But a machine that can learn through both methods would require nearly opposite kinds of systems: one that can operate deductively, by following hard-coded procedures; and one that can work inductively, by recognizing patterns in the data and computing the statistical probabilities of when they occur.
|
|
They usually reason inductively from several examples, but cannot yet reason deductively because they do not understand how the properties of shapes are related. Level 2. Abstraction: At this level, properties are ordered. The objects of thought are geometric properties, which the student has learned to connect deductively.
|
|
In the AGM framework, a belief set is represented by a deductively closed set of propositional formulae. While such sets are infinite, they can always be finitely representable. However, working with deductively closed sets of formulae leads to the implicit assumption that equivalent belief sets should be considered equal when revising. This is called the principle of irrelevance of syntax.
|
|
In propositional logic, the set of all true propositions is deductively closed. This is to say that only true statements are derivable from other true statements.
|
|
This approach can be realized by using knowledge bases that are not deductively closed and assuming that all formulae in the knowledge base represent self-standing beliefs, that is, they are not derived beliefs. In order to distinguish the foundational approach to belief revision to that based on deductively closed knowledge bases, the latter is called the coherentist approach. This name has been chosen because the coherentist approach aims at restoring the coherence (consistency) among all beliefs, both self-standing and derived ones. This approach is related to coherentism in philosophy.
|
|
He contended that a full explanation of a phenomenon should deductively entail it; that is, the conclusion (the phenomenon) must follow necessarily from the premises (the specifications of the explanation). By contrast, he said, no matter how complete a physical explanation was, it would not entail subjective consciousness.
|
|
For example, one can infer from "The Sun is yellow" that "Either the Sun is yellow, or it is wrong to murder". But this provides no relevant moral guidance; absent a contradiction, one cannot deductively infer that "it is wrong to murder" solely from non-moral premises alone, adherents argue.
|
|
However, Hewitt and Agha [1991] claimed that the resulting systems were not deductive in the following sense: computational steps of the concurrent logic programming systems do not follow deductively from previous steps (see Indeterminacy in concurrent computation). Recently, logic programming has been integrated into the actor model in a way that maintains logical semantics.
|
|
Efficient means are recognized inductively in heads or brains or minds. Legitimate ends are felt deductively in hearts or guts or souls. Instrumental rationality provides intellectual tools—scientific and technological facts and theories—that appear to be impersonal, value-free means. Value rationality provides legitimate rules—moral valuations—that appear to be emotionally satisfying, fact-free ends.
|
|
All of the jurors expressed a belief that fraud had taken place but during the subsequent civil trial Daniel M. Petrocelli had deductively disproven all of the blood planting conspiracy claims made at the criminal trial by Scheck. Petrocelli noted that the evidence used to disprove those claims was available at the criminal trial which lead to further criticism that the jury discarded evidence and the verdict was a racially motivated Jury nullification. The only fraud claim that could not be deductively disproven was Fuhrman planting the glove at Simpson's home but there was no physical or eyewitness evidence to support this. Jeffrey Toobin wrote that the defense was planning on making that claim months before the trial began because that was the only explanation for why that glove was found at Simpson's home.
|
|
Scholars have generally believed that either Parmenides was responding to Heraclitus, or Heraclitus to Parmenides. Parmenides' main surviving work does not seem to be a refutation of any specific philosopher as much as it is the first deductively valid schema upon which the truth can be reached. His argument can be summarized by the following logical notation: The "Way of Truth" (where Being is P): Being is and non-being is notP \land \urcorner (\urcorner P) \therefore PThe deductive validity of the premises holds true and the way of truth thus represents a tautology This is contrasted by the "Way of Opinion": Being is not, therefore non-being is\urcorner (P) \therefore \urcorner PWhile this is deductively valid, the validity of this notation rests on an ambiguity of language. "For if this statement were true, it would not be possible for you to conceive of non-being, nor to name it".
|
|
The solution-focused approach was developed inductively rather than deductively; Berg, de Shazer and their teamShazer, SD. (1982) Patterns of brief family therapy: an ecosystemic approach. Guilford Press. spent thousands of hours carefully observing live and recorded therapy sessions. Any behaviors or words on the part of the therapist that reliably led to positive therapeutic change on the part of the clients were painstakingly noted and incorporated into the SFBT approach.
|
|
For Kelsen as for other central European contemporaries, norms occur not singly but in sets, termed 'orders'. The ordering principle of an order of moral norms—and of an order of natural law, if one could exist—would be logical, as deduction. From the general norm 'do not kill other human beings', it follows deductively that A must not kill any other human being. Kelsen calls this a 'static' order.
|
|
If you know that Q follows logically from P, then no information about the possible interpretations of P or Q will affect that knowledge. Our knowledge that Q is a logical consequence of P cannot be influenced by empirical knowledge. Deductively valid arguments can be known to be so without recourse to experience, so they must be knowable a priori. However, formality alone does not guarantee that logical consequence is not influenced by empirical knowledge.
|
|
Grammar–translation classes are usually conducted in the students' native language. Grammatical rules are learned deductively; students learn grammar rules by rote, and then practice the rules by doing grammar drills and translating sentences to and from the target language. More attention is paid to the form of the sentences being translated than to their content. When students reach more advanced levels of achievement, they may translate entire texts from the target language.
|
|
Perplexing, fascinating, and difficult to classify in a literary sense, he succeeds in transmitting a certain mystique to the inquisitive reader. At one moment he seems coolly logical and shows an admirable ability to reason deductively, and the next moment he is overcome by absurd flights of fancy into a surrealistic world where apparently nothing makes any sense. His verse is light, colloquial and much less declamatory than that of many of his predecessors.
|
|
The fact that there are numerous black ravens supports the assumption. Our assumption, however, becomes invalid once it is discovered that there are white ravens. Therefore, the general rule "all ravens are black" is not the kind of statement that can ever be certain. Hume further argued that it is impossible to justify inductive reasoning: this is because it cannot be justified deductively, so our only option is to justify it inductively.
|
|
However, in doing so, you sacrifice internal validity. The apparent contradiction of internal validity and external validity is, however, only superficial. The question of whether results from a particular study generalize to other people, places or times arises only when one follows an inductivist research strategy. If the goal of a study is to deductively test a theory, one is only concerned with factors which might undermine the rigor of the study, i.e.
|
|
Evolving in phases, inductivism's conceptual reign spanned four centuries since Francis Bacon's 1620 proposal of it against Western Europe's prevailing model, scholasticism, which reasoned deductively from preconceived beliefs. From the 19th and 20th centuries, inductivism succumbed to hypotheticodeductivism—sometimes worded deductivism—as scientific method's realistic idealization. Yet scientific theories per se are now widely attributed to occasions of inference to the best explanation, IBE, which, like scientists' actual methods, are diverse and not formally prescribable.
|
|
Intuitively, it seems to be the case that we know certain things with absolute, complete, utter, unshakable certainty. For example, if you travel to the Arctic and touch an iceberg, you know that it would feel cold. These things that we know from experience are known through induction. The problem of induction in short; (1) any inductive statement (like the sun will rise tomorrow) can only be deductively shown if one assumes that nature is uniform.
|
|
Eqrem Basha is an enigmatic poet. Perplexing, fascinating, and difficult to classify in a literary sense, he succeeds in transmitting a certain mystique to the inquisitive reader. At one moment he seems coolly logical and shows an admirable ability to reason deductively, and the next moment he is overcome by absurd flights of fancy into a surrealistic world where apparently nothing makes any sense. Basha has an urbane view of things and delights in the daily absurdities of life.
|
|
A precursor of Boolean algebra was Gottfried Wilhelm Leibniz's algebra of concepts. Leibniz's algebra of concepts is deductively equivalent to the Boolean algebra of sets. Boole's algebra predated the modern developments in abstract algebra and mathematical logic; it is however seen as connected to the origins of both fields. In an abstract setting, Boolean algebra was perfected in the late 19th century by Jevons, Schröder, Huntington and others, until it reached the modern conception of an (abstract) mathematical structure.
|
|
A different realization of the foundational approach to belief revision is based on explicitly declaring the dependences among beliefs. In the truth maintenance systems, dependence links among beliefs can be specified. In other worlds, one can explicitly declare that a given fact is believed because of one or more other facts; such a dependency is called a justification. Beliefs not having any justifications play the role of non- derived beliefs in the non-deductively closed knowledge base approach.
|
|
The problem calls into question the traditional inductivist account of all empirical claims made in everyday life or through the scientific method, and, for that reason, C. D. Broad once said that "induction is the glory of science and the scandal of philosophy". In contrast, Karl Popper's critical rationalism claimed that induction is never used in science and proposed instead that science is based on the procedure of conjecturing hypotheses, deductively calculating consequences, and then empirically attempting to falsify them.
|
|
Edward N. Zalta, "A (Leibnizian) Theory of Concepts", Philosophiegeschichte und logische Analyse / Logical Analysis and History of Philosophy, 3 (2000): 137–183. (deductively equivalent to the Boolean algebra) and the associated metaphysics, are of interest in present-day computational metaphysics.Jesse Alama, Paul E. Oppenheimer, Edward N. Zalta, "Automating Leibniz's Theory of Concepts", in A. Felty and A. Middeldorp (eds.), Automated Deduction – CADE 25: Proceedings of the 25th International Conference on Automated Deduction (Lecture Notes in Artificial Intelligence: Volume 9195), Berlin: Springer, 2015, pp. 73–97.
|
|
The law of falling bodies was published by Galileo in 1638. But in the 20th century some authorities challenged the reality of Galileo's experiments. In particular, the French historian of science Alexandre Koyré bases his doubt on the fact that the experiments reported in Two New Sciences to determine the law of acceleration of falling bodies, required accurate measurements of time which appeared to be impossible with the technology of 1600. According to Koyré, the law was created deductively, and the experiments were merely illustrative thought experiments.
|
|
An inference is deductively valid if and only if there is no possible situation in which all the premises are true but the conclusion false. An inference is inductively strong if and only if its premises give some degree of probability to its conclusion. The notion of deductive validity can be rigorously stated for systems of formal logic in terms of the well-understood notions of semantics. Inductive validity, on the other hand, requires us to define a reliable generalization of some set of observations.
|
|
The informal fallacy of accident (also called destroying the exception or a dicto simpliciter ad dictum secundum quid) is a deductively valid but unsound argument occurring in a statistical syllogism (an argument based on a generalization) when an exception to a rule of thumb is ignored. It is one of the thirteen fallacies originally identified by Aristotle in Sophistical Refutations. The fallacy occurs when one attempts to apply a general rule to an irrelevant situation. For example: It is easy to construct fallacious arguments by applying general statements to specific incidents that are obviously exceptions.
|
|
Arthur M. Diamond argues Hayek's problems arise when he goes beyond claims that can be evaluated within economic science. Diamond argued: > The human mind, Hayek says, is not just limited in its ability to synthesize > a vast array of concrete facts, it is also limited in its ability to give a > deductively sound ground to ethics. Here is where the tension develops, for > he also wants to give a reasoned moral defense of the free market. He is an > intellectual skeptic who wants to give political philosophy a secure > intellectual foundation.
|
|
Oliver Wendell Holmes Jr. cautioned that "the proper derivation of general principles in both common and constitutional law ... arise gradually, in the emergence of a consensus from a multitude of particularized prior decisions."Frederic R. Kellog, Law, Morals, and Justice Holmes, 69 Judicature 214 (1986). Justice Cardozo noted the "common law does not work from pre-established truths of universal and inflexible validity to conclusions derived from them deductively", but "[i]ts method is inductive, and it draws its generalizations from particulars".Benjamin N. Cardozo, The Nature of the Judicial Process 22–23 (1921).
