# Relationship of philosophy and logic

### Philosophy of logic | jingle-bells.info

Logic. Philosophy of logic, the study, from a philosophical perspective, of the nature and types of logic, including problems in the field and the relation of logic to. Logic is the study of the process of reason. It is concerned with the form of argument. Take the syllogism, for a concrete and rather hackneyed example: All men. Philosophy: Logic. classical logic within it, albeit as a minor part. It resembles a mathematical calculus and deals with the relations of symbols to each other.

This new logic, expounded in their joint work "Principia Mathematica", is much broader in scope than Aristotelian logicand even contains classical logic within it, albeit as a minor part. It resembles a mathematical calculus and deals with the relations of symbols to each other. Formal Logic is what we think of as traditional logic or philosophical logic, namely the study of inference with purely formal and explicit content i.

See the section on Deductive Logic below. A formal system also called a logical calculus is used to derive one expression conclusion from one or more other expressions premises. These premises may be axioms a self-evident proposition, taken for granted or theorems derived using a fixed set of inference rules and axioms, without any additional assumptions.

Formalism is the philosophical theory that formal statements logical or mathematical have no intrinsic meaning but that its symbols which are regarded as physical entities exhibit a form that has useful applications.

Informal Logic is a recent discipline which studies natural language arguments, and attempts to develop a logic to assess, analyze and improve ordinary language or "everyday" reasoning.

Natural language here means a language that is spoken, written or signed by humans for general-purpose communication, as distinguished from formal languages such as computer-programming languages or constructed languages such as Esperanto. It focuses on the reasoning and argument one finds in personal exchange, advertising, political debate, legal argument, and the social commentary that characterizes newspapers, television, the Internet and other forms of mass media.

Symbolic Logic is the study of symbolic abstractions that capture the formal features of logical inference. It deals with the relations of symbols to each other, often using complex mathematical calculus, in an attempt to solve intractable problems traditional formal logic is not able to address.

It is often divided into two sub-branches: See the section on Predicate Logic below. Propositional Logic or Sentential Logic: See the section on Propositional Logic below.

Both the application of the techniques of formal logic to mathematics and mathematical reasoning, and, conversely, the application of mathematical techniques to the representation and analysis of formal logic. The earliest use of mathematics and geometry in relation to logic and philosophy goes back to the Ancient Greeks such as Euclid, Plato and Aristotle.

### Philosophy of logic - Logic and other disciplines | jingle-bells.info

In the s and s, researchers predicted that when human knowledge could be expressed using logic with mathematical notation, it would be possible to create a machine that reasons or artificial intelligencealthough this turned out to be more difficult than expected because of the complexity of human reasoning. Deductive Logic Back to Top Deductive reasoning concerns what follows necessarily from given premises i.

An inference is deductively valid if and only if there is no possible situation in which all the premises are true and the conclusion false. However, it should be remembered that a false premise can possibly lead to a false conclusion.

## Philosophy of logic

Deductive reasoning was developed by AristotleThalesPythagoras and other Greek philosophers of the Classical Period. At the core of deductive reasoning is the syllogism also known as term logic ,usually attributed to Aristotlewhere one proposition the conclusion is inferred from two others the premiseseach of which has one term in common with the conclusion. All humans are mortal. An example of deduction is: All apples are fruit.

All fruits grow on trees. Therefore all apples grow on trees.

One might deny the initial premises, and therefore deny the conclusion. But anyone who accepts the premises must accept the conclusion. Today, some academics claim that Aristotle's system has little more than historical value, being made obsolete by the advent of Predicate Logic and Propositional Logic see the sections below. Inductive Logic Back to Top Inductive reasoning is the process of deriving a reliable generalization from observations i.

Inductive logic is not concerned with validity or conclusiveness, but with the soundness of those inferences for which the evidence is not conclusive. Many philosophers, including David HumeKarl Popper and David Miller, have disputed or denied the logical admissibility of inductive reasoning.

In particular, Hume argued that it requires inductive reasoning to arrive at the premises for the principle of inductive reasoning, and therefore the justification for inductive reasoning is a circular argument. An example of strong induction an argument in which the truth of the premise would make the truth of the conclusion probable but not definite is: All observed crows are black.

All crows are black. An example of weak induction an argument in which the link between the premise and the conclusion is weak, and the conclusion is not even necessarily probable is: I always hang pictures on nails. All pictures hang from nails.

Modal Logic Modal Logic is any system of formal logic that attempts to deal with modalities expressions associated with notions of possibility, probability and necessity. Modal Logic, therefore, deals with terms such as "eventually", "formerly", "possibly", "can", "could", "might", "may", "must", etc. Modalities are ways in which propositions can be true or false.

Types of modality include: Includes possibility and necessity, as well as impossibility and contingency. Hence the step from Turing machines to finite automata which are not assumed to have access to an infinite tape is an important one.

This limitation does not dissociate computer science from logic, however, for other parts of logic are also relevant to computer science and are constantly employed there. There are also close connections between automata theory and the logical and algebraic study of formal languages.

An interesting topic on the borderline of logic and computer science is mechanical theorem proving, which derives some of its interest from being a clear-cut instance of the problems of artificial intelligenceespecially of the problems of realizing various heuristic modes of thinking on computers. In theoretical discussions in this area, it is nevertheless not always understood how much textbook logic is basically trivial and where the distinctively nontrivial truths of logic including first-order logic lie.

Methodology of the empirical sciences The quest for theoretical self-awareness in the empirical sciences has led to interest in methodological and foundational problems as well as to attempts to axiomatize different empirical theories.

Moreover, general methodological problems, such as the nature of scientific explanations, have been discussed intensively among philosophers of science. In all of these endeavours, logic plays an important role. By and large, there are here three different lines of thought. Sometimes, claims regarding the usefulness of logic in the methodology of the empirical sciences are, in effect, restricted to such rudimentary applications.

This restriction is misleading, however, for most of the interesting and promising connections between methodology and logic lie on a higher level, especially in the area of model theory. In addition to those employing simple logic, two other contrasting types of theorists can be distinguished: Both approaches have advantages.

In spite of the oversimplification that first-order formulations often entail, however, they can yield theoretical insights because first-order logic including its model theory is mastered by logicians much more thoroughly than is set theory.

Many empirical sciences, especially the social sciences, use mathematical tools borrowed from probability theory and statistics, together with such outgrowths of these as decision theorygame theoryutility theory, and operations research. A modest but not uninteresting beginning in the study of their foundations has been made in modern inductive logic. Wouldn't you say that if I like people I should like animals as well?

That's because since in science and especially in philosophy we are pursuing definite and certain knowledge about beings, only arguments that are logically necessary and do not entail uncertain implications are recognized as acceptable arguments.

And since the strongest form of argument is deductionthey are the primary form of argument in philosophy. Additionally to ascertain that beyond the formal validity of arguments, their constituent premises axioms are also true all statements must be reducible to the most basic and evident truths whose validity is percent certain and definite. These self-evident truths or principles include the law of identity and non-contradiction.

**What is Logic? (Philosophical Definition)**

See this article for primer discussion. Every other premise beyond them must be ultimately traced back to them via logically valid line of analysis. But if your axioms have not been directly or indirectly inferred from the first-evident principles, through a logically valid line of reasoning -- where only deduction yields percent certainty -- then it means that you have simply no philosophy.

In other words if your axioms are 'shaky' then it means that the entire system of statements inferred from them will be consequently shaky; a house of cards that will partially or entirely collapse once some or all of your premises are negated. We first form a problem: Then form a general hypothesis: