In propositional logic, disjunction elimination ( sometimes named proof by cases or case analysis ), is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof.

Alice Whealy, who supports the partial authenticity of the Testimonium, has rejected the arguments by Kenneth Olson regarding the total fabrication of the Testimonium by Eusebius, stating that Olson's analysis includes inaccurate readings of both the works of Josephus and Eusebius, as well as logical flaws in his argument.

But a critical logical analysis shows that this definition is too naive to be proper, and so it must be qualified as follows:

Strunk and White have been proven wrong on this point by logical analysis of quantification in natural language ( like Pinker following Lewis and others above ) — distributive expressions are neither exclusively singular nor exclusively plural, they are typically indeterminate in number.

Even in the case of there is and once, logical analysis views many of these as distributive statements equivalent to, out of all cases there is at least one.

By objects, Wittgenstein did not mean physical objects in the world, but the absolute base of logical analysis, that can be combined but not divided ( TLP 2. 02 – 2. 0201 ).

The most basic level consists of literary analysis of the text without the help of commentaries, designed to bring out the tzurata di-shema ' ta, i. e. the logical and narrative structure of the passage.

The former are those “ manifested by his observed behaviour, including preferences possibly based on erroneous factual beliefs, or on careless logical analysis, or on strong emotions that at the moment greatly hinder rational choice ” whereas the latter are “ the preferences he would have if he had all the relevant factual information, always reasoned with the greatest possible care, and were in a state of mind most conducive to rational choice .” It is the latter that preference utilitarianism tries to satisfy.

In Ayer's view, Heidegger proposed vast, overarching theories regarding existence, which are completely unverifiable through empirical demonstration and logical analysis.

Some have argued that since this action is missing from the logical school's approach, it must be an incomplete analysis.

The second was through logical analysis, which relied on the rules of formal logic to show that contradictions did not exist but were subjective to the reader.

One immediate application is the definition of the basic concepts of analysis such as derivative and integral in a direct fashion, without passing via logical complications of multiple quantifiers.

Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results.

Aristotle was the first logician to attempt a systematic analysis of logical syntax, into noun ( or term ), and verb.

Their analysis centered on the definition of necessary logical entailment, " vyapti ", also known as invariable concomitance or pervasion.

Any process of evaluation or analysis, that may be called rational, is expected to be highly objective, logical and " mechanical ".

From this perspective, heuristics are part of a larger experiential processing system that is often adaptive, but vulnerable to error in situations that require logical analysis.

A dependence diagram is equivalent to a success tree analysis ( STA ), the logical inverse of an FTA, and depicts the system using paths instead of gates.

The model views planning as a logical and technical process that uses the analysis of quantitative data to decide how to best invest resources in new and existing transportation infrastructure.

They began calling themselves " ufologists " in the 1950s and felt that logical analysis of sighting reports would validate the notion of extraterrestrial visitation.

This hypothesis does not explain the muscle paralysis of REM sleep ; however, a logical analysis might suggest that the muscle paralysis exists to prevent the animal from fully waking up unnecessarily, and allowing it to return easily to deeper sleep.

Generally speaking, soft computing techniques resemble biological processes more closely than traditional techniques, which are largely based on formal logical systems, such as sentential logic and predicate logic, or rely heavily on computer-aided numerical analysis ( as in finite element analysis ).

Peacock's main contribution to mathematical analysis is his attempt to place algebra on a strictly logical basis.

When I question them as to what they mean by concepts like liberty and democracy, I find that they fall into two categories: the simpler ones who have simply accepted the shibboleths of their faith without analysis ; ;

Fromm's analysis of alienation in the sphere of production centers around the concepts of the bureaucratization of the corporation, the separation of ownership from control, and the broad ( and thus from the point of view of corporate control, ineffective ) dispersion of stock ownership.

Whilst critical theorists usually are defined as Marxist intellectuals, their tendency to denounce Marxist concepts, and to synthesise Marxian analysis with other sociologic and philosophic traditions has been attacked as revisionism, by Classical, Orthodox, and Analytical Marxists, and by Marxist-Leninist philosophers.

With the expansion of the mass media and mass / popular culture in the 1960s and 1970s and the blending of social and cultural criticism and literary criticism, the methods of both kinds of critical theory sometimes intertwined in the analysis of phenomena of popular culture, as in the emerging field of cultural studies, in which concepts deriving from Marxian theory, post-structuralism, semiology, psychoanalysis and feminist theory would be found in the same interpretive work.

Many concepts and techniques of analysis and differential equations have been generalized to the setting of Riemannian manifolds.

In finance, discounted cash flow ( DCF ) analysis is a method of valuing a project, company, or asset using the concepts of the time value of money.

Marcuse ’ s analysis of capitalism derives partially from one of Karl Marx ’ s main concepts: Objectification, which under capitalism becomes Alienation.

Modern scholarship dating from the Wissenschaft des Judentums movement of 19th century Germany, as well as textual analysis influenced by the 20th Century discovery of the Dead Sea Scrolls, suggests that dating from this period there existed " liturgical formulations of a communal nature designated for particular occasions and conducted in a centre totally independent of Jerusalem and the Temple, making use of terminology and theological concepts that were later to become dominant in Jewish and, in some cases, Christian prayer.

Some recent work has been done in analysis using concepts from non-standard analysis, particularly in investigating limiting processes of statistics and mathematical physics.

This is not the case when R is the real or complex numbers, whence the two concepts are not always distinguished in analysis.

Generally speaking, rhetorical analysis makes use of rhetorical concepts ( ethos, logos, kairos, mediation, etc.

The concepts remain " works in progress ," and understanding those terms develops through the analysis of a text.

These more general concepts are particularly useful in fields such as computer science and natural language processing where many of the basic elements of analysis are non-numerical.

Real analysis is an area of analysis that studies concepts such as sequences and their limits, continuity, differentiation, integration and sequences of functions.

Key concepts in real analysis are filters, nets, real sequences and their limits, convergence, continuity, differentiation, and integration.

Sorting algorithms are prevalent in introductory computer science classes, where the abundance of algorithms for the problem provides a gentle introduction to a variety of core algorithm concepts, such as big O notation, divide and conquer algorithms, data structures, randomized algorithms, best, worst and average case analysis, time-space tradeoffs, and upper and lower bounds.

Topology developed as a field of study out of geometry and set theory, through analysis of such concepts as space, dimension, and transformation.

The concepts of later tensor analysis arose from the work of Carl Friedrich Gauss in differential geometry, and the formulation was much influenced by the theory of algebraic forms and invariants developed during the middle of the nineteenth century.

In his new role as social theorist, Adorno's philosophical analysis of cultural phenomena heavily relied on the language of historical materialism, as concepts like reification, false consciousness and ideology came to play an ever more prominent role in his work.

Because Adorno believed that sociology needs to be self-reflective and self-critical, he believed that the language the sociologist uses, like the language of the ordinary person, is a political construct in large measure that uses, often unreflectingly, concepts installed by dominant classes and social structures ( such as our notion of " deviance " which includes both genuinely deviant individual and " hustlers " operating below social norms because they lack the capital to operate above: for an analysis of this phenomenon, cf.

The remainder of this article will deal with this case, which is one of the concepts of functional analysis.

This kind of analysis falls under the concepts of Stress testing or scenario analysis.