|
|
Skinner argued that many theories had the effect of halting research or generating useless research. Skinner's work did have a basis in theory, though his theories were different from those that he criticized. Mecca Chiesa notes that Skinner's theories are inductively derived, while those that he attacked were deductively derived.Chiesa, Mecca (2005) Radical Behaviorism: The Philosophy and the Science The theories that Skinner opposed often relied on mediating mechanisms and structures—such as a mechanism for memory as a part of the mind—which were not measurable or observable.
|
|
Lewis seems to offer both deductive and inductive versions of the argument from desire. In The Pilgrim’s Regress, Lewis appears to argue deductively as follows: # Nature makes nothing (or at least no natural human desire) in vain. # Humans have a natural desire (Joy) that would be vain unless some object that is never fully given in my present mode of existence is obtainable by me in some future mode of existence. # Therefore, the object of this otherwise vain natural desire must exist and be obtainable in some future mode of existence.
|
|
Some sources even state that the Aristotelian conceptualization of induction is different from its modern mainstream interpretations due to its position that inductive arguments are deductively valid. The early form of modern inductionism is associated with the philosophies of thinkers such as Francis Bacon. This can be demonstrated in the way Bacon favored the steady and incremental collection of empirical evidence using a method that derives general principles from the senses and particulars, gradually leading to the most general principles. Inductionism is also said to be based on Newtonian physics.
|
|
Hund argues that this is a misconception based on a failure to acknowledge the importance of the internal element. In his view, by using the criteria described above, there is not this problem in deciphering what constitutes "law" in a particular community. According to Hund, the second form of rule scepticism says that, though a community may have rules, those rules are not arrived at 'deductively', i.e. they are not created through legal/moral reasoning only but are instead driven by the personal/political motives of those who create them.
|
|
The movement was initiated by Muhammad Iqbal, and later spearheaded by Ghulam Ahmed Pervez. In his writings and speeches, Ghulam Ahmed Pervez, who succeeded Iqbal as Tolu-e-Islam's lead scholar, has deductively analyzed Quranic verses with little or no emphasis on hadith.Latif, Abu Ruqayyah Farasat, The Qurʾāniyūn of the Twentieth Century, academia.edu, Accessed December 5, 2013 He also provided a new commentary on the Quran based on a re- translation of key verses, based on applying proper rules of classical Arabic and its conventions, which have been overlooked by the mainstream sects.
|
|
Aristotle, a Greek philosopher, started documenting deductive reasoning in the 4th century BC. René Descartes, in his book Discourse on Method, refined the idea for the Scientific Revolution. Developing four rules to follow for proving an idea deductively, Decartes laid the foundation for the deductive portion of the scientific method. Decartes' background in geometry and mathematics influenced his ideas on the truth and reasoning, causing him to develop a system of general reasoning now used for most mathematical reasoning. Similar to postulates, Decartes believed that ideas could be self-evident and that reasoning alone must prove that observations are reliable.
|
|
Called the Euthyphro dilemma, it goes as follows: "Is what is morally good commanded by God because it is morally good, or is it morally good because it is commanded by God?" The implication is that if the latter is true, then justice is beyond mortal understanding; if the former is true, then morality exists independently from God, and is therefore subject to the judgment of mortals. A response, popularized in two contexts by Immanuel Kant and C. S. Lewis, is that it is deductively valid to say that the existence of an objective morality implies the existence of God and vice versa.
|
|
Thus, Sandnes argues deductively: Since such familiarity with Homer was limited to the upper stratum of society, and since the authors of Mark and Luke-Acts (nor their audiences) are not believed to belong to this stratum, then the authors of Mark and Luke-Acts simply could not have imitated Homer in the way MacDonald suggests. MacDonald's response has been threefold. First, a more sure decision about the education of the authors of Mark and Luke-Acts would result from an inductive approach to the question, rather than Sandnes' deductive approach. Second, access to Homer was not restricted to the cultural elite.
