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Principle Of Sufficient Reason
The principle of sufficient reason states that everything must have a reason or a cause. The principle was articulated and made prominent by Gottfried Wilhelm Leibniz, with many antecedents, and was further used and developed by Arthur Schopenhauer and Sir William Hamilton, 9th Baronet. History The modern formulation of the principle is usually ascribed to early Enlightenment philosopher Gottfried Leibniz. Leibniz formulated it, but was not an originator.See chapter on Leibniz and Spinoza in A. O. Lovejoy, ''The Great Chain of Being''. The idea was conceived of and utilized by various philosophers who preceded him, including Anaximander, Parmenides, Archimedes, Plato and Aristotle,Hamilton 1860:66 Cicero, Avicenna, Thomas Aquinas, and Spinoza. One often pointed to is in Anselm of Canterbury: his phras''quia Deus nihil sine ratione facit''and the formulation of the ontological argument for the existence of God. A clearer connection is with the cosmological argument for the ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reason (argument)
In the most general terms, a reason is a consideration which justifies or explains an action, a belief, an attitude, or a fact. ''Normative reasons'' are what people appeal to when making arguments about what people should do or believe. For example, that a doctor's patient is grimacing is a reason to believe the patient is in pain. That the patient is in pain is a reason for the doctor to do things to alleviate the pain. Explanatory reasons are explanations of why things happened. For example, the reason the patient is in pain is that her nerves are sending signals from her tissues to her brain. A reason, in many cases, is brought up by the question "why?", and answered following the word ''because''. Additionally, words and phrases such as ''since'', ''due to'', ''as'', ''considering'' (''that''), ''a result'' (''of''), and ''in order to'', for example, all serve as explanatory locutions that precede the reason to which they refer. Types of reason In philosophy, it is common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ontological Argument For The Existence Of God
An ontological argument is a philosophical argument, made from an ontological basis, that is advanced in support of the existence of God. Such arguments tend to refer to the state of being or existing. More specifically, ontological arguments are commonly conceived ''a priori'' in regard to the organization of the universe, whereby, if such organizational structure is true, God must exist. The first ontological argument in Western Christian traditionSzatkowski, Miroslaw, ed. 2012. ''Ontological Proofs Today''. Ontos Verlag. "There are three main periods in the history of ontological arguments. The first was in 11th century, when St. Anselm of Canterbury came up with the first ontological argument" (p. 22). was proposed by Saint Anselm of Canterbury in his 1078 work, ''Proslogion'' (), in which he defines God as "a being than which no greater can be conceived," and argues that such being must exist in the mind, even in that of the person who denies the existence of God. Oppy, Gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Non-contradiction
In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "''p is the case''" and "''p is not the case''" are mutually exclusive. Formally this is expressed as the tautology ¬(p ∧ ¬p). The law is not to be confused with the law of excluded middle which states that at least one, "p is the case" or "p is not the case" holds. One reason to have this law is the principle of explosion, which states that anything follows from a contradiction. The law is employed in a ''reductio ad absurdum'' proof. To express the fact that the law is tenseless and to avoid equivocation, sometimes the law is amended to say "contradictory propositions cannot both be true 'at the same time and in the same sense'". It is one of the so called three laws of thought, along with i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Identity
In logic, the law of identity states that each thing is identical with itself. It is the first of the historical three laws of thought, along with the law of noncontradiction, and the law of excluded middle. However, few systems of logic are built on just these laws. History Ancient philosophy The earliest recorded use of the law appears to occur in Plato's dialogue ''Theaetetus'' (185a), wherein Socrates attempts to establish that what we call "sounds" and "colours" are two different classes of thing: It is used explicitly only once in Aristotle, in a proof in the ''Prior Analytics'': Medieval philosophy Aristotle believed the law of non-contradiction to be the most fundamental law. Both Thomas Aquinas (''Met.'' IV, lect. 6) and Duns Scotus (''Quaest. sup. Met.'' IV, Q. 3) follow Aristotle in this respect. Antonius Andreas, the Spanish disciple of Scotus (d. 1320), argues that the first place should belong to the law "Every Being is a Being" (''Omne Ens est Ens'', Qq. in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-contradiction
