Is Logic Biased Towards Atheism?

[Grace_and_Glory]

atheos_sum:

Perhaps it is the idea that logic alone will not lead one to God. One needs to have faith in order to believe in God. So, without faith, and with only logic, perhaps one is inclined to be an atheist. Maybe that is what this person was saying. Logic is a kind of reason, and there is an inverse relationship between reason and faith.

I agree that logic alone will not generally lead one to God. On the other hand, I don’t think that there is an inverse relationship between reason and faith. Reason and faith are supposed to complement and enhance one another. John Paul II even wrote an encyclical about the relationship between faith and reason, Fides et Ratio, and he certainly didn’t portray reason as having an inverse relationship with faith. I understand that you, as an atheist, wouldn’t accept the Catholic understanding of faith and reason as true, but I think it is important to note that the Catholic Church promotes reason in order to better understand where Catholics are coming from in discussions of logic and reasoning. Obviously, not all Catholics understand this, and so you do get the people who think/act as though reason and faith can’t coexist.

 

[atheos_sum]

Grace and Glory:

I agree that logic alone will not generally lead one to God. On the other hand, I don’t think that there is an inverse relationship between reason and faith. Reason and faith are supposed to complement and enhance one another. John Paul II even wrote an encyclical about the relationship between faith and reason, Fides et Ratio, and he certainly didn’t portray reason as having an inverse relationship with faith. I understand that you, as an atheist, wouldn’t accept the Catholic understanding of faith and reason as true, but I think it is important to note that the Catholic Church promotes reason in order to better understand where Catholics are coming from in discussions of logic and reasoning. Obviously, not all Catholics understand this, and so you do get the people who think/act as though reason and faith can’t coexist.

if you have proof that X, how can you also have faith that X? If you had proof that God exists, what would be your need to have faith that God exists?

immanuel Kant wrote, quite humorously for Kant, that he “found it necessary to deny knowledge of God… in order to find a place for faith.”

and it was Tertullian who asked, “what has jerusalem to do with athens?”

 

[David_Brown]

Bobby A. Greene:

errrrr, what’s a “modal logician”? Remember what I mentioned in another post, logic is not math and math is not logic - so you might want to rethink the oxymoron Modal Logician.

For example, what aspects of logic are found in Modal Logic that are not already contained in Logic?

Using mathematics to prove the existence of God is taking a totally different approach than using logic to prove the existence of God.

Modal logic is not mathematical logic. It is standard formal (modern symbolic) logic that adds operators for “possibility” and “necessity.” Alvin Plantinga is a noted example of someone using modal logic (S5) in an ontological proof for God’s existence. Modal logic is well-established but has critics like W. V. Quine.

David

 

[David_Brown]

Bobby A. Greene:

.

**There is no such thing as “Mathematical Logic”! ** I keep having this debate with various professors who have jumped on the math/phil logic bandwagon. Mathematics uses logic. Mathematics does not contain a logic independent of Formal Logic itself. Algebraic or Mathematical manipulation is not logic, it is simply induction. Mathematical induction is what makes math work.

Please review your History of Logic and you will find under the History of Logic there exists various ‘reasoning systems’ which do not fall under the rubric of Logic.

Also, there is no such thing as “Philosophical Logic”! What is that?

Please visit: en.wikipedia.org/wiki/History_of_logic
(written by my logic professor ) and you will read that ‘Mathematical Logic’ is still the logic of Aristotle!

“The expressions ‘logic’, ‘formal logic’, ‘symbolic logic’, and mathematical logic’ are in the just acceptation synonyms. They refer to a discipline created by Aristotle, extended by the Stoics, studied by the Scholastics, developed in the esoteric writings of Leibniz, and sent on its modern career in the late nineteenth century…Presently logic is cultivated as a branch of both philosophy and mathematics” Logic: Techniques of Formal Reasoning , 4th ed. by Kalish, Montague, and Mar, p. xv.

You can go to www.amazon.com and type in “mathematical logic” and get dozens and dozens of books on the subject (as well as “philosophical logic”). If you look at their table of contents you will get an idea of what they talk about that is not in Aristotle. Perhaps you should tell them all they have nothing to write about. By the way, wikipedia is not a resource professional philosophers or logicians use–even if they write some of the articles.

David

 

[David_Brown]

Bobby A. Greene:

I am also observing the word ‘logic’ being very loosely used. There are not several different types of logic, but there are several different types of ‘systems of reasoning’ which are not true logic.

I have never heard of “true logic” or any criteria to distinguish it from “systems of reasoning.” In The Blackwell Guide to Philosophical Logic, ed. Lou Goble, there are several non-classical systems listed, among which:

• Intuitionistic Logic
• Free Logics
• Relevant Logics
• Many-Valued Logics
• Nonmonotonic Logics
• Probability Logic

I know you denied the existence of “philosophical logic” in post #36 above, but Blackwell is not in the habit of issuing guides for non-subjects.

David

 

[Catholic2003]

“The expressions ‘logic’, ‘formal logic’, ‘symbolic logic’, and mathematical logic’ are in the just acceptation synonyms. They refer to a discipline created by Aristotle, extended by the Stoics, studied by the Scholastics, developed in the esoteric writings of Leibniz, and sent on its modern career in the late nineteenth century…Presently logic is cultivated as a branch of both philosophy and mathematics” Logic: Techniques of Formal Reasoning , 4th ed. by Kalish, Montague, and Mar, p. xv.

The Handbook of Mathematical Logic, ed. by Jon Barwise, discusses the following sub-fields of mathematical logic: model theory, set theory, recursion theory, and proof theory.
David Brown:

You can go to www.amazon.com and type in “mathematical logic” and get dozens and dozens of books on the subject (as well as “philosophical logic”). If you look at their table of contents you will get an idea of what they talk about that is not in Aristotle. Perhaps you should tell them all they have nothing to write about. By the way, wikipedia is not a resource professional philosophers or logicians use–even if they write some of the articles.

What’s your opinion of the Stanford Encyclopedia of Philosophy? All the articles that I’ve read (and knew something about) seemed very accurate.

 

[David_Brown]

Catholic2003:

The Handbook of Mathematical Logic, ed. by Jon Barwise, discusses the following sub-fields of mathematical logic: model theory, set theory, recursion theory, and proof theory.

What’s your opinion of the Stanford Encyclopedia of Philosophy? All the articles that I’ve read (and knew something about) seemed very accurate.

Barwise is very good. I have students use the Stanford Encyclopedia of Philosophy online (which I like better than Wikipedia) for general stuff, but have also found superior stuff from the Catholic Encyclopedia at New Advent for more historical questions. I didn’t mean to discourage people from using these resources but only from taking them as authoritative (you will not, for example, find a philosophy journal article that cites wikipedia). However, the standard encyclopedias of philosophy are The Encyclopedia of Philosophy ed. Paul Edwards, which is a bit dated but excellent and the Routledge Encyclopedia of Philosophy which seems to be the new standard. Routledge is available online for libraries that subscribe.

For questions on the history and development of Logic The Development of Logic by William and Martha Kneale is a major authority.

David

 

[Catholic2003]

atheos_sum:

I am slightly confused. Didn’t you just plug in a value?

Maybe we are talking about different things by the phrase “plug in a value”. What I meant was that things like “(x = y) or (x <> y)”, where x and y are integers, are true in constructive mathematics because you can always plug in given values of x and y and figure out which case is true.

atheos_sum:

You are much more knowledgeable than i am.

Thanks again. I may not be very good at explaning this, however, but I will keep on trying.

atheos_sum:

What would it look like if plugging in values didn’t work?

In things like “(Fermat’s Last Theorem is true) or (Fermat’s Last Theorem is false)”, you can’t just plug in a few numbers and determine which case is true, because there are an infinite number of different values to try.

atheos_sum:

It isn’t clear to me that this value will work:

For all natural numbers: even or (not even)
the answer is clearly both (odd and even). so is this where the intuitionist logic applies?

In constructive mathematics, “(x is even) or (x is odd)” is true, because for any given value of x, you can plug that value in and determine whether it is even or odd.

atheos_sum:

But isn’t it more difficult to have direct proof of something’s non-existence?

This is another place where my explanations fell short. In constructive logic, negatives are weaker statements. To prove “(not A)”, what you need to show is that assuming A leads to a contradiction. Thus, “(not (God exists))” means that the assumption of God’s existence leads to a contradiction, e.g., if an omnipotent and good God existed, then there wouldn’t be evil in the world.

If assuming “(not A)” leads to a contradiction, then what you have established in constructive logic is “(not (not A))”, which is a much weaker statement than A. The syllogism “(not (not A)) ==> A” is rejected by constructive logic on the same grounds as proof by contradiction and the law of the excluded middle.

 

[David_Brown]

Catholic2003:

If assuming “(not A)” leads to a contradiction, then what you have established in constructive logic is “(not (not A))”, which is a much weaker statement than A. The syllogism “(not (not A)) ==> A” is rejected by constructive logic on the same grounds as proof by contradiction and the law of the excluded middle.

The assumption is also the standard reductio ad absurdam in regular formal logic, except the conclusion “(not (notA))” is seen as identical to “A” by double negation.

A question: How is “(not (not A)) → A” a syllogism? It appears to have only one premise and therfore no middle term. It looks more like an immediate inference (substitution rule). Just a question.

David

 

[Catholic2003]

David Brown:

A question: How is “(not (not A)) → A” a syllogism? It appears to have only one premise and therfore no middle term. It looks more like an immediate inference (substitution rule). Just a question.