|
|
A formal system is syntactically complete or deductively complete or maximally complete if for each sentence (closed formula) φ of the language of the system either φ or ¬φ is a theorem of . This is also called negation completeness, and is stronger than semantic completeness. In another sense, a formal system is syntactically complete if and only if no unprovable sentence can be added to it without introducing an inconsistency. Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example, the propositional logic statement consisting of a single propositional variable A is not a theorem, and neither is its negation).
|
|
Theories are distinct from theorems. A theorem is derived deductively from axioms (basic assumptions) according to a formal system of rules, sometimes as an end in itself and sometimes as a first step toward being tested or applied in a concrete situation; theorems are said to be true in the sense that the conclusions of a theorem are logical consequences of the axioms. Theories are abstract and conceptual, and are supported or challenged by observations in the world. They are 'rigorously tentative', meaning that they are proposed as true and expected to satisfy careful examination to account for the possibility of faulty inference or incorrect observation.
|
|
Even then, the distinction between rationalists and empiricists was drawn at a later period and would not have been recognized by the philosophers involved. Also, the distinction between the two philosophies is not as clear-cut as is sometimes suggested; for example, Descartes and Locke have similar views about the nature of human ideas. Proponents of some varieties of rationalism argue that, starting with foundational basic principles, like the axioms of geometry, one could deductively derive the rest of all possible knowledge. Notable philosophers who held this view most clearly were Baruch Spinoza and Gottfried Leibniz, whose attempts to grapple with the epistemological and metaphysical problems raised by Descartes led to a development of the fundamental approach of rationalism.
|
|
Gris was presented to the public as one of the 'purest' and one of the most 'classical' of the leading Cubists.Christopher Green, Juan Gris, MoMA, Grove Art Online, Oxford University Press, 2009 Pablo Picasso, 1918, Arlequin au violon (Harlequin with Violin), oil on canvas, 142 x 100.3 cm, Cleveland Museum of Art, Ohio Gris claimed to manipulate flat abstract planar surfaces first, and only in subsequent stages of his painting process would he 'qualify' them so that the subject-matter became readable. He worked 'deductively' on the global concept first, then consecrated on the perceptive details. Gris referred to this technique as 'synthetic', in contradistinction from the process of 'analysis' intrinsic to his earlier works.
|
|
During the twentieth century, Olivieri was the subject of a misunderstanding in the historiography of Renaissance sculpture in Brescia, after Antonio Morassi, in two studies of the 1930s, transformed his biography from that of a bronze artist and woodcarver to the principal Brescian stone sculptor of the early 16th century. The reconstruction, based on an incorrect assumption, i.e. the dating of the Martinengo mausoleum, and conducted purely deductively without the aid of documentary sources, generated considerable confusion in the attribution and cultural framework of many works of art. Only from 1977, with the archival researches of Camillo Boselli, was Maffeo Olivieri's oeuvre restored to its correct artistic sphere, following the organic reconsideration of Gasparo Cairano and his work.
|
|
The scope for such influence is created by the loose and undefined nature of customary law, which, Hund argues, grants customary-lawmakers (often through traditional 'judicial processes') a wide discretion in its application. Yet, Hund contends that the fact that rules might sometimes be arrived at in the more ad hoc way, does not mean that this defines the system. If one requires a perfect system, where laws are created only deductively, then one is left with a system with no rules. For Hund, this cannot be so and an explanation for these kinds of law-making processes is found in Hart's conception of "secondary rules" (rules in terms of which the main body of norms are recognised).
|
|
Dignāga's famous "wheel of reason" (Hetucakra) is a method of indicating when one thing (such as smoke) can be taken as an invariable sign of another thing (like fire), but the inference is often inductive and based on past observation. Matilal remarks that Dignāga's analysis is much like John Stuart Mill's Joint Method of Agreement and Difference, which is inductive.Matilal, 17 In addition, the traditional five- member Indian syllogism, though deductively valid, has repetitions that are unnecessary to its logical validity. As a result, some commentators see the traditional Indian syllogism as a rhetorical form that is entirely natural in many cultures of the world, and yet not as a logical form—not in the sense that all logically unnecessary elements have been omitted for the sake of analysis.
