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Logic of  Propositional Attitudes  Introduction

NOTE: This whole text is being (re)written and a prepublication

1. Introduction

In this book I shall give the outlines and some results concerning a simple formal logical system to discuss problems of belief and desire, of meaning and denotation, of social and ethical norms, of free will  and rational actions, of probability and uncertainty, and of power and happiness. Also, the book starts with introductory chapters to philosophy, logic and probability theory that provide a sufficient intellectual and mathematical basis  for the rest of it, that attempts to state and solve aspects of the problems mentioned in formal logical  terms.

This formal logic presented extends classical logic and is minimally adequate to the problems of free will, rational action, meaning and denotation, and social knowledge and norms, in the sense that its formalisms allow a clearer statement of these problems and clearer arguments and proofs from clearer assumptions than is possible in natural language. This has many advantages, including the possibility of easily refuting or correcting my claims.  The one disadvantage of this formal approach is that many would-be scientists are not really up to it -  but then this book is not written for the lazy or the stupid.

2. Outline of the contents: 

Since what I am doing in fact is part of a number of academic disciplines - notably: philosophy, mathematics, and psychology - and since most of what I am doing is original, I shall start with two chapters that outline my views of Basic Philosophy and Basic Logic. These two chapters are also original and embody a somewhat different approach of presenting their subjects than is currently normal. (And those who are familiar with ordinary philosophy and dislike its pretentions and vagueness need not fear: My approach is different, and even if it is wholly false is so in clear and refutable English.)

The first two chapters are followed by chapters on Classical Proposititional Logic and Classical Probability Theory, that contain no new material  but serve to present my notation while reminding the reader of a number of basic important theorems in these subjects while showing how these may be proved.

In these first four chapters I outline most of my views of philosophy and logic that are necessary to understand the rest of the book, and that will also be generally useful to the reader even if he disagrees with the rest - which essentially consists of motivated additional assumptions and proofs of consequences of these. 

The next two chapters that follow the above outline are the foundations of Extended Propositional Logic and the basis of the Logic of Propositional Attitudes, which is a formal extension of extended propositional logic which in turn extends classical propositional logic. Extended propositional logic, in brief, extends classical propositional logic with a bi-valent way to reason about undecided propositions. This in turn  is used for an extension that surrect a set of formal assumptions minimally adequate to reasoning with propositional attitudesdes, which are statements about the beliefs, desires, experiences and actions of speakers of a language.

Up to this point the logic introduced and explained is a-temporal, but the next chapter introduce a number of formal assumptions that relate logic. probability and time  that allows a new approach to probability and to propositions about the future, the present and the past.

Having arrived at this point, all the necessary formalities have been surrected and explained, and the next chapters apply these.

First, there is a chapter outlining a new theory of free will and rational action, that shows how these are possible and that settles a problem of Sidgwick, Broad and Ross. This is followed by two chapters that outline a new theory of meaning and denotation, first somewhat informally and next somewhat formally. This in turn is followed by a chapter that explains something about the logic of society, gives a foundation ethics, and states a basis for the logic of mind a.k.a. psychology.0020The next chapter gives some further applications concerning power, happiness, economics and psychiatry, and the final chapter provides a summary of the book and its main theses.

3. Requirements and summary

Anybody who is sufficiently familiar with introductions to mathematical logic to read and work with ease in first-order predicate logic and in standard naive set theory is sufficiently qualified to understand what is said and written in these lectures with ease, since the content is conceptually new but not mathematically involved (and indeed not more so than ordinary algebra, of which it indeed also is an instance and extension).

Readers who desire to read a point by point survey of what is in these lectures may consult the last lecture, which contains a such a summary survey and some discussion of how what is presented in these lectures differs from other logical systems and why this is so.

All in all any reader with a clear mind and some basic knowledge of science, mathematics, philosophy and English should be able to read this book with understanding, and indeed all that is really needed is only a clear mind and the will to use it rationally. 


All files LPA

Foundations of Philosophy, Logic and Probability

LPA01  Natural Philosophy
LPA02  Natural Logic
LPA03  Propositional Logic
LPA04  Probability Theory - science, deduction, abduction, induction

Extended Logic 

LPA05  Extended Propositional Logic
LPA06  Basic Logic of Propositional Attitudes
LPA07  Quantified and iterated propositional attitudes

Propositions and time

LPA08  Kinds of propositions
LPA09  Propositions in time

Human Action

LPA10  Rational action and free will

Human Language

LPA11  Meaning and denotation

LPA12  Language and society

Human Society

  Norms and society 
LPA14  Power and happiness



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