L. Magnani & C. Casadio (eds.), Model-Based Reasoning in Science and Technology, Springer, Cham 2016, pp. 489-505., 2016
The nature of the scientific method has been a main concern of
philosophy from Plato to Mill. In ... more The nature of the scientific method has been a main concern of
philosophy from Plato to Mill. In that period logic has been considered to be
a part of the methodology of science. Since Mill, however, the situation has
completely changed. Logic has ceased to be a part of the methodology of
science, and no Discourse on method has been written. Both logic and the
methodology of science have stopped dealing with the process of discovery,
and generally with the actual process of scientific research. As a result,
several first-rate scientists, from Feynman and Weinberg to Dyson and
Hawkins, have concluded that philosophy has become useless and totally
irrelevant to science. The aim of this paper is to give some indications as to
how to develop a logic concerned with the process of discovery and a methodology of science dealing with the actual process of scientific research.
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This is because, according to today’s dominant philosophy, analytic philosophy, philosophy is not acquisition of knowledge, namely an inquiry aimed at acquiring knowledge, and this is how it should be, because acquisition of knowledge is the task of science, not of philosophy. As a result, instead of being acquisition of knowledge, analytic philosophy deals with artifactual puzzles of no abiding significance.
To overcome the present impasse of philosophy, this book puts forward a view of philosophy as acquisition of knowledge, according to which philosophy can open new ways to knowledge, and can even contribute to the creation of new sciences. This is what philosophy has done until recently, and there is no reason why it could not do so in the future.
This book offers an alternative approach, heuristic philosophy of mathematics, according to which the philosophy of mathematics can concern itself with the making of mathematics, in particular discovery. On this basis, the book argues that mathematics is problem solving by the analytic method, and that this can account for all the main features of mathematics: mathematical method, objects, demonstrations, definitions, diagrams, notations, explanations, beauty, applicability, and knowledge.
Review: https://www.exeter.ac.uk/research/groups/education/pmej/pome41/Marshall%20Gordon%20%20%20Review%20of%20Heuristic%20Philosophy%20of%20Mathematics%20by%20Carlo%20Cellucci.docx
The abandonment of the view that philosophy aims at knowledge and methods to acquire knowledge, has contributed to the increasing irrelevance of the subject, so much so that several scientists, and even some philosophers, have concluded that philosophy is dead and has dissolved into the sciences. The question then arises whether philosophy can still be fruitful, and what kind of philosophy can be such.
In order to answer this question, this book attempts to revive the view that philosophy aims at knowledge and methods to acquire knowledge. Reviving it requires a rethinking of knowledge. The importance of such rethinking depends on the central role knowledge plays in human life. In particular, a rethinking of knowledge requires a rethinking of mathematical knowledge, which raises special problems.
The purpose of this book is to explain how the present condition of logic came about and to propose an alternative to it. To this end, the book first gives an overview of how logic and its relation to the scientific method have been conceived in antiquity and in the modern age, because this provides indications for a new approach to the subject. Then the book proposes a new view of logic and its relation to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also proposes a new view of philosophy and its relation to knowledge, because seeing logic in a wider context helps to place it on a more satisfactory basis. In terms of the proposed new view, logic is primarily a logic of discovery. Accordingly, the book deals with the rules of discovery.
Papers
abandoned, the attempt to give a rational account of discovery has been given up, and logic has been disconnected from discovery. This paper outlines a way of reconnecting logic with discovery.
expression of the view that the method of mathematics is the axiomatic method. In this article it is argued that these two views of the mathematical method are really
opposed. In order to answer the question whether mathematics is problem solving or theorem proving, the article retraces the Greek origins of the question and
Hilbert’s answer. Then it argues that, by Gödel’s incompleteness results and other reasons, only the view that mathematics is problem solving is tenable.
philosophy from Plato to Mill. In that period logic has been considered to be
a part of the methodology of science. Since Mill, however, the situation has
completely changed. Logic has ceased to be a part of the methodology of
science, and no Discourse on method has been written. Both logic and the
methodology of science have stopped dealing with the process of discovery,
and generally with the actual process of scientific research. As a result,
several first-rate scientists, from Feynman and Weinberg to Dyson and
Hawkins, have concluded that philosophy has become useless and totally
irrelevant to science. The aim of this paper is to give some indications as to
how to develop a logic concerned with the process of discovery and a methodology of science dealing with the actual process of scientific research.
This is because, according to today’s dominant philosophy, analytic philosophy, philosophy is not acquisition of knowledge, namely an inquiry aimed at acquiring knowledge, and this is how it should be, because acquisition of knowledge is the task of science, not of philosophy. As a result, instead of being acquisition of knowledge, analytic philosophy deals with artifactual puzzles of no abiding significance.
To overcome the present impasse of philosophy, this book puts forward a view of philosophy as acquisition of knowledge, according to which philosophy can open new ways to knowledge, and can even contribute to the creation of new sciences. This is what philosophy has done until recently, and there is no reason why it could not do so in the future.
This book offers an alternative approach, heuristic philosophy of mathematics, according to which the philosophy of mathematics can concern itself with the making of mathematics, in particular discovery. On this basis, the book argues that mathematics is problem solving by the analytic method, and that this can account for all the main features of mathematics: mathematical method, objects, demonstrations, definitions, diagrams, notations, explanations, beauty, applicability, and knowledge.
Review: https://www.exeter.ac.uk/research/groups/education/pmej/pome41/Marshall%20Gordon%20%20%20Review%20of%20Heuristic%20Philosophy%20of%20Mathematics%20by%20Carlo%20Cellucci.docx
The abandonment of the view that philosophy aims at knowledge and methods to acquire knowledge, has contributed to the increasing irrelevance of the subject, so much so that several scientists, and even some philosophers, have concluded that philosophy is dead and has dissolved into the sciences. The question then arises whether philosophy can still be fruitful, and what kind of philosophy can be such.
In order to answer this question, this book attempts to revive the view that philosophy aims at knowledge and methods to acquire knowledge. Reviving it requires a rethinking of knowledge. The importance of such rethinking depends on the central role knowledge plays in human life. In particular, a rethinking of knowledge requires a rethinking of mathematical knowledge, which raises special problems.
The purpose of this book is to explain how the present condition of logic came about and to propose an alternative to it. To this end, the book first gives an overview of how logic and its relation to the scientific method have been conceived in antiquity and in the modern age, because this provides indications for a new approach to the subject. Then the book proposes a new view of logic and its relation to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also proposes a new view of philosophy and its relation to knowledge, because seeing logic in a wider context helps to place it on a more satisfactory basis. In terms of the proposed new view, logic is primarily a logic of discovery. Accordingly, the book deals with the rules of discovery.
abandoned, the attempt to give a rational account of discovery has been given up, and logic has been disconnected from discovery. This paper outlines a way of reconnecting logic with discovery.
expression of the view that the method of mathematics is the axiomatic method. In this article it is argued that these two views of the mathematical method are really
opposed. In order to answer the question whether mathematics is problem solving or theorem proving, the article retraces the Greek origins of the question and
Hilbert’s answer. Then it argues that, by Gödel’s incompleteness results and other reasons, only the view that mathematics is problem solving is tenable.
philosophy from Plato to Mill. In that period logic has been considered to be
a part of the methodology of science. Since Mill, however, the situation has
completely changed. Logic has ceased to be a part of the methodology of
science, and no Discourse on method has been written. Both logic and the
methodology of science have stopped dealing with the process of discovery,
and generally with the actual process of scientific research. As a result,
several first-rate scientists, from Feynman and Weinberg to Dyson and
Hawkins, have concluded that philosophy has become useless and totally
irrelevant to science. The aim of this paper is to give some indications as to
how to develop a logic concerned with the process of discovery and a methodology of science dealing with the actual process of scientific research.
mathematical beauty to mathematical research, and claims that a piece of
mathematics is beautiful when it is enlightening. He stops short, however, of
explaining what he means by ‘enlightening’. This paper proposes an
alternative approach, according to which a mathematical demonstration or
theorem is beautiful when it provides understanding. Mathematical beauty
thus considered can have a role in mathematical discovery because it can
guide the mathematician in selecting which hypothesis to consider and which
to disregard. Thus aesthetic factors can have an epistemic role qua aesthetic
factors in mathematical research.
discipline essentially different from the sciences. While the sciences describe the world as it is in itself, independent of perspective, philosophy tries to make sense of ourselves and of our activities. Only the humanistic disciplines, in particular philosophy, can do this, the sciences have nothing to say about it. In this note I point out some limitations of Williams’ view and outline an alternative view.
knowledge is faced with the problem that all attempts so far to define that
concept are subject to counterexamples. As an alternative, this paper argues
that the subject matter of epistemology is knowledge itself rather than the
concept of knowledge. Moreover, knowledge is not merely a state of mind
but rather a certain kind of response to the environment that is essential for
survival. In this perspective, the paper outlines an answer to four basic
questions about knowledge: What is the role of knowledge in human life?
What is the relation between knowledge and reality? How is knowledge
acquired? Is there any a priori knowledge?
of natural science is truth. In particular, this is a basic tenet of
contemporary scientific realism. However, all concepts of truth that have
been put forward are inadequate to modern science because they do not
provide a criterion of truth. This means that we will generally be unable
to recognize a scientific truth when we reach it. As an alternative, this
paper argues that the goal of natural science is plausibility and considers
some characters of plausibility.