In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "''p is the case''" and "''p is not the case''" are mutually exclusive. Formally this is expressed as the tautology ¬(p ∧ ¬p). The law is not to be confused with the law of excluded middle which states that at least one, "p is the case" or "p is not the case" holds. One reason to have this law is the principle of explosion, which states that anything follows from a contradiction. The law is employed in a ''reductio ad absurdum'' proof. To express the fact that the law is tenseless and to avoid equivocation, sometimes the law is amended to say "contradictory propositions cannot both be true 'at the same time and in the same sense'". It is one of the so called three laws of thought, along with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gödel's Incompleteness Theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency. Employing a diagonal argument, Gödel's in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deductive Reasoning
Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if 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. Psychology is interested in deductive reasoning as a psychological process, i.e. how people ''actually'' dra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'. The term has subtle differences in definition when used in the context of different fields of study. As defined in classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. As used in modern logic, an axiom is a premise or starting point for reasoning. As used in mathematics, the term ''axiom'' is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (''A'' and ''B'') implies ''A''), while non-logical axioms (e.g., ) are actua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
On The Fourfold Root Of The Principle Of Sufficient Reason
''On the Fourfold Root of the Principle of Sufficient Reason'' (german: Ueber die vierfache Wurzel des Satzes vom zureichenden Grunde) is an elaboration on the classical Principle of Sufficient Reason, written by German philosopher Arthur Schopenhauer as his doctoral dissertation in 1813. The principle of sufficient reason is a powerful and controversial philosophical principle stipulating that everything must have a reason or cause. Schopenhauer revised and re-published it in 1847. The work articulated the centerpiece of many of Schopenhauer's arguments, and throughout his later works he consistently refers his readers to it as the necessary beginning point for a full understanding of his further writings. Background Historical In January 1813, after suffering their disastrous defeat in Russia, the first remnants of Napoleon's ''Grande Armée'' were arriving in Berlin. The sick and wounded quickly filled up the hospitals, and the risk of an epidemic grew high. A patriotic, mili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contrapositive
In logic and mathematics, contraposition refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as proof by contraposition. The contrapositive of a statement has its antecedent and consequent inverted and flipped. Conditional statement P \rightarrow Q. In formulas: the contrapositive of P \rightarrow Q is \neg Q \rightarrow \neg P . If ''P'', Then ''Q''. — If not ''Q'', Then not ''P''. ''"''If ''it is raining,'' then ''I wear my coat" —'' "If ''I don't wear my coat,'' then ''it isn't raining."'' The law of contraposition says that a conditional statement is true if, and only if, its contrapositive is true. The contrapositive ( \neg Q \rightarrow \neg P ) can be compared with three other statements: ; Inversion (the inverse), \neg P \rightarrow \neg Q:"If ''it is not raining,'' then ''I don't wear my coat''." Unlike the contrapositive, the inverse's truth value is not at all d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modus Tollens
In propositional logic, ''modus tollens'' () (MT), also known as ''modus tollendo tollens'' (Latin for "method of removing by taking away") and denying the consequent, is a deductive argument form and a rule of inference. ''Modus tollens'' takes the form of "If P, then Q. Not Q. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from ''P implies Q'' to ''the negation of Q implies the negation of P'' is a valid argument. The history of the inference rule ''modus tollens'' goes back to antiquity. The first to explicitly describe the argument form ''modus tollens'' was Theophrastus. ''Modus tollens'' is closely related to ''modus ponens''. There are two similar, but invalid, forms of argument: affirming the consequent and denying the antecedent. See also contraposition and proof by contrapositive. Explanation The form of a ''modus tollens'' argument resembles a syllo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modus Ponens
In propositional logic, ''modus ponens'' (; MP), also known as ''modus ponendo ponens'' (Latin for "method of putting by placing") or implication elimination or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "''P implies Q.'' ''P'' is true. Therefore ''Q'' must also be true." ''Modus ponens'' is closely related to another valid form of argument, '' modus tollens''. Both have apparently similar but invalid forms such as affirming the consequent, denying the antecedent, and evidence of absence. Constructive dilemma is the disjunctive version of ''modus ponens''. Hypothetical syllogism is closely related to ''modus ponens'' and sometimes thought of as "double ''modus ponens''." The history of ''modus ponens'' goes back to antiquity. The first to explicitly describe the argument form ''modus ponens'' was Theophrastus. It, along with '' modus tollens'', is one of the standard patterns of inference that can be appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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