Doxastic logic is a modal logic concerned with reasoning about beliefs. The term doxastic derives from the ancient Greek δόξα, doxa, which means "belief." Typically, a doxastic logic uses 'Bx' to mean "It is believed that x is the case," and the set Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{B}

denotes a set of beliefs. In doxastic logic, belief is treated as a modal operator.

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{B}

{Failed to parse (Missing texvc executable; please see math/README to configure.): b_{1},b_{2},...,b_{n}

}

There is complete parallelism between a person who believes propositions and a formal system that derives propositions. Using doxastic logic, one can express the epistemic counterpart of Gödel's incompleteness theorem of metalogic, as well as Löb's theorem, and other metalogical results in terms of belief.^[1]

Types of reasoners[link]

To demonstrate the properties of sets of beliefs, Raymond Smullyan defines the following types of reasoners:

• Accurate reasoner:^{[1][Need quotation to verify][2][dead link][3][dead link][4][Need quotation to verify]} An accurate reasoner never believes any false proposition. (modal axiom T)

Failed to parse (Missing texvc executable; please see math/README to configure.): \forall p: \mathcal{B}p \to p

• Inaccurate reasoner:^[1][2][3][4] An inaccurate reasoner believes at least one false proposition.

Failed to parse (Missing texvc executable; please see math/README to configure.): \exists p: \neg p \wedge \mathcal{B}p

• Conceited reasoner:^[1][4] A conceited reasoner believes his or her beliefs are never inaccurate. A conceited reasoner will necessarily lapse into an inaccuracy.

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal{B}[\neg\exists p: \neg p \wedge \mathcal{B}p]

• Consistent reasoner:^[1][2][3][4] A consistent reasoner never simultaneously believes a proposition and its negation. (modal axiom D)

Failed to parse (Missing texvc executable; please see math/README to configure.): \neg\exists p: \mathcal{B}p \wedge \mathcal{B}\neg p

• Normal reasoner:^[1][2][3][4] A normal reasoner is one who, while believing p, also believes he or she believes p (modal axiom 4).

Failed to parse (Missing texvc executable; please see math/README to configure.): \forall p: \mathcal{B}p \to \mathcal{BB}p

• Peculiar reasoner:^[1][4] A peculiar reasoner believes proposition p while also believing he or she does not believe p. Although a peculiar reasoner may seem like a strange psychological phenomenon (see Moore's paradox), a peculiar reasoner is necessarily inaccurate but not necessarily inconsistent.

Failed to parse (Missing texvc executable; please see math/README to configure.): \exists p: \mathcal{B}p \wedge \mathcal{B\neg B}p

• Regular reasoner:^[1][2][3][4] A regular reasoner is one for whom all beliefs are distributive over logical operations. (modal axiom K)

Failed to parse (Missing texvc executable; please see math/README to configure.): \forall p: \forall q: \mathcal{B}(p \to q) \to (\mathcal{B}p \to \mathcal{B}q)

• Reflexive reasoner:^[1][4] A reflexive reasoner is one for whom every proposition p has some q such that the reasoner believes q≡(Bq→p). So if a reflexive reasoner of type 4 [see below] believes Bp→p, he or she will believe p. This is a parallelism of Löb's theorem for reasoners.

• Unstable reasoner:^[1][4] An unstable reasoner is one for whom there is some proposition p such that he or she believes he or she believes p, but who does not really believe p. This is just as strange a psychological phenomenon as peculiarity; however, an unstable reasoner is not necessarily inconsistent.

• Stable reasoner:^[1][4] A stable reasoner is not unstable. That is, for every p, if he or she believes Bp then he or she believes p. Note that stability is the converse of normality. We will say that a reasoner believes he or she is stable if for every proposition p, he or she believes BBp→Bp (believing: "If I should ever believe that I believe p, then I really will believe p").

Failed to parse (Missing texvc executable; please see math/README to configure.): \forall p: \mathcal{BB}p\to\mathcal{B}p

• Modest reasoner:^[1][4] A modest reasoner is one for whom every believed proposition p, Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal{B}p \to p

only if he or she believes p. A modest reasoner never believes Bp→p unless he or she believes p. Any reflexive reasoner of type 4 is modest. (Löb's Theorem)

Failed to parse (Missing texvc executable; please see math/README to configure.): \forall p: \mathcal{B}(\mathcal{B}p \to p) \to \mathcal{B}p

• Queer reasoner:^[4] A queer reasoner is of type G and believes he or she is inconsistent—but is wrong in this belief.

