No. 4   -   A u t u m n   1 9 9 7    
http://www.pip.com.pl/MathUniversalis/4/index.html   --   ISSN 1426-3513



MATHESIS
u n i v e r s a l i s


In this Issue
Intelligent Beliefs - a Challenge to AI



No. 4   Contents

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THE CONTENTS OF
PREVIOUS ISSUES


1 9 9 6


No. 1 / Winter

QED Initiative
Mechanization of Reasoning
The Centenary
of Lvov-Warsaw School
- G.Falkenberg. J.Jadacki

No. 2 / Spring

Descartes, Leibniz (Anniversaries)
Formalized Mathematics -J.Harrison
Formalizing Mathematics
by Reformulations - M.Kerber
A Format for Proof Presentation - J.Grundy
Leibniz and Knowledge Engineering - W.Marciszewski)
On Logic and Rhetoric - J.Woleński et al

No. 3 / Summer

Introduction to MSE
Teaching Logic with MSE - H.J.Hoover & P.Rudnicki
Suppositional Logic in MSE - W.Marciszewski
MSE Introduction to Logic - M.Mostowski
Mizar MSE SOFTWARE




Intelligent Belief - a Challenge to AI.
Introductory Comment by the Editor.

1. Intellectual Clearness according to Descartes.
Comments on selected passages of Discours and Principia, to define a rationalistic approach in the theory of belief.

2. Empirical Clearness according to Peirce. Comments on selected passages of Peirce's How to Make Our Ideas Clear , to define a pragmatist approach in the theory of belief.

3. Pragmatic Clearness according to James. This item includes the famous James' essay The Will to Believe, 1897, commemorated in its centenary (the text copied from James Fieser's resources), and a comment on his pragmatic notion of belief.

4. Intelligent Beliefs which Lack Clearness. On Pascal's Esprit de Finesse and Demon Procedures. - by Witold Marciszewski.

This text is an abridged and modified version of the paper entitled "Rational Beliefs as Produced by Computational Processes" which appeared in Foundations of Science, 2 (1997), 87-106, Kluwer, Dordrecht.

The items which follow do not fall under the heading if this issue. Instead, they continue some themes of the previous ones.

Item 5, below, is related to commemorating the Centenary of the Lvov-Warsaw School with No.1 of this journal (item 4). Among the School's original ideas there is S.Lesniewski's Ontology. Its originality can be measured by its distance to the mainstram logic. That Ontology does possess that quality is argued by Peter Simons, as reported in G.Falkenberg's review of Simons' book Philosophy and Logic in Central Europe from Bolzano to Tarski, Kluwer 1992.
A different approach is represented by L.Ridder who elaborates a set-theoretical semantical account of a fragment of Ontology, the so called "Elementary Ontology", together with a sketched proof of the soundness and the completeness of this system relative to the proposed semantic. The syntax of the system is formulated in the language of first order logic and the completeness proof is accomplished in Henkin-style in the crucial step.
The paper, accompanied by the author's biographical note, is formatted in LaTex. It is available in ASCII form (15 K) for downloading by LaTeX users. The paper is not refereed.

5. Eine vollstaendige mengentheoretische Charakterisierung der elementaren Ontologie - by Lothar Ridder.

6. Introductory Comment to Pages concerning the Solution of Robbins Problem.
In the field of automated theorem-proving (discussed in No.2 and No.3 of this journal) there was an important event in 1996, to wit a solution of the Robbins problem: whether the algebra resulting from Robbins' alteration of Huntington's postulates is Boolean?
The problem is reported in this comment. It includes links to some pages of W.McCunne who obtained the result in question (two pages of him are reproduced here with his kind permission).

7. Do Post's Logics Belong to Alternative Logics?
This is a brief comment - referring to a passage in The Development of Logic by W.Kneale and M.Kneale - to suggest a theme of discussion at the Emil Post Workshop in Bialystok, Poland, December 1997.

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