The truth values of logical formulas usually form a finite set, generally restricted to two values: true and false, but logic can also be continuous-valued, e. g., fuzzy logic.

Husserl also talked about what he called " logic of truth " which consists of the formal laws of possible truth and its modalities, and precedes the third logical third stratum.

Husserl responds by saying that truth itself as well as logical laws always remain valid regardless of psychological " evidence " that they are true.

On one extreme is logical positivism, which denies the validity of any beliefs held by faith ; on the other extreme is fideism, which holds that true belief can only arise from faith, because reason and physical evidence cannot lead to truth.

Traditionally, in Aristotle's classical logical calculus, in evaluating any proposition there are only two possible truth values, " true " and " false.

It puts one in the position of asserting or implying that truth or standards of logical consistency are relative to a particular thinker or group and that under some other standard, the position is correct despite its failure to stand up to logic.

In logic, a logical connective ( also called a logical operator or a truth function ) is a symbol or word used to connect two or more sentences ( of either a formal or a natural language ) in a grammatically valid way, such that the sense of the compound sentence produced depends only on the original sentences.

The and in ( C ) is a logical connective, since the truth of ( C ) is completely determined by ( A ) and ( B ): it would make no sense to affirm ( A ) and ( B ) but deny ( C ).

The verifiability criterion of meaning did not seem verifiable ; but neither was it simply a logical tautology, since it had implications for the practice of science and the empirical truth of other statements.

The logical calculus preserves justification, rather than truth, across transformations yielding derived propositions.

# A deity is able to do anything that is in accord with its own nature ( thus, for instance, if it is a logical consequence of a deity's nature that what it speaks is truth, then it is not able to lie ).

The logical predicate thus obtained would be elaborated further, e. g. using truth theory models, which ultimately relate meanings to a set of Tarskiian universals, which may lie outside the logic.

The truth of a sentence, and more interestingly, its logical relation to other sentences, is then evaluated relative to a model.

The opposite of truth is falsehood, which, correspondingly, can also take on a logical, factual, or ethical meaning.

Logicians use formal languages to express the truths which they are concerned with, and as such there is only truth under some interpretation or truth within some logical system.

A proposition such as " If p and q, then p ." is considered to be logical truth because it is true because of the meaning of the symbols and words in it and not because of any facts of any particular world.

In logic, Ockham wrote down in words the formulae that would later be called De Morgan's Laws, and he pondered ternary logic, that is, a logical system with three truth values ; a concept that would be taken up again in the mathematical logic of the 19th and 20th centuries.

Since it is absurd to have no logical method by which to settle on one hypothesis amongst an infinite number of equally data-compliant hypotheses, we should choose the simplest theory: " either science is irrational the way it judges theories and predictions probable or the principle of simplicity is a fundamental synthetic a priori truth " ( Swinburne 1997 ).

Given these assumptions, the constraint that time travel must not lead to inconsistent outcomes could be seen merely as a tautology, a self-evident truth that cannot possibly be false, because if you make the assumption that it is false this would lead to a logical paradox.

The two values can also be interpreted as logical values ( true / false, yes / no ), algebraic signs (+/−), activation states ( on / off ), or any other two-valued attribute.

A central processing unit ( CPU ), also referred to as a central processor unit, is the hardware within a computer system which carries out the instructions of a computer program by performing the basic arithmetical, logical, and input / output operations of the system.

In logic and mathematics, a two-place logical connective or, is a logical disjunction, also known as inclusive disjunction or alternation, that results in true whenever one or more of its operands are true.

One may also wish to talk about definable complex numbers: complex numbers which are uniquely defined by a logical formula.

This is also the logical structure of contemporary database indexes.

This line also includes a masculine caesura after θεά, a natural break that separates the line into two logical parts.

Psychologists have also not been successful in showing how from induction or psychological processes we can justify the absolute certainty of logical principles, such as the principles of identity and non-contradiction.