• Timid reasoner:^[4] A timid reasoner is afraid to believe p [i.e., he or she does not believe p] if he or she believes Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal{B}p \to \mathcal{B}\bot

Increasing levels of rationality[link]

• Type 1 reasoner:^{[1][2][3][4][5]} A type 1 reasoner has a complete knowledge of propositional logic i.e., he or she sooner or later believes every tautology (any proposition provable by truth tables) (modal axiom N). Also, his or her set of beliefs (past, present and future) is logically closed under modus ponens. If he or she ever believes p and believes p→q (p implies q) then he or she will (sooner or later) believe q (modal axiom K). This is equivalent to modal system K.

• p Failed to parse (Missing texvc executable; please see math/README to configure.): \vdash

Bp

• (Bp&B(pFailed to parse (Missing texvc executable; please see math/README to configure.): \to

q))Failed to parse (Missing texvc executable; please see math/README to configure.): \to Bq

• Type 1* reasoner:^[1][2][3][4] A type 1* reasoner believes all tautologies; his or her set of beliefs (past, present and future) is logically closed under modus ponens, and for any propositions p and q, if he or she believes p→q, then he or she will believe that if he or she believes p then he or she will believe q. The type 1* reasoner has a shade more self awareness than a type 1 reasoner.

• B(pFailed to parse (Missing texvc executable; please see math/README to configure.): \to

q)Failed to parse (Missing texvc executable; please see math/README to configure.): \to B(BpFailed to parse (Missing texvc executable; please see math/README to configure.): \to Bq)

• Type 2 reasoner:^[1][2][3][4] A reasoner is of type 2 if he or she is of type 1, and if for every p and q he or she (correctly) believes: "If I should ever believe both p and p→q, then I will believe q." Being of type 1, he or she also believes the logically equivalent proposition: B(p→q)→(Bp→Bq). A type 2 reasoner knows his or her beliefs are closed under modus ponens.

• B((Bp&B(pFailed to parse (Missing texvc executable; please see math/README to configure.): \to

q))Failed to parse (Missing texvc executable; please see math/README to configure.): \to Bq)

• Type 3 reasoner:^[1][2][3][4] A reasoner is of type 3 if he or she is a normal reasoner of type 2.

• Type 4 reasoner:^{[1][2][3][4][5]} A reasoner is of type 4 if he or she is of type 3 and also believes he or she is normal.

• Type G reasoner:^[1][4] A reasoner of type 4 who believes he or she is modest.

Gödel incompleteness and doxastic undecidability[link]

Let us say an accurate reasoner is faced with the task of assigning a truth value to a statement posed to him or her. There exists a statement which the reasoner must either remain forever undecided about or lose his or her accuracy. One solution is the statement:

S: "I will never believe this statement."

If the reasoner ever believes the statement S, it becomes falsified by that fact, making S an untrue belief and hence making the reasoner inaccurate in believing S.

Therefore, since the reasoner is accurate, he or she will never believe S. Hence the statement was true, because that is exactly what it claimed. It further follows that the reasoner will never have the false belief that S is true. The reasoner cannot believe either that the statement is true or false without becoming inconsistent (i.e. holding two contradictory beliefs). And so the reasoner must remain forever undecided as to whether the statement S is true or false.

The equivalent theorem is that for any formal system F, there exists a mathematical statement which can be interpreted as "This statement is not provable in formal system F". If the system F is consistent, neither the statement nor its opposite will be provable in it.^[1][4]

Inconsistency and peculiarity of conceited reasoners[link]

A reasoner of type 1 is faced with the statement "I will never believe this sentence." The interesting thing now is that if the reasoner believes he or she is always accurate, then he or she will become inaccurate. Such a reasoner will reason: "If I believe the statement then it will be made false by that fact, which means that I will be inaccurate. This is impossible, since I'm always accurate. Therefore I can't believe the statement: it must be false."

At this point the reasoner believes that the statement is false, which makes the statement true. Thus the reasoner is inaccurate in believing that the statement is false. If the reasoner hadn't assumed his or her own accuracy, he or she would never have lapsed into an inaccuracy.

