that Lukasiewicz's three-valued logic
does not satisfy his philosophical intuitions. For this purpose more appropriate seems to be
sentential calculus based on the so-called supervaluation. It is three-valued, non-extentional
calculus, which nevertheless preserves all tautologies of the classical logic. At the end of
the article I consider the possibility of introducing to this calculus modal operators.
Archives:
Jan Lukasiewicz, Logic and the problem of foundation of mathematics.
