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| Author | John Stuart Mill |
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| Language | English |
Publication date | 1843 |
| Publication place | United Kingdom |
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A System of Logic, Ratiocinative and Inductive is an 1843 book by English philosopher John Stuart Mill.
| | |
| Author | John Stuart Mill |
|---|---|
| Language | English |
Publication date | 1843 |
| Publication place | United Kingdom |
| Media type | |
A System of Logic, Ratiocinative and Inductive is an 1843 book by English philosopher John Stuart Mill.
In this work, he formulated the five principles of inductive reasoning that are known as Mill's Methods. This work is important in the philosophy of science, and more generally, insofar as it outlines the empirical principles Mill would use to justify his moral and political philosophies.
An article in "Philosophy of Recent Times" has described this book as an "attempt to expound a psychological system of logic within empiricist principles.”
This work was important to the history of science, being a strong influence on scientists such as Dirac. [1] [2] A System of Logic also had an impression on Gottlob Frege, who rebuked many of Mill's ideas about the philosophy of mathematics in his work The Foundations of Arithmetic . [3]
Mill revised the original work several times over the course of thirty years in response to critiques and commentary by Whewell, Bain, and others.
A System of Logic begins with a discussion of difficulty of a preliminary definition of what Logic is but gives one. Mill asserts his right to do this, " I do this by virtue of the right I claim for every author, to give whatever provisional definition he pleases of his own subject". He concludes with "Logic, then, is the science of the operations of the understanding which are subservient to the estimation of evidence"
This Book is headed "Of Names and Propositions".
Mill begins with a "simple" quotation from Thomas Hobbes which although simple contains the essence of what leads to the greater complexities there are in naming things and ideas.
In Chapter VI of this book Mill gives a look back at the different kinds of proposition. "We then examined the different kinds of Propositions, and found that, with the exception of those which are merely verbal, they assert five different kinds of matters of fact, namely, Existence, Order in Place, Order in Time, Causation, and Resemblance; that in every proposition one of these five is either affirmed, or denied, of some fact or phenomenon, or of some object the unknown source of a fact or phenomenon."
This book is headed "Of Inference, or Reasoning, in General".
Mill begins with the retrospect that we have concluded that propositions assert. We now move "to the peculiar problem of the Science of Logic, namely, how the assertions, of which we have analysed the import, are proved or disproved"
In Chapter I of this book Mill emphasies the practicality of the type of Logic He values and hopes this book will promote. "There is no more important intellectual habit, nor any the cultivation of which falls more strictly within the province of the art of logic, than that of discerning rapidly and surely the identity of an assertion when disguised under diversity of language".
This book is headed "Of Induction"
The centrality of Induction to Mill's System of Logic is emphasized by such statements as, "What Induction is, therefore, and what conditions render it legitimate, cannot but be deemed the main question of the science of logic, the question which includes all others."
This book is headed "Of Operations Subsidiary to Induction"
Mill writes that this book is needed because,
"The consideration of Induction, however, does not end with the direct rules for its performance. Something must be said of those other operations of the mind, which are either necessarily presupposed in all induction, or are instrumental to the more difficult and complicated inductive processes".
This book is headed "On Fallacies"
The five classes of fallacies being, Fallacies of Simple inspection, or a priori fallacies, Fallacies of Observation, Fallacies of Generalization, Fallacies of Ratiocination, Fallacies of Confusion.
This book is headed "On the Logic of the Moral Sciences".
John Stuart Mill thought this a very important chapter for the social progress he so keenly sought.
"The backward state of the Moral Sciences can only be remedied by applying to them the methods of Physical Science, duly extended and generalized".
Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation by JOHN STUART MILL BOOKS I-III AND APPENDICES [4]
Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation by JOHN STUART MILL BOOKS IV-VI AND APPENDICES [5]
In philosophy, empiricism is an epistemological view which holds that true knowledge or justification comes only or primarily from sensory experience and empirical evidence. It is one of several competing views within epistemology, along with rationalism and skepticism. Empiricists argue that empiricism is a more reliable method of finding the truth than purely using logical reasoning, because humans have cognitive biases and limitations which lead to errors of judgement. Empiricism emphasizes the central role of empirical evidence in the formation of ideas, rather than innate ideas or traditions. Empiricists may argue that traditions arise due to relations of previous sensory experiences.