It can also be shown that a conceited reasoner is peculiar.^[1][4]

Self fulfilling beliefs[link]

For systems, we define reflexivity to mean that for any p (in the language of the system) there is some q such that q≡(Bq→p) is provable in the system. Löb's theorem (in a general form) is that for any reflexive system of type 4, if Bp→p is provable in the system, so is p.^[1][4]

Inconsistency of the belief in one's stability[link]

If a consistent reflexive reasoner of type 4 believes that he or she is stable, then he or she will become unstable. Stated otherwise, if a stable reflexive reasoner of type 4 believes that he or she is stable, then he or she will become inconsistent. Why is this? Suppose that a stable reflexive reasoner of type 4 believes that he or she is stable. We will show that he or she will (sooner or later) believe every proposition p (and hence be inconsistent). Take any proposition p. The reasoner believes BBp→Bp, hence by Löb's theorem he or she will believe Bp (because he or she believes Br→r, where r is the proposition Bp, and so he or she will believe r, which is the proposition Bp). Being stable, he or she will then believe p.^[1][4]

See also[link]

Logic portal

• Modal logic
• Raymond Smullyan
• Jaakko Hintikka
• George Boolos
• Belief revision
• Common knowledge (logic)

Further reading[link]

• Lindström, St. and Wl. Rabinowicz: DDL Unlimited. Dynamic Doxastic Logic for Introspective Agents. In: Erkenntnis 51, 1999, p. 353-385.
• Linski, L.: On Interpreting Doxastic Logic. In: The Journal of Philosophy 65, 1968, p. 500-502.
• Segerberg, Kr.: Default Logic as Dynamic Doxastic Logic. In: Erkenntnis 51, 1999, p. 333-352.
• Wansing,H.: A Reduction of Doxastic Logic to Action Logic. In: Erkenntnis 53, 2000, p. 267-283.

References[link]

Ravi Zacharias
Born	1946 (1946) (age 66) Chennai, Madras Presidency, British India
Residence	Atlanta, Georgia, USA
Nationality	Indian, Canadian and American
Occupation	Christian apologist, Founder and Chairman of the Board of Ravi Zacharias International Ministries
Religion	Christian
Website
http://www.rzim.org

Frederick Antony Ravi Kumar Zacharias (born 1946) is an Indian-born, Canadian-American evangelical Christian apologist. Zacharias is the author of numerous Christian books, including Gold Medallion Book Award winner Can Man Live Without God?^[1] and bestsellers Light in the Shadow of Jihad^[2] and The Grand Weaver.^[3] He is the founder and chairman of the board of Ravi Zacharias International Ministries, host of the radio programs Let My People Think and Just Thinking, and visiting professor at Wycliffe Hall of Oxford, where he teaches apologetics and evangelism.^[4] Zacharias studied as a visiting scholar at Cambridge University and held the chair in Evangelism and Contemporary Thought at Alliance Theological Seminary from 1981 to 1984.^[5] Commentator Chuck Colson referred to Zacharias as "the great apologist of our time."^[6]

Biography[link]

Early life[link]

Zacharias was born in Madras, India. Zacharias claims descent from a woman (of the Nambudiri Brahmin caste) and a low caste Boatman^[7]. Missionaries spoke to one of his ancestors about Christianity and thereafter the family was converted. Zacharias grew up in a nominal Anglican household,^[7] and he himself was an atheist until the age of 17, when he unsuccessfully tried to commit suicide by swallowing poison. While in the hospital, a local Christian worker brought him a Bible and instructed his mother to read to him out of John 14. Zacharias says that it was John 14:19 that touched him and caused him to commit his life to Christ.^[7]

He immigrated with his family to Canada in 1966, earning his undergraduate degree from Ontario Bible College in 1972 (now Tyndale University College & Seminary) and his M. Div. from Trinity International University. In May 1972, Zacharias married Margaret ("Margie") Reynolds, whom he met at his church's youth group.^[7] They have three children, Sarah, Naomi and Nathan.^[8] He was later ordained by the Christian and Missionary Alliance and commissioned as an international evangelist.^[9] He founded Ravi Zacharias International Ministries in 1984 to pursue his calling as a "classical evangelist in the arena of the intellectually resistant."^[9]

Ministry[link]

