Western Logic

 Logic and arguments

Logic is the study of valid reasoning. A valid argument is one in which the conclusion follows necessarily from the premises. An invalid argument is one in which the conclusion does not follow necessarily from the premises.

Deductive and inductive arguments

Deductive arguments are arguments in which the conclusion follows necessarily from the premises. Inductive arguments are arguments in which the conclusion follows probably from the premises.

Truth and validity

A true statement is one that corresponds to reality. A valid argument is one in which the conclusion follows necessarily from the premises. It is important to note that even a valid argument can have false premises and therefore a false conclusion.

Functions of language

Language has many different functions, including:

• Communication: Language is used to communicate our thoughts and feelings to others.
• Expression: Language is used to express ourselves and our creativity.
• Persuasion: Language is used to persuade others to adopt our point of view.
• Explanation: Language is used to explain things to others.

Definition

A definition is a statement that explains the meaning of a word or phrase. There are two main types of definitions:

• Lexical definitions: Lexical definitions are definitions that are found in dictionaries. They typically explain the meaning of a word or phrase by providing synonyms, examples, and antonyms.
• Real definitions: Real definitions are definitions that explain the essential nature of something. They typically provide a more detailed and nuanced explanation of the meaning of a word or phrase than lexical definitions.

Informal fallacies

Informal fallacies are errors in reasoning that are not specific to any particular type of argument. Some common examples of informal fallacies include:

• Ad hominem: Attacking the person making the argument instead of the argument itself.
• Straw man: Misrepresenting the other person's argument in order to make it easier to attack.
• Begging the question: Assuming the truth of the conclusion in order to prove it.
• False dichotomy: Presenting only two options when there are more than two.

Categorical propositions and classes

Categorical propositions are statements that make claims about the relationship between two classes. There are four types of categorical propositions:

• A propositions: All members of class A are members of class B.
• E propositions: No members of class A are members of class B.
• I propositions: Some members of class A are members of class B.
• O propositions: Some members of class A are not members of class B.

The quality of a categorical proposition refers to whether it is affirmative (all or some) or negative (no or not). The quantity of a categorical proposition refers to whether it is universal (all) or particular (some). The distribution of a term in a categorical proposition refers to whether the term is distributed (all or none) or undistributed (some).

Translating categorical propositions into standard form

To translate a categorical proposition into standard form, the subject of the proposition must be placed in the first position, the predicate of the proposition must be placed in the third position, and the copula (the word "is" or "are") must be placed in the second position.

Immediate inferences

Immediate inferences are inferences that can be drawn from a single categorical proposition. There are three main types of immediate inferences: conversion, obversion, and contraposition.

Conversion is the process of reversing the subject and predicate of a categorical proposition. However, conversion is only valid for I and O propositions.

Obversion is the process of negating the predicate of a categorical proposition and reversing the quality of the proposition. However, obversion is only valid for E and I propositions.

Contraposition is the process of negating the predicate of a categorical proposition and converting the proposition. However, contraposition is only valid for A and E propositions.

Traditional square of opposition

The traditional square of opposition is a diagram that shows the relationships between the four types of categorical propositions.

Categorical syllogism

A categorical syllogism is an argument that consists of three categorical propositions, the first two of which are the premises and the third of which is the conclusion.

Standard form of categorical syllogism

The standard form of a categorical syllogism is as follows:

• Premise 1: All A are B.
• Premise 2: All C are A.
• Conclusion: All C are B.

The formal nature of syllogistic argument

Syllogistic arguments are formal arguments, which means that their validity depends on the form of the argument rather than the content of theCausal connections

Causal connections are relationships between events in which one event causes the other. The event that causes the other event is known as the cause, and the event that is caused is known as the effect.

The meaning of "cause"

The meaning of the word "cause" is a complex issue that has been debated by philosophers for centuries. One common definition of cause is that it is an event that necessarily precedes another event and is sufficient to produce that event.

Induction by simple enumeration

Induction by simple enumeration is a type of inductive argument in which the conclusion is based on the observation of a number of instances of a phenomenon. The argument form is as follows:

• Premise 1: All observed instances of A are B.
• Premise 2: There are many observed instances of A.
• Conclusion: Therefore, all A are B.

Mill's methods of experimental inquiry

John Stuart Mill proposed a number of methods of experimental inquiry, which are designed to help us to identify causal relationships. These methods include:

• The method of agreement: This method involves identifying a common factor in all cases of a phenomenon.
• The method of difference: This method involves identifying a factor that is present in all cases of a phenomenon and absent in all cases of the absence of the phenomenon.
• The joint method of agreement and difference: This method combines the methods of agreement and difference to provide stronger evidence of a causal relationship.
• The method of residues: This method involves identifying all of the possible causes of a phenomenon and then eliminating all of the causes that are not present in all cases of the phenomenon.
• The method of concomitant variation: This method involves observing how changes in one variable affect changes in another variable.

Criticism of Mill's method

Mill's methods of experimental inquiry have been criticized on a number of grounds. One criticism is that they are not always possible to apply in practice. Another criticism is that they are not always sufficient to establish causal relationships.

Symbolic logic

Symbolic logic is a branch of logic that uses symbols to represent logical concepts. This allows us to construct logical arguments in a more formal and precise way.

The value of special symbols

Special symbols in symbolic logic allow us to represent complex logical concepts in a concise and unambiguous way. This makes it easier to analyze and understand logical arguments.

Truth-functions

Truth-functions are functions that take the truth-values of propositions as input and return a truth-value as output. The most common truth-functions are negation, conjunction, disjunction, conditional statements, and material implications.

Symbols for negation, conjunctions, disjunctions, conditional statements, and material implications

The following table shows the symbols for the most common truth-functions in symbolic logic:

| Truth-function | Symbol | |---|---|---| | Negation | ¬ | | Conjunction | ∧ | | Disjunction | ∨ | | Conditional statement | → | | Material implication | ⊃ |

Tautologous, contradictory, and contingent statement-forms

A tautologous statement-form is a statement-form that is always true, regardless of the truth-values of its component propositions. A contradictory statement-form is a statement-form that is always false, regardless of the truth-values of its component propositions. A contingent statement-form is a statement-form that is neither tautologous nor contradictory.

The three laws of thought

The three laws of thought are the law of identity, the law of non-contradiction, and the law of excluded middle.

• The law of identity: Every proposition is equivalent to itself.
• The law of non-contradiction: No proposition can be both true and false at the same time.
• The law of excluded middle: Every proposition is either true or false.

Testing statement-form and statement & validity of argument-form and argument by the method of truth-table

The method of truth-tables can be used to test the statement-form and statement of an argument to determine whether the argument is valid. An argument is valid if and only if the conclusion is true in every case in which the premises are true.

Science and hypothesis

Science is the systematic study of the natural world. Hypotheses are proposed explanations for phenomena that can be tested by observation and experimentation.

Scientific and unscientific explanation

A scientific explanation is an explanation that is based on evidence and can be tested. An unscientific explanation is an explanation that is not based on evidence or cannot be tested.

Criteria of evaluation of hypothesis

Hypotheses are evaluated based on a number of criteria, including:

• Testability: The hypothesis must be testable by observation and experimentation.
• Explanatory power: The hypothesis must be able to explain