INTRODUCTION : PHILOSOPHY OF LOGIC TODAY
LOGIC AND PHILOSOPHY
It is standard in works dedicated to topics in philosophy and logic to distinguish between philosophy of logic and philosophical logic. There is no universally agreed upon way of dividing up these categories, and some authors prefer to conflate the two and treat the two phrases as more or less synonymous.
I do not have particularly strong reasons for distinguishing or running these concepts together. If pressed, I favor a terminology in which philosophical logic involves applications of any recognized methods of logic to philosophical problems or for purposes of advancing philosophical discussions, whereas philosophy of logic is the consideration of philosophical problems that arise in relation to work in any recognized branch of logic.By this stipulation, all of the papers in this volume belong squarely in the category of philosophical logic, and thereby also fall under the category of philosophy of logic so defined. The essays all raise problems for philosophical reflection at the same time that they illustrate the methods of logic in particular applications. By addressing the nature and limits of logic from both a theoretical and practical point of view, in the context of explaining the wide variety of different types of logic that have emerged in the recent proliferation of formal logical systems, the papers directly and indirectly engage central issues in the philosophy of logic while commenting on the principles of logic and its uses primarily in philosophy, mathematics and science.
Logic, like any other subject, depends on philosophical presuppositions. It raises conceptual and especially foundational questions that can only be profitably engaged by thinkers with rigorous philosophical training. The fact that so many logicians have also been philosophers, and that the motivation for so many important innovations in logic have derived from philosophical concerns about the clarification of concepts, problems and distinctions, means that logic and philosophy of logic are historically at least if not also thematically inseparably intertwined. It is only by understanding the complex justifications for formal logical apparatus, for the exact expression of ideas and deductively valid inference of sentences, that we can hope to fathom the explosion of logical systems that have appeared since the late nineteenth century through the latter half of the twentieth and continuing now into the twenty-first century. With every new addition to the vocabulary and mechanisms of formal symbolic logic there arise an exponentially greater number of philosophical questions about the meaning and implications of what logic introduces to the realms of mathematics and science.
IN THE LOGIC CANDY STORE
I want to introduce this handbook of essays in the philosophy of logic by raising a problem that I think holds a vital key to understanding the nature of logic in contemporary philosophy and mathematics. Not all of the papers in this volume do not directly address the question, but they provide ample raw material for reflecting on the kinds of answers that might be given.
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WHAT IS LOGIC?
Jaakko Hintikka and Gabriel Sandu
1 LOGIC AND INFERENCE
It is far from clear what is meant by logic or what should be meant by it. It is nevertheless reasonable to identify logic as the study of inferences and inferential relations. The obvious practical use of logic is in any case to help us to reason well, to draw good inferences. And the typical form the theory of any part of logic seems to be a set of rules of inference.
This answer already introduces some structure into a discussion of the nature of logic, for in an inference we can distinguish the input called a premise or premises from the output known as the conclusion. The transition from a premise or a number of premises to the conclusion is governed by a rule of inference. If the inference is in accordance with the appropriate rule, it is called valid. Rules of inference are often thought of as the alpha and omega of logic. Conceiving of logic as the study of inference is nevertheless only the first approximation to the title question, in that it prompts more questions than it answers. It is not clear what counts as an inference or what a theory of such inferences might look like. What are the rules of inference based on? Where do we find them? The ultimate end one tries to reach through a series of inferences is usually supposed to be a true proposition. Frege [1970, 126] wrote that “the word ‘true’ characterizes logic.” But how does this desideratum determine the rules of inference? A few distinctions will illustrate the embarrassment of riches covered by the term “logic” and at the same time sharpen the issues.
Handbook of the Philosophy of Science. Philosophy of Logic
Volume editor:Dale Jacquette
General editors:Dov M. Gabbay, Paul Thagard and John Woods
2007 Elsevier B.V. All rights reserved.
link
LOGIC AND PHILOSOPHY
It is standard in works dedicated to topics in philosophy and logic to distinguish between philosophy of logic and philosophical logic. There is no universally agreed upon way of dividing up these categories, and some authors prefer to conflate the two and treat the two phrases as more or less synonymous.
