Intuitionistic logic substitutes constructability for abstract truth and is associated with a transition from the proof to model theory of abstract truth in modern mathematics.

Intuitionistic logic can be defined using the following Hilbert-style calculus.

Today many other such calculi are in use, including Per Martin-Löf's Intuitionistic type theory, Jean-Yves Girard's System F and the Calculus of Constructions.

" Semantical Analysis of Intuitionistic Logic I ", In Formal Systems and Recursive Functions, edited by M. Dummett and J. N. Crossley.

* 19-" Semantical Analysis of Intuitionistic Logic II.

The Proof Theory and Semantics of Intuitionistic Modal Logic.

Intuitionistic analogues of these classes would have to be developed first.

Intuitionistic logic, or constructive logic, is a symbolic logic system differing from classical logic in its definition of the meaning of a statement being true.

* Troelstra, A. S. ( no date but later than 1990 ), " A History of Constructivism in the 20th Century ", http :// staff. science. uva. nl /~ anne / hhhist. pdf, A detailed survey for specialists: § 1 Introduction, § 2 Finitism & § 2. 2 Actualism, § 3 Predicativism and Semi-Intuitionism, § 4 Brouwerian Intuitionism, § 5 Intuitionistic Logic and Arithmetic, § 6 Intuitionistic Analysis and Stronger Theories, § 7 Constructive Recursive Mathematics, § 8 Bishop's Constructivism, § 9 Concluding Remarks.

All artistic and mythological representations, therefore, are `` imitations of imitations '' and are completely superseded by the truth value of `` dialectic '', the proper use of the inquiring intellect.

She states: " Since we do not succeed in fleeing it, let us therefore try to look the truth in the face.

She therefore always worked with parliament and advisers she could trust to tell her the truth — a style of government that her Stuart successors failed to follow.

According to René Descartes, rationality is built first upon the realization of the absolute truth " I think therefore I am ", which requires no faith.

The idea that nothing is real except in the mind of the individual finds its roots in the Greek Sophists, who argued that since nothing can be perceived except through the senses — and since all individuals sense, and therefore perceive, things differently — there is no absolute truth, only relative truth.

In this way, the law of excluded middle is true, but because truth itself, and therefore disjunction, is not exclusive, it says next to nothing if one of the disjuncts is paradoxical, or both true and false.

Liar statements and liar-like statements are ungrounded, and therefore have no truth value.

Since therefore all that the inspired authors or sacred writers affirm should be regarded as affirmed by the Holy Spirit, we must acknowledge that the books of Scripture firmly, faithfully, and without error teach that truth which God, for the sake of our salvation, wished to see confided to the Sacred Scriptures.

But if he was telling the truth, then he was violating those guidelines and is therefore unethical ; and if he ’ s unethical, then was he telling the truth?

The Church has, therefore, according to Pius XII, a common aim with Christ himself, teaching all men the truth, and, offering to God a pleasing and acceptable sacrifice.

In these commentaries he presents his own philosophical system as a faithful interpretation of Plato, and in this he did not differ from other Neoplatonists, as he considered the Platonic texts to be divinely inspired ( ho theios Platon -- The divine Plato, inspired by God ) and therefore that they spoke often of things under a veil, hiding the truth from the philosophically uninitiate.

" However, in the view of soft secularism, " the attainment of absolute truth was impossible and therefore skepticism and tolerance should be the principle and overriding values in the discussion of science and religion.

In 1963 the US Supreme Court ruled that confessions produced as a result of ingestion of truth serum was " unconstitutionally coerced ", and therefore inadmissible.

Hinduism embraces universalism by conceiving the whole world as a single family that deifies the one truth, and therefore it accepts all forms of beliefs and dismisses labels of distinct religions which would imply a division of identity.

Deduction allows one to formulate a specific truth from a general truth: all crows are black ; this is a crow ; therefore this is black.

Induction somehow allows one to formulate a general truth from some series of specific observations: this is a crow and it is black ; that is a crow and it is black ; no crow has been seen that is not black ; therefore all crows are black.