In the philosophy of language, a proper name – examples include a name of a specific person or place – is a name which ordinarily is taken to uniquely identify its referent in the world. As such it presents particular challenges for theories of meaning, and it has become a central problem in analytic philosophy. The common-sense view was originally formulated by John Stuart Mill in A System of Logic (1843), where he defines it as "a word that answers the purpose of showing what thing it is that we are talking about but not of telling anything about it". This view was criticized when philosophers applied principles of formal logic to linguistic propositions. Gottlob Frege pointed out that proper names may apply to imaginary or nonexistent entities, without becoming meaningless, and he showed that sometimes more than one proper name may identify the same entity without having the same sense, so that the phrase "Homer believed the morning star was the evening star" could be meaningful and not tautological in spite of the fact that the morning star and the evening star identifies the same referent. This example became known as Frege's puzzle and is a central issue in the theory of proper names.
In classical rhetoric and logic, begging the question or assuming the conclusion is an informal fallacy that occurs when an argument's premises assume the truth of the conclusion. Historically, begging the question refers to a fault in a dialectical argument in which the speaker assumes some premise that has not been demonstrated to be true. In modern usage, it has come to refer to an argument in which the premises assume the conclusion without supporting it. This makes it an example of circular reasoning.
A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
Friedrich Ludwig Gottlob Frege was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever.
The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. The Stoics, especially Chrysippus, began the development of predicate logic.
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid. An argument is sound if it is valid and all its premises are true. Some theorists define deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: it is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning.
A singular term is a paradigmatic referring device in a language. Singular terms are defined as expressions that purport to denote or designate particular individual people, places, or other objects. They contrast with general terms which can apply to more than one thing.
Hume's principle or HP says that the number of Fs is equal to the number of Gs if and only if there is a one-to-one correspondence between the Fs and the Gs. HP can be stated formally in systems of second-order logic. Hume's principle is named for the Scottish philosopher David Hume and was coined by George Boolos.
In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, the Peripatetics. It was revived after the third century CE by Porphyry's Isagoge.
Inductive reasoning is any of various methods of reasoning in which broad generalizations or principles are derived from a body of observations. This article is concerned with the inductive reasoning other than deductive reasoning, where the conclusion of a deductive argument is certain given the premises are correct; in contrast, the truth of the conclusion of an inductive argument is at best probable, based upon the evidence given.
The Organon is the standard collection of Aristotle's six works on logical analysis and dialectic. The name Organon was given by Aristotle's followers, the Peripatetics, who maintained against the Stoics that Logic was "an instrument" of Philosophy.
Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises. The premises and the conclusion are propositions, i.e. true or false claims about what is the case. Together, they form an argument. Logical reasoning is norm-governed in the sense that it aims to formulate correct arguments that any rational person would find convincing. The main discipline studying logical reasoning is logic.
In logic and philosophy, a formal fallacy is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic. It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion. Thus, a formal fallacy is a fallacy in which deduction goes wrong, and is no longer a logical process. This may not affect the truth of the conclusion, since validity and truth are separate in formal logic.
In metalogic and metamathematics, Frege's theorem is a metatheorem that states that the Peano axioms of arithmetic can be derived in second-order logic from Hume's principle. It was first proven, informally, by Gottlob Frege in his 1884 Die Grundlagen der Arithmetik and proven more formally in his 1893 Grundgesetze der Arithmetik I. The theorem was re-discovered by Crispin Wright in the early 1980s and has since been the focus of significant work. It is at the core of the philosophy of mathematics known as neo-logicism.
Inductivism is the traditional and still commonplace philosophy of scientific method to develop scientific theories. Inductivism aims to neutrally observe a domain, infer laws from examined cases—hence, inductive reasoning—and thus objectively discover the sole naturally true theory of the observed.
The Foundations of Arithmetic is a book by Gottlob Frege, published in 1884, which investigates the philosophical foundations of arithmetic. Frege refutes other idealist and materialist theories of number and develops his own platonist theory of numbers. The Grundlagen also helped to motivate Frege's later works in logicism.
The following events related to sociology occurred in the 1840s.
British philosophy refers to the philosophical tradition of the British people. "The native characteristics of British philosophy are these: common sense, dislike of complication, a strong preference for the concrete over the abstract and a certain awkward honesty of method in which an occasional pearl of poetry is embedded".
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.
Farmelo also discusses, across several chapters, the influences of John Stuart Mill...
A System of Logic public domain audiobook at LibriVox