I thought “syllogism” was a synonym for “inference rule”. Thanks for the correction! (You learn something new every day.)

 

[atheos_sum]

Catholic2003:

This is another place where my explanations fell short. In constructive logic, negatives are weaker statements. To prove “(not A)”, what you need to show is that assuming A leads to a contradiction. Thus, “(not (God exists))” means that the assumption of God’s existence leads to a contradiction, e.g., if an omnipotent and good God existed, then there wouldn’t be evil in the world.

And the other half of my question was, Could there be a direct proof of God’s non-existence in theory?

More generally speaking, how do you achieve a direct proof of anything non-existent?

Perhaps intuitionist/contructivist logic is biased towards things extant?

Catholic2003:

If assuming “(not A)” leads to a contradiction, then what you have established in constructive logic is “(not (not A))”, which is a much weaker statement than A. The syllogism “(not (not A)) ==> A” is rejected by constructive logic on the same grounds as proof by contradiction and the law of the excluded middle.

But surely proof by contradiction and the law of excluded middle should apply in a discussion of metaphysical propositions such as God’s existence?

 

[MysticRose]

I have a serious question …

Can it be proven as Scientific Fact that God does not exist? NO

The FACT, that an Atheist asserts logically that God does not exist is based upon the exclusion of things and therefore also upon the basis of belief that this exclusion is enough to prove the THEORY that God does not exist which is their assertion is therefore relatively Truthful.

Fact we believed for the longest time that our Solar System only contained nine planets, and that this was Scientifically correct and factual, until the other day when the existence of another planet was discovered because of the newer developments we have made in Science and Space exploration.

Therefore, Fact, man and manmade Facts that are done by exclusion are then not infallible. They can be and often are erroneous.

Exclusion, that man is a credible source of Factual information. This is based upon many years of proven fact then retration of fact by the course of new discovery which then nullifies the first fact.

Fact, man is fallible and cannot be relied upon for as the source of complete and accurate knowledge as this is a continual learning process to man which they themselves are, although skilled in assessing information, cannot be totally 100 % accurate in their assenment of to claim that the theory is an actual Factiod.

This then means that they rely on their belief and Faith in the assertions made that they are Fact.

We must remember that it men thatr also defined the word Faith, and that the Word itself has many meanings.

faith (fth)

NOUN:

1)Confident belief in the truth, value, or trustworthiness of a person, idea, or thing.
2)Belief that does not rest on logical proof or material evidence. See Synonyms at belief, trust.
3)Loyalty to a person or thing; allegiance: keeping faith with one’s supporters.
3)often Faith Christianity The theological virtue defined as secure belief in God and a trusting acceptance of God’s will.
4)The body of dogma of a religion: the Muslim faith.
5)A set of principles or beliefs.

Please take note that Faith does not have to be necessarily have to mean that it based BLINDLY upon something and that there is a Total absence …

Definitions one and five would work very well in this instance and still be suited to Atheism that claims to be void of these virtues in any form …

You do not have to believe in God to have belief Faith and Trust especially in something’s accuracy and Truth.

Therefore, subjectively, for the Atheist that claims to be void of this altogether that would be an incorrect assessment.

 

[Ignatius]

atheos_sum:

Throughout these posts and in conversations with believers, atheistic reasoning is often objected to and dismissed as being a kind of “biased logic.”

The ultimate in logic and rationality can be found in the writings of Thomas Aquinas. As them to read Aquinas.

 

[Catholic2003]

atheos_sum:

And the other half of my question was, Could there be a direct proof of God’s non-existence in theory?

More generally speaking, how do you achieve a direct proof of anything non-existent?

Perhaps intuitionist/contructivist logic is biased towards things extant?

You are correct; only positive statements can have direct proofs. Negative statements can only have indirect proofs. Because of this, indirect proofs are allowed in constructive logic, but only for negative statements. Thus, negative statements are “easier” to prove in constructive logic, but are also not held in as high esteem as positive statements. Constructive mathematicians would much rather see a proof of “A” than a proof of “(not (not A))”.

Interestingly enough, “(not (not (not A)))” is equivalent to “(not A)” in constructive logic.

atheos_sum:

But surely proof by contradiction and the law of excluded middle should apply in a discussion of metaphysical propositions such as God’s existence?

Classical logic is widely accepted, so there should be no problem using it in your proofs of God’s existence.

 

[Bobby_A.Greene]

MysticRose:

I have a serious question …

Can it be proven as Scientific Fact that God does not exist? NO

That is because General Existance Statements cannot be disproven.

 

[Bobby_A.Greene]

Ignatius:

The ultimate in logic and rationality can be found in the writings of Thomas Aquinas. As them to read Aquinas.