In Sacred Scripture, therefore, while the truth and holiness of God always remains intact, the marvelous " condescension " of eternal wisdom is clearly shown, " that we may learn the gentle kindness of God, which words cannot express, and how far He has gone in adapting His language with thoughtful concern for our weak human nature ".

If the bezel could be turned the other way this could suggest to a diver that the elapsed time was shorter than the truth, thus giving a falsely low elapsed time reading and therefore an assumed falsely low air consumption reading and falsely high remaining air reading, all of which could be highly dangerous.

Idealism, ( associated with Plato and his school ), claims that there is a " higher " reality, from which certain people can directly arrive at truth without needing to rely only upon the senses, and that this higher reality is therefore the primary source of truth.

I have, therefore, chosen this time and place to discuss a topic on which ignorance too often abounds and the truth too rarely perceived.

To my knowledge, Lincoln remains the only Head of State and Commander-in-Chief who, while fighting a fearful war whose issue was in doubt, proved man enough to say this publicly -- to give his foe the benefit of the fact that in all human truth there is some error, and in all our error, some truth.

Banquo remains skeptical after the encounter, wondering aloud if evil can ever speak the truth.

The 2003 discovery of the fossil remains of Homo floresiensis was cited by paleontologist Henry Gee, editor of the journal Nature as possible evidence that humanoid cryptids like the Orang Pendek and yeti were " founded on grains of truth ".

Nonetheless she remains a greatly respected figure for her spiritual writings, and political boldness to " speak truth to power "— it being exceptional for a woman, in her time period, to have had such influence in politics and on world history.

As Sarris explains to Jason, Mathesar is incredibly naïve to the truth, as are the others of his crew ; however, he remains loyal to Nesmith and the other actors and sees them as heroes.

Hamlet remains uncertain whether the Ghost has told him the truth, but the arrival of a troupe of actors at Elsinore presents him with a solution.

Others have not accepted some or all of their suggestions, and have interpreted the evidence in other ways, and the truth of the matter remains very uncertain.

One quote often heard from Holmes is " When you have eliminated the impossible, whatever remains, however improbable, must be the truth ".

Although Mao Zedong Thought nominally remains the state ideology, Deng's admonition to seek truth from facts means that state policies are judged on their practical consequences ; the role of ideology in determining policy, in many areas, has thus been considerably reduced.

Sorting out who was telling the truth then and now remains difficult.

Whether this was based on truth remains unknown.

Parliamentary democracy is, in truth, little more than a means of securing a periodical change in the management team, which is then allowed to preside over a system that remains in essence intact.

The truth regarding Lansky's wealth and influence remains a mystery.

On the other hand, the converse of a statement with mutually inclusive terms remains true, given the truth of the original proposition.

However, the truth remains hidden and the project is artificially kept alive until the Day Zero finally comes (" Big Bang ").

The speech of Flavian remains, concluding with this appeal to the bishop of Dorylaeum: " Let your reverence condescend to visit him and argue with him about the true faith, and if he shall be found in very truth to err, then he shall be called to our holy assembly, and shall answer for himself.

It remains unclear whether this was the truth, as in her memoirs Maria stated that her mother influenced her choice to marry Athenasius, possibly due to an illegitimate pregnancy.

For Kenneth Clark, The Raft of the Medusa " remains the chief example of romantic pathos expressed through the nude ; and that obsession with death, which drove Géricault to frequent mortuary chambers and places of public execution, gives truth to his figures of the dead and the dying.

The hearings, whose findings include that the Justice Department had " bargained away the truth ," ultimately still did not fully reveal the special grand jury's report to the public, which remains sealed by the DOJ courts.

After several trials, the truth about who is behind the murder of Borsellino, and fellow judge Giovanni Falcone, remains elusive.

He must review doubtful titles, purge out interpolations, expose forgeries ; but he does so only to manifest the truth, and exhibit the genuine remains of antiquity in their real character.

Behold, I am an apostle of God unto you, to confirm the truth of whatever there still remains of the Torah, and to give the glad tiding of an apostle who shall come after me, whose name shall be Ahmed.