|
|
Fresnel's initial derivation of the "surface of elasticity" had been purely geometric, and not deductively rigorous. His first attempt at a mechanical derivation, contained in a "supplement" dated 13 January 1822, assumed that (i) there were three mutually perpendicular directions in which a displacement produced a reaction in the same direction, (ii) the reaction was otherwise a linear function of the displacement, and (iii) the radius of the surface in any direction was the square root of the component, in that direction, of the reaction to a unit displacement in that direction. The last assumption recognized the requirement that if a wave was to maintain a fixed direction of propagation and a fixed direction of vibration, the reaction must not be outside the plane of those two directions.Buchwald, 1989, pp. 279–80.
|
|
Viewed as a theory of elementary particles, Lorentz's electron/ether theory was superseded during the first few decades of the 20th century, first by quantum mechanics and then by quantum field theory. As a general theory of dynamics, Lorentz and Poincare had already (by about 1905) found it necessary to invoke the principle of relativity itself in order to make the theory match all the available empirical data. By this point, most vestiges of a substantial aether had been eliminated from Lorentz's "aether" theory, and it became both empirically and deductively equivalent to special relativity. The main difference was the metaphysical postulate of a unique absolute rest frame, which was empirically undetectable and played no role in the physical predictions of the theory, as Lorentz wrote in 1909,Lorentz 1909, p.
|
|
Johann Friedrich Herbart (1776–1841) emphasized the connection between individual development and the resulting societal contribution. The five key ideas which composed his concept of individual maturation were Inner Freedom, Perfection, Benevolence, Justice, and Equity or Recompense. According to Herbart, abilities were not innate but could be instilled, so a thorough education could provide the framework for moral and intellectual development. In order to develop a child to lead to a consciousness of social responsibility, Herbart advocated that teachers utilize a methodology with five formal steps: "Using this structure a teacher prepared a topic of interest to the children, presented that topic, and questioned them inductively, so that they reached new knowledge based on what they had already known, looked back, and deductively summed up the lesson's achievements, then related them to moral precepts for daily living".
|
|
Scholars such as Clark Butler hold that a good portion of the Logic is formalizable, proceeding deductively via indirect proof. Others, such as Hans-Georg Gadamer, believe that Hegel's course in the Logic is determined primarily by the associations of ordinary words in the German language. However, regardless of its status as a formal logic, Hegel clearly understood the course of his logic to be reflected in the course of history: > ...different stages of the logical Idea assume the shape of successive > systems, each based on a particular definition of the Absolute. As the > logical Idea is seen to unfold itself in a process from the abstract to the > concrete, so in the history of philosophy the earliest systems are the most > abstract, and thus at the same time the poorest... Hegel's categories are, in part, carried over from his Lectures on the History of Philosophy.
|
|
Legend has it that Adikpo Songo from Akpagher; Mbatyav in the present day Gboko local government area of Benue State, Nigeria, was the originator of Kwagh-hir. Adikpo Songu, in an interview with Iyorwuese Hagher, a scholar of Kwagh-hir, attempted to corroborate this view held by several kwagh-hir group leaders and notable elders in Tivland. Songu, an ardent supporter of the United Middle Belt Congress (UMBC) revealed that in December 1960 during the outbreak of the political crisis in Tivland known as Nande- Nande (the burning cycle) whereby members of the UMBC rose against the ruling Northern People's Congress (NPC), burning their properties, including that of government workers and chiefs, he had escaped to Mkar Christian Hospital, near Gboko, for medical treatment, but deductively, to escape arrest from the police. On his way back from Mkar Christian Hospital, having traveled for about 12 miles, he arrived near the Orkoor River when suddenly he heard the sound of fascinating music.
|
|