Also, read the Jewish philosopher Moses Maimonides in his ‘Guide to the Perplexed’. “Judaism had to be formulated and defended with a view not so much to the dangers threatening from Christianity and Mohammedanism as to those endangering all religions alike, namely, the opinions of science and philosophy as taught especially by the Aristotelians.”

Moses Maimonides was known to medieval Latin theologians as Rabbi Moyses (Aegyptius). “Maimonides major influence outside Judaism has been exercised through his Guide to the Perplexed, published in Arabic in 1190, the Guide appeared with the author’s apporval in the Hebrew version of Samuel ibn Tibbon Nov. 30, 1204 under the title Moreh N’Bukim.”

“The Latin version of the Guide to the Perplexed, DUX NEUTRORUM known to 13th century Christian Theologians seems to have been produced before 1240 and appears to have stem from a Hebrew translation by Judah al-Harizi.”

“Hence Maimonides treated for the most part of the same problems as the Mohammendan Mutakallimum before him, and Thomas Aquinas the Christian had no scruple in making the Jewish philosopher’s method his own when he undertook to defend the Catholic Faith Contra Gentiles.”

“In 1520 a printing of the medieveal Latin version (Guide to the Perplexed) was published in Paris by Augustinus Justinianus, and a Latin translation of the ibn Tibbon version was published as DUX PERPLEXORUM by John Buxtorf the Younger at Basil in 1629. It was in the Buxtorf edition the the Guide was known to Leibniz, where as Spinoza possessed the Hebrew version of ibn Tibbon.”

 

[Bobby_A.Greene]

David Brown:

I have never heard of “true logic” or any criteria to distinguish it from “systems of reasoning.”

That is why you must spend a moment and review the HISTORY OF LOGIC. There are many ‘reasoning systems’ that are not Logic, and mathematical manipulation is one of them.

Please visit:
fmag.unict.it/~polphil/PolPhil/Lukas/Lukas.html
and read up on Jan Lukasiewicz, founder of the History of Logic.

Also, please read: THE DEVELOPMENT OF LOGIC by William Kneale, Martha Kneale (required reading in my History of Logic course).

GREEK, INDIAN AND ARABIC LOGIC (Handbook of the History of Logic) by Dov Gabay, John Hayden Woods.

These works give comprehensive descriptions of ‘reasoning systems’ which do not fall into the category of LOGIC.

 

[Bobby_A.Greene]

By the way, wikipedia is not a resource professional philosophers or logicians use–even if they write some of the articles.

Hi David,

Yes, I agree. The same is true of encyclopedias - any encyclopedia. One of my history professors was in the habit of dropping you a grade if you dare included an encyclopedia as one of your sources in a history paper. The Stanford Encyclopedia of Philosophy is no exception, just another generalized compendium of loose definitions, just like wikipedia.

I included the wikipedia cite simply because it gave a good working overview of the History of Logic written by an expert - my professor.

The quality of scholarship in major American universities has declined sharply, and the trendy definitions found within the Stanford Encylopedia of Philosophy is a major indicator of that decline. Already what has been called Mathematical Logic has been more accurately called ‘Proof theory’, and not logic.

My logic professor (and myself) would like to correct any misuse of the term ‘Logic’ whenever we find it, hence my constant debates with professors at various philosophy workshops in the Boston area.

 

[David_Brown]

Bobby A. Greene:

That is why you must spend a moment and review the HISTORY OF LOGIC. There are many ‘reasoning systems’ that are not Logic, and mathematical manipulation is one of them.

Please visit:
fmag.unict.it/~polphil/PolPhil/Lukas/Lukas.html
and read up on Jan Lukasiewicz, founder of the History of Logic.

Also, please read: THE DEVELOPMENT OF LOGIC by William Kneale, Martha Kneale (required reading in my History of Logic course).

GREEK, INDIAN AND ARABIC LOGIC (Handbook of the History of Logic) by Dov Gabay, John Hayden Woods.

These works give comprehensive descriptions of ‘reasoning systems’ which do not fall into the category of LOGIC.

Kneale and Kneale also deal with non-traditional logics as did the references I cited.

Unless you just define “logic” to be the logic of Aristotle and its development and just define everything else as “reasoning systems,” you haven’t made your case that there are no other logics, or that there is nothing to Mathematical Logic or Philosophical Logic. Given the evidence to the contrary (the references I cited and the numerous books on those logics which anyone can find at www.amazon.com)), there is no reason to accept your definitions.

Good luck with your quixotic quest (I like Aristotelian logic too).

David

 

[Bobby_A.Greene]

What’s your opinion of the Stanford Encyclopedia of Philosophy? All the articles that I’ve read (and knew something about) seemed very accurate.

I prefer the Oxford Dictionary of Philosophy, it appears to offer more objective and superior definitions than the politically correct bias found in the Stanford Encyclopedia of Philosophy