The Art Of Reasoning: An Introduction To Logic ...
A standard logic-oriented critical thinking text that is commonly used in introductory logic and critical thinking courses taught in philosophy departments. There's enough here for a two-term course, or you could pick a selection of topics for a one-term course.
The art of reasoning: An introduction to logic ...
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics.
Systems of logic are theoretical frameworks for assessing the correctness of reasoning and arguments. Logic has been studied since antiquity; early approaches include Aristotelian logic, Stoic logic, Anviksiki, and the Mohists. Modern formal logic has its roots in the work of late 19th-century mathematicians such as Gottlob Frege. While Aristotelian logic focuses on reasoning in the form of syllogisms, in the modern era its traditional dominance was replaced by classical logic, a set of fundamental logical intuitions shared by most logicians. It consists of propositional logic, which only considers the logical relations on the level of propositions, and first-order logic, which also articulates the internal structure of propositions using various linguistic devices, such as predicates and quantifiers. Extended logics accept the basic intuitions behind classical logic and extend it to other fields, such as metaphysics, ethics, and epistemology. Deviant logics, on the other hand, reject certain classical intuitions and provide alternative accounts of the fundamental laws of logic.
The word "logic" originates from the Greek word "logos", which has a variety of translations, such as reason, discourse, or language.[1][2] Logic is traditionally defined as the study of the laws of thought or correct reasoning,[3] and is usually understood in terms of inferences or arguments. Reasoning may be seen as the activity of drawing inferences whose outward expression is given in arguments.[3][4][5] An inference or an argument is a set of premises together with a conclusion. Logic is interested in whether arguments are good or inferences are valid, i.e. whether the premises support their conclusions.[6][7][8] These general characterizations apply to logic in the widest sense, since they are true both for formal and informal logic, but many definitions of logic focus on the more paradigmatic formal logic. In this narrower sense, logic is a formal science that studies how conclusions follow from premises in a topic-neutral way.[9][10][11] In this regard, logic is sometimes contrasted with the theory of rationality, which is wider since it covers all forms of good reasoning.[12]
As a formal science, logic contrasts with both the natural and social sciences in that it tries to characterize the inferential relations between premises and conclusions based on their structure alone.[15][16] This means that the actual content of these propositions, i.e. their specific topic, is not important for whether the inference is valid or not.[9][10] Valid inferences are characterized by the fact that the truth of their premises ensures the truth of their conclusion: it is impossible for the premises to be true and the conclusion to be false.[8][17] The general logical structures characterizing valid inferences are called rules of inference.[6] In this sense, logic is often defined as the study of valid arguments.[4] This contrasts with another prominent characterization of logic as the science of logical truths.[18] A proposition is logically true if its truth depends only on the logical vocabulary used in it. This means that it is true in all possible worlds and under all interpretations of its non-logical terms.[19] These two characterizations of logic are closely related to each other: an inference is valid if the material conditional from its premises to its conclusion is logically true.[18]
The term "logic" can also be used in a slightly different sense as a countable noun. In this sense, a logic is a logical formal system. Distinct logics differ from each other concerning the rules of inference they accept as valid and concerning the formal languages used to express them.[4][20][21] Starting in the late 19th century, many new formal systems have been proposed. There are various disagreements concerning what makes a formal system a logic.[4][21] For example, it has been suggested that only logically complete systems qualify as logics. For such reasons, some theorists deny that higher-order logics and fuzzy logic are logics in the strict sense.[4][22][23]
Logic encompasses both formal and informal logic.[4][24] Formal logic is the traditionally dominant field,[17] but applying its insights to actual everyday arguments has prompted modern developments of informal logic,[24][25][26] which considers problems that formal logic on its own is unable to address.[17][26] Both provide criteria for assessing the correctness of arguments and distinguishing them from fallacies.[11][17] Various suggestions have been made concerning how to draw the distinction between the two, but there is no universally accepted answer.[26][27]
Another approach draws the distinction according to the different types of inferences analyzed.[24][36][37] This perspective understands formal logic as the study of deductive inferences in contrast to informal logic as the study of non-deductive inferences, like inductive or abductive inferences.[24][37] The characteristic of deductive inferences is that the truth of their premises ensures the truth of their conclusion. This means that if all the premises are true, it is impossible for the conclusion to be false.[8][17] For this reason, deductive inferences are in a sense trivial or uninteresting since they do not provide the thinker with any new information not already found in the premises.[38][39] Non-deductive inferences, on the other hand, are ampliative: they help the thinker learn something above and beyond what is already stated in the premises. They achieve this at the cost of certainty: even if all premises are true, the conclusion of an ampliative argument may still be false.[18][40][41]
One more approach tries to link the difference between formal and informal logic to the distinction between formal and informal fallacies.[24][26][35] This distinction is often drawn in relation to the form, content, and context of arguments. In the case of formal fallacies, the error is found on the level of the argument's form, whereas for informal fallacies, the content and context of the argument are responsible.[42][43][44] Formal logic abstracts away from the argument's content and is only interested in its form, specifically whether it follows a valid rule of inference.[9][10] In this regard, it is not important for the validity of a formal argument whether its premises are true or false. Informal logic, on the other hand, also takes the content and context of an argument into consideration.[17][26][28] A false dilemma, for example, involves an error of content by excluding viable options, as in "you are either with us or against us; you are not with us; therefore, you are against us".[45][43] For the strawman fallacy, on the other hand, the error is found on the level of context: a weak position is first described and then defeated, even though the opponent does not hold this position. But in another context, against an opponent that actually defends the strawman position, the argument is correct.[33][43]
Other accounts draw the distinction based on investigating general forms of arguments in contrast to particular instances, or on the study of logical constants instead of substantive concepts. A further approach focuses on the discussion of logical topics with or without formal devices, or on the role of epistemology for the assessment of arguments.[17][26]
Premises and conclusions are the basic parts of inferences or arguments and therefore play a central role in logic. In the case of a valid inference or a correct argument, the conclusion follows from the premises, or in other words, the premises support the conclusion.[7][46] For instance, the premises "Mars is red" and "Mars is a planet" support the conclusion "Mars is a red planet". For most types of logic, it is accepted that premises and conclusions have to be truth-bearers.[7][46][i] This means that they have a truth value: they are either true or false. Thus contemporary philosophy generally sees them either as propositions or as sentences.[7] Propositions are the denotations of sentences and are usually understood as abstract objects.[48][49]
Propositional theories of premises and conclusions are often criticized because of the difficulties involved in specifying the identity criteria of abstract objects or because of naturalist considerations.[7] These objections are avoided by seeing premises and conclusions not as propositions but as sentences, i.e. as concrete linguistic objects like the symbols displayed on a page of a book. But this approach comes with new problems of its own: sentences are often context-dependent and ambiguous, meaning an argument's validity would not only depend on its parts but also on its context and on how it is interpreted.[7][50] Another approach is to understand premises and conclusions in psychological terms as thoughts or judgments. This position is known as psychologism and was heavily criticized around the turn of the 20th century.[7][51][52] 041b061a72