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
LPA13 Norms and society
LPA14 Power and happiness
LPA15 Summary
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