Zacharias was invited to spend the summer of 1971 in Vietnam, where he evangelized to the American soldiers, as well as to POWs and Viet Cong.^[7] After graduating from Ontario Bible College, he began an itinerant ministry with the Christian and Missionary Alliance in Canada.^[7] In 1974 the C&MA sent him to Cambodia, where he preached only a short time before its fall to the Khmer Rouge.^[7] In 1977, after graduating from Trinity, Zacharias was commissioned to preach worldwide.^[7]

In 1983, Zacharias was invited to speak in Amsterdam at the Billy Graham Evangelistic Association's annual evangelists' conference. It was here that he first noticed a lack of ministry in the area of Christian apologetics.^[7] After Amsterdam, Zacharias spent the summer evangelizing in India, where he continued to see the need for apologetics ministry, both to lead people to Christ and to train Christian leaders. In August 1984 Ravi Zacharias International Ministries was founded in Toronto, Canada. Today its headquarters is located in Atlanta, Georgia, and has offices in Canada, England, India, Singapore and the United Arab Emirates.^[7]

In 1989, shortly after the fall of the Berlin Wall, Zacharias was invited to speak in Moscow. While there he spoke to students at the Lenin Military Academy as well as political leaders at the Center for Geopolitical Strategy.^[7] This was the first of many evangelism opportunities towards the political world. Future events included an invitation to Bogota, Colombia in 1993, where he spoke to the judiciary committee on the importance of having a solid moral foundation.^[7]

Zacharias took a sabbatical in 1990 and spent part of that year as a visiting scholar at Cambridge University. There he heard lectures by men such as Stephen Hawking and studied under professors such as John Polkinghorne and Don Cupitt. He also wrote his first book, A Shattered Visage: The Real Face of Atheism.^[7] In 1993 Zacharias was invited to speak at his first Veritas Forum at Harvard University,^[7] and later that year was one of the keynote speakers at Urbana.^[10] Zacharias continues to be a frequent guest at these forums,^[11] both giving lectures and answering students in question and answer sessions at academic institutions such as the University of Georgia,^[12] the University of Michigan,^[13] and Penn State.^[14]

Zacharias attracted media attention when in 2004 The Church of Jesus Christ of Latter-day Saints (LDS Church) opened its signature pulpit at the Salt Lake Tabernacle to him for a series of messages. Zacharias delivered a sermon on "Who Is the Truth? Defending Jesus Christ as The Way, The Truth and The Life" to some 7,000 lay-persons and scholars from both LDS and Protestant camps in an initiatory move towards open dialog between the camps.^[15]

Some evangelicals criticized Zacharias' decision not to use this opportunity to directly address the "deep and foundational" differences between the historic Christian faith and that of the LDS church. He responded by asserting that Christians should not immediately condemn Mormonism's theological differences but "graciously build one step at a time in communicating our faith with clarity and conviction". He said this is just as effective as showing someone the faults of their faith.^[16] The speaking engagement was nearly sabotaged by a claim by event organizer Greg Johnson, president of Standing Together, that Zacharias had nothing to do with editing the book The Kingdom of the Cults and had only loaned his name to the latest edition. Johnson later apologized for his comment.^[17]

Zacharias is a frequent keynote lecturer within the evangelical community at events such as the Future of Truth conference in 2004,^[18] the National Religious Broadcasters' Convention and Exposition in 2005,^[19] the National Conference on Christian Apologetics in 2006.^[20] On successive nights in October 2007, he addressed first the students and faculty of Virginia Tech, then the community of Blacksburg, Virginia, on the topic of evil and suffering in the wake of the Virginia Tech massacre.^[21] Zacharias has represented the evangelical community at occasions such as the National Day of Prayer in Washington, DC, the Annual Prayer Breakfast at the United Nations, and the African Union Prayer Breakfast in Maputo, Mozambique, and was named honorary chairman of the 2008 National Day of Prayer task force.^[22]

Zacharias was interviewed in Focus on the Family's Truth Project. In November 2009, Zacharias signed an ecumenical statement known as the Manhattan Declaration calling on Evangelicals, Catholics and Orthodox to engage in civil disobedience with regard to laws which the declaration claims would force them to accept abortion, same-sex marriage or other matters that go against their religious consciences.^[23]

Philosophy[link]