I do not have particularly strong reasons for distinguishing or running these concepts together. If pressed, I favor a terminology in which philosophical logic involves applications of any recognized methods of logic to philosophical problems or for purposes of advancing philosophical discussions, whereas philosophy of logic is the consideration of philosophical problems that arise in relation to work in any recognized branch of logic.By this stipulation, all of the papers in this volume belong squarely in the category of philosophical logic, and thereby also fall under the category of philosophy of logic so defined. The essays all raise problems for philosophical reflection at the same time that they illustrate the methods of logic in particular applications. By addressing the nature and limits of logic from both a theoretical and practical point of view, in the context of explaining the wide variety of different types of logic that have emerged in the recent proliferation of formal logical systems, the papers directly and indirectly engage central issues in the philosophy of logic while commenting on the principles of logic and its uses primarily in philosophy, mathematics and science.
Logic, like any other subject, depends on philosophical presuppositions. It raises conceptual and especially foundational questions that can only be profitably engaged by thinkers with rigorous philosophical training. The fact that so many logicians have also been philosophers, and that the motivation for so many important innovations in logic have derived from philosophical concerns about the clarification of concepts, problems and distinctions, means that logic and philosophy of logic are historically at least if not also thematically inseparably intertwined. It is only by understanding the complex justifications for formal logical apparatus, for the exact expression of ideas and deductively valid inference of sentences, that we can hope to fathom the explosion of logical systems that have appeared since the late nineteenth century through the latter half of the twentieth and continuing now into the twenty-first century. With every new addition to the vocabulary and mechanisms of formal symbolic logic there arise an exponentially greater number of philosophical questions about the meaning and implications of what logic introduces to the realms of mathematics and science.
IN THE LOGIC CANDY STORE
I want to introduce this handbook of essays in the philosophy of logic by raising a problem that I think holds a vital key to understanding the nature of logic in contemporary philosophy and mathematics. Not all of the papers in this volume do not directly address the question, but they provide ample raw material for reflecting on the kinds of answers that might be given.
~~~~~~~~~~ ~~~~~~~~~~~ ~~~~~~~~~~~
~~~~~~~~~~ ~~~~~~~~~~~ ~~~~~~~~~~~
WHAT IS LOGIC?
Jaakko Hintikka and Gabriel Sandu
1 LOGIC AND INFERENCE
It is far from clear what is meant by logic or what should be meant by it. It is nevertheless reasonable to identify logic as the study of inferences and inferential relations. The obvious practical use of logic is in any case to help us to reason well, to draw good inferences. And the typical form the theory of any part of logic seems to be a set of rules of inference.
This answer already introduces some structure into a discussion of the nature of logic, for in an inference we can distinguish the input called a premise or premises from the output known as the conclusion. The transition from a premise or a number of premises to the conclusion is governed by a rule of inference. If the inference is in accordance with the appropriate rule, it is called valid. Rules of inference are often thought of as the alpha and omega of logic. Conceiving of logic as the study of inference is nevertheless only the first approximation to the title question, in that it prompts more questions than it answers. It is not clear what counts as an inference or what a theory of such inferences might look like. What are the rules of inference based on? Where do we find them? The ultimate end one tries to reach through a series of inferences is usually supposed to be a true proposition. Frege [1970, 126] wrote that “the word ‘true’ characterizes logic.” But how does this desideratum determine the rules of inference? A few distinctions will illustrate the embarrassment of riches covered by the term “logic” and at the same time sharpen the issues.
Handbook of the Philosophy of Science. Philosophy of Logic
Volume editor:Dale Jacquette
General editors:Dov M. Gabbay, Paul Thagard and John Woods
2007 Elsevier B.V. All rights reserved.
link