This means that we should regard logical and mathematical laws as being independent of the human mind, and also as an autonomy of meanings.

The images may also function as animation frames in an animated GIF file, but again these need not fill the entire logical screen.

They restricted themselves to a compilation of the principal methods of logical deduction, which they called " middot " ( measures ), although the other rules also were known by that term ( comp.

The puzzles were logical but also required close attention to the clues and hints given in the story, causing most gamers to keep copious notes as they went along.

Radcliffe, however, not only wrote little but also took a certain iconoclastic pride in having read little, remarking once of some vials of herbs and a skeleton in his study: “ This is Radcliffe ’ s library .” However, he bequeathed a substantial sum of money to Oxford for the founding of the Radcliffe Library, an endowment which, Samuel Garth quipped, was “ about as logical as if a eunuch should found a seraglio .”

A false dilemma ( also called false dichotomy, the either-or fallacy, fallacy of false choice, black-and-white thinking, or the fallacy of exhaustive hypotheses ) is a type of logical fallacy that involves a situation in which only two alternatives are considered, when in fact there is at least one additional option.

Loglan is the first among, and the main inspiration for, the languages known as logical languages, which also includes Lojban and Ceqli.

It also lends itself to elaboration, because its tight syntax holds even the longest and most complex sentence together as a logical unit.

In logic and mathematics, a two-place logical operator and, also known as logical conjunction, results in true if both of its operands are true, otherwise the value of false.

The most common logical connectives are binary connectives ( also called dyadic connectives ) which join two sentences which can be thought of as the function's operands.

The word " not " ( negation ) and the phrases " it is false that " ( negation ) and " it is not the case that " ( negation ) also express a logical connective – even though they are applied to a single statement, and do not connect two statements.

Niven has also written a logical fantasy series The Magic Goes Away, which utilizes an exhaustible resource called Mana to power a rule-based " technological " magic.

The Cutter Expansive Classification, although adopted by comparatively few libraries, mostly in New England, has been called one of the most logical and scholarly of American classifications.

The reason this is called " disjunctive syllogism " is that, first, it is a syllogism, a three-step argument, and second, it contains a logical disjunction, which simply means an " or " statement.

A normalised design will often store different but related pieces of information in separate logical tables ( called relations ).

These symbols are called " logical connectives ", " logical operators ", " propositional operators ", or, in classical logic, " truth-functional connectives ".

* The omega set is a finite set of elements called operator symbols or logical connectives.

While it is one of the most commonly used concepts in logic it must not be mistaken for a logical law ; rather, it is one of the accepted mechanisms for the construction of deductive proofs that includes the " rule of definition " and the " rule of substitution " Modus ponens allows one to eliminate a conditional statement from a logical proof or argument ( the antecedents ) and thereby not carry these antecedents forward in an ever-lengthening string of symbols ; for this reason modus ponens is sometimes called the rule of detachment.

Halliday's early grammatical descriptions of English, called " Notes on Transitivity and Theme in English – Parts 1 – 3 " include reference to " four components in the grammar of English representing four functions that the language as a communication system is required to carry out: the experiential, the logical, the discoursal and the speech functional or interpersonal ".

With the omission of the law of the excluded middle as an axiom, the remaining logical system has an existence property which classical logic does not: whenever is proven constructively, then in fact is proven constructively for ( at least ) one particular, often called a witness.

There are further logical examples that seem to undermine even this restricted definition, such as the following one ( called " The Strengthened Divine Liar "):

It has a purely logical subset, called " pure Prolog ", as well as a number of extralogical features.

This degree of support of H by E has been called the logical probability of H given E, or the epistemic probability of H given E, or the inductive probability of H given E.

The initial version of VHDL, designed to IEEE standard 1076-1987, included a wide range of data types, including numerical ( integer and real ), logical ( bit and boolean ), character and time, plus arrays of < tt > bit </ tt > called < tt > bit_vector </ tt > and of < tt > character </ tt > called string.