Zacharias states that a coherent worldview must be able to satisfactorily answer four questions: that of origin, meaning of life, morality and destiny. He says that while every major religion makes exclusive claims about truth, the Christian faith is unique in its ability to answer all four of these questions.^[24] He routinely speaks on the coherency of the Christian worldview,^[25] saying that Christianity is capable of withstanding the toughest philosophical attacks.^[26] Zacharias believes that the apologist must argue from three levels: the theoretical, to line up the logic of the argument; the arts, to illustrate; and "kitchen table talk", to conclude and apply.^[27]

Zacharias's style of apologetic focuses predominantly on Christianity's answers to life's great existential questions,^[28] with logical and scientifically inclined defense of God. In some discussion Zacharias appropriates to scientific matters, he answers the question of human origin. He has voiced skepticism over what he believes to be inadequate empirical evidence in the fossil records for an honest endorsement of the theory of evolution. He believes that evolution is incompatible with the second law of thermodynamics, saying that the two are inconsistent and irreconcilable.^[29] This view is rejected by many in the scientific community.^[30]

Ravi Zacharias also believes that in Christianity homosexual acts are an “aberration” and “violation” of human sexuality and that though some people may have a homosexual “disposition,” they are not justified in expressing that disposition.^[31]

Works[link]

• A Shattered Visage: The Real Face of Atheism (1994, 2004) ISBN 0-8010-6511-9
• Can Man Live Without God? (1994, 1996) ISBN 0-8499-3943-7
• Deliver Us From Evil (1996, 1998) ISBN 0-8499-3950-X
• Cries of the Heart (1998, 2002) ISBN 0-8499-4387-6
• The Merchant and the Thief (1999) (Children’s) ISBN 0-7814-3296-0
• The Broken Promise (2000) (Children's) ISBN 0-7814-3451-3
• Jesus Among Other Gods (2000, 2002) ISBN 0-8499-4327-2
• Jesus Among Other Gods (Youth Edition) (2000) ISBN 0-8499-4217-9
• The Lotus and the Cross: Jesus Talks with Buddha (2001) ISBN 1-57673-854-X
• Sense and Sensuality: Jesus Talks with Oscar Wilde (2002) ISBN 1-59052-014-9
• Light in the Shadow of Jihad: The Struggle For Truth (2002) ISBN 1-57673-989-9
• Recapture the Wonder (2003) ISBN 1-59145-276-7
• Is Your Church Ready?: Motivating Leaders to Live an Apologetic Life (2003) (Editor, with Norman Geisler) ISBN 0-310-25061-7
• Who Made God? And Answers to Over 100 Other Tough Questions of Faith (2003) (General Editor, with Norman Geisler) ISBN 0-310-24710-1
• The Kingdom of the Cults (2003) (Editor) ISBN 0-7642-2821-8
• I, Isaac Take Thee, Rebekah: Moving From Romance to Lasting Love (2004) ISBN 0-8499-0822-1
• The Prince and the Prophet: Jesus Talks With Mohammed (Copyright 2004, to be released posthumously) ISBN 1-59052-319-9
• The Lamb and the Führer: Jesus Talks with Hitler (2005) ISBN 1-59052-394-6
• Walking From East to West: God in the Shadows (With R.S.B. Sawyer) (2006) ISBN 0-310-25915-0
• The Grand Weaver: How God Shapes Us Through the Events of Our Lives (2007) ISBN 0-310-26952-0
• Beyond Opinion: Living the Faith We Defend (2008) ISBN 0-8499-1968-1
• The End of Reason: A Response to the New Atheists (2008) ISBN 0-310-28251-9
• Is There Not a Cause (2008) (National Day of Prayer Feature Book)
• New Birth or Rebirth: Jesus Talks with Krishna (2008) ISBN 1-59052-725-9
• There is a Plan (2009) (excerpts from The Grand Weaver) ISBN 0-310-31849-1
• Has Christianity Failed You? (2010) ISBN 0-310-26955-5
• The Lotus and the Cross: Jesus Talks with Buddha (2010) ISBN 1-60142-318-7
• Why Jesus? Rediscovering His Truth in an Age of Mass Marketed Spirituality (2012) ISBN 978-0-89296-319-5

References[link]

External links[link]

	Christianity portal
	Biography portal

• Ravi Zacharias International Ministries
• Ravi Zacharias Radio Broadcasts Just Thinking and Let My People Think