Is Logic Biased Towards Atheism?

[Catholic2003]

atheos_sum:

The laws of logic are not, as you suppose, only one set of basic principles among many possible sets. These laws are not selected arbitrarily or by convention. There are no “alternative logics.”

The laws of logic are not arbitrary, but they are by convention. The majority of mathematicians follow Hilbert’s classical logic, but there are those who follow Brouwer’s intuitionism or Kronecker’s constructivism. This was a matter of some controversy in the late 1800’s (and early 1900’s).

atheos_sum:

Remove, say, the law of contradiction from your system and replace it with a substitute, and what do you get? Some bizarre alternative system? No. You get no system at all, and no assertion at all, for you have removed the condition of intelligible statement in any system whatever. When you change the law of contradiction what do you change to?

If you remove excluded middle, you get likewise nonsense.

Constructive logic is an alternative logic, but it is by no means bizarre. (I would agree that relevant logic is somewhat bizarre.)

In constructive logic, “A or (not A)” is not always a true statement, unless you can prove “A” or prove “(not A)”. If you can’t prove either, then how can you be sure that “A or (not A)” is true?

P.S. I also left out the various quantum logics, which attempt to model the reality of quantum physics as classical logic models the reality of classical physics.

 

[pilchard]

Peregrinator said pretty much exactly what I was going to say…

Mind you - I think GKC beat us both to the punch

Logic and truth, as a matter of fact, have very little to do with each other. Logic is concerned merely with the fidelity and accuracy with which a certain process is performed, a process which can be performed with any materials, with any assumption. You can be as logical about griffins and basilisks as about sheep and pigs. On the assumption that a man has two ears, it is good logic that three men have six ears, but on the assumption that a man has four ears, it is equally good logic that three men have twelve. And the power of seeing how many ears the average man, as a fact, possesses, the power of counting a gentleman’s ears accurately and without mathematical confusion, is not a logical thing but a primary and direct experience, like a physical sense, like a religious vision. The power of counting ears may be limited by a blow on the head; it may be disturbed and even augmented by two bottles of champagne; but it cannot be affected by argument. Logic has again and again been expended, and expended most brilliantly and effectively, on things that do not exist at all. There is far more logic, more sustained consistency of the mind, in the science of heraldry than in the science of biology. There is more logic in Alice in Wonderland than in the Statute Book or the Blue Books. The relations of logic to truth depend, then, not upon its perfection as logic, but upon certain pre-logical faculties and certain pre-logical discoveries, upon the possession of those faculties, upon the power of making those discoveries. If a man starts with certain assumptions, he may be a good logician and a good citizen, a wise man, a successful figure. If he starts with certain other assumptions, he may be an equally good logician and a bankrupt, a criminal, a raving lunatic. Logic, then, is not necessarily an instrument for finding truth; on the contrary, truth is necessarily an instrument for using logic—for using it, that is, for the discovery of further truth and for the profit of humanity. Briefly, you can only find truth with logic if you have already found truth without it.

G. K. Chesterton (Daily News, Feb 25, 1905)

 

[Bobby_A.Greene]

Logic is geared toward objectivity. Logic is the basis of the scientific method, in that there is no room for the unseen. The unseen being concepts and abstractions, such as history, democrary, the state, religion, the mind, the soul, and other such abstractions.

Logic is a tool, a methodology for distilling the truth - but it is not a fool proof method. Logic has no use for intuition, foresight, ESP, precognition, hunches, or serendipity (plain dumb luck).

The philosopher pretends to atheism to claim unbiased objectivity, while the theologian uses both philosophy, history, and religion to justify their arguments. Both the philosopher and theologian use logic to prove their arguments (examine Aristotle and St. Thomas Aquinas).

The real evil exists within our Judicial system, using LOGIC, where the rule of evidence states that if you cannot see it, touch it, or put it on a table, then ‘it’ doesn’t exist. Which is why the courts demand everything be put on paper, codified - a receipt.

But how do you prove an agreement or a conspiracy in a court of law? How does the court prove the existance of God under such limiitations? In view of the large amount of wrongful incarcerations under the U.S. legal system, it is apparent that logic has failed and the rule of law cannot be trusted.

The Catholic theologian using logic can still be trusted and the Magesterium is still infallible, not the U.S. court system.

 

[atheos_sum]

Catholic2003:

The laws of logic are not arbitrary, but they are by convention. The majority of mathematicians follow Hilbert’s classical logic, but there are those who follow Brouwer’s intuitionism or Kronecker’s constructivism. This was a matter of some controversy in the late 1800’s (and early 1900’s).

The breadth of your knowledge about systems of logic is impressive.

i read some of your links, and i found another one which talks about the exluded middle controversy.

Catholic2003:

Constructive logic is an alternative logic, but it is by no means bizarre. (I would agree that relevant logic is somewhat bizarre.)

In constructive logic, “A or (not A)” is not always a true statement, unless you can prove “A” or prove “(not A)”. If you can’t prove either, then how can you be sure that “A or (not A)” is true?

Be careful, because excluded middle does have a tendency to lend itself to the “false dilemma” fallacy, though it’s not excluded middle’s fault.

So, you’re saying that the intuitionist critique of excluded middle goes like this: Unless we can prove “A” or “not A” then how can we be sure whether “A or (not A)” is correct?

Shouldn’t we try plugging in values?

We cannot prove whether Jake is “man” nor can we prove that Jake is “not man” (because he may be a dog, we don’t know.) But, it seems upon reflection, we can be sure that Jake is one of the two. If he is a dog, then he is “not man.” And if he is a fish, he is likewise “not man.” Whatever Jake could possibly be, it appears these two alternatives apply.

Perhaps that was a bad example, so I’m asking you whether this is coherent. Perhaps we have to first have certain assumptions about what limitations there are to “Jake.” Or maybe I’m only using excluded middle in a classical sense.

Catholic2003:

P.S. I also left out the various quantum logics, which attempt to model the reality of quantum physics as classical logic models the reality of classical physics.

I was not aware of the intuitionist denial of excluded middle, although i feel as though I should, seeing how i am entering my second year as a philosophy and economics student.

But let’s get back to the discussion of God and atheism and logical systems, and suppose we ask a different question.

Which logical system should be used in the discussion over the existence of God?

This seems a fair enough question to me. Would it make more sense to use ,say, the intuitionist logic? Would that be biased in one direction or another? Or does it make no difference to the discussion whether we accept the law of excluded middle or not?

I have a hunch that, since this is a classical question, it requires classical thinking, thus we need an excluded middle. But i’m open to your thoughts.

 

[nucatholic]

Logic is logic. Plain and simple. It is not biased towards any one system of belief. It is a system of its own, and does not hinder faith. Especially if you happen to be a fideist, but thats a nother topic…

 

[Bobby_A.Greene]

Let’s not confuse Logic with Mathematics. Math uses logic, Math is not logic! Math and logic do not nor ever combine into one system, that is the current mistake of set theorists. Algerbraic manipulation of exponents is not logic, it is not even a system of logic, it is simply mathematical manipulation.

If you study the History of Logic you will find that Logic and Math are two distinct concepts, they are not one in the same. Not even number theory or set theory can escape from the use of logic. I have this debate with MIT math professors all the time.

Again, logic is only a problem solving tool which does not take intuition or *a priori * reasoning into consideration, and logic does not consider the existence or non-existance of God within its methodology.

Please review: newadvent.org/cathen/09324a.htm

Logic is divided into two parts: Formal and Informal Logic.

Formal logic is the use of inductive and deductive reasoning methods and the use of syllogistic methods.

Informal logic is the existing fallacies in reason.

Again, Mathematics is not logic and logic is not mathematics.

 

[Bobby_A.Greene]

Which logical system should be used in the discussion over the existence of God?

The Catholic Church had adopted Aristotelian logical system for use in the discussion over the existence of God, and Platonism to a lesser degree.

The Catholic Church is against neo-platonism.

 

[Sherlock]

I haven’t read the responses here, so I’m throwing in my two cents without the benefit of the wisdom of others: no, I don’t think logic is biased in favor of atheism…Aquinas comes instantly to mind as one who used formal logic beautifully, in defense of faith. Logic is a system, or maybe tool would be a better term.

 

[atheos_sum]

Bobby A. Greene:

Let’s not confuse Logic with Mathematics. Math uses logic, Math is not logic! Math and logic do not nor ever combine into one system, that is the current mistake of set theorists. Algerbraic manipulation of exponents is not logic, it is not even a system of logic, it is simply mathematical manipulation.

If you study the History of Logic you will find that Logic and Math are two distinct concepts, they are not one in the same. Not even number theory or set theory can escape from the use of logic. I have this debate with MIT math professors all the time.

Again, logic is only a problem solving tool which does not take intuition or *a priori *reasoning into consideration, and logic does not consider the existence or non-existance of God within its methodology.

Please review: newadvent.org/cathen/09324a.htm

Logic is divided into two parts: Formal and Informal Logic.

Formal logic is the use of inductive and deductive reasoning methods and the use of syllogistic methods.

Informal logic is the existing fallacies in reason.

Again, Mathematics is not logic and logic is not mathematics.

Then I’m confused as to why you introduced mathematical logics into a discussion concerning philosophical logics. We cannot use mathematical logic to discern the existence of God, so we must use philosophical logic. I’m not sure why you initially were in favor of saying that intuitionism is an alternative logic to classical-philosophical ones, when they are in two entirely different ballparks. So, intuitionism is not an alternative to the three laws I posted (vide supra), insofar as intuitionism is concerned with things mathematical and we are concerned with things philosophical.

 

[atheos_sum]

Bobby A. Greene:

The Catholic Church had adopted Aristotelian logical system for use in the discussion over the existence of God, and Platonism to a lesser degree.

The Catholic Church is against neo-platonism.

There are also modal logicians in favor of God. A lot of them are Calvinists, however. What of them?

So can Aristotelian logic arrive at the existence of the Catholic idea of God? Or can Aristotelian logic arrive only at an Aristotelian idea of God?

 

[David_Brown]

atheos_sum:

So can Aristotelian logic arrive at the existence of the Catholic idea of God? Or can Aristotelian logic arrive only at an Aristotelian idea of God?

Since an Aristotelian logic is based on a substance metaphysic using a subject-predicate form, it will be limited to discussing what can be properly put in that form. One of the “developments” of modern symbloic logic was the move away from the notion of existence so that logic would not entail existence. Henry Veatch studied this in great detail in his Two Logics: The Conflict Between Classical and Neo-Analytic Philosophy

Aquinas recognized this. Aquinas, in his Commentary on the De Trinitate of Boethius Q. 2, A. 3, said:

The gifts of grace are added to nature in such a way that they do not destroy it, but rather perfect it. So too the light of faith, which is imparted to us as a gift, does not do away with the light of natural reason given to us by God. And even though the natural light of the mind is inadequate to make known what is revealed by faith, nevertheless what is divinely taught to us by faith cannot be contrary to what we are endowed with by nature. One or the other would have to be false, and since we have both of them from God, he would be the cause of our error, which is impossible. Rather, since what is imperfect bears a resemblacne to what is perfect, what we know by natural reason has some likeness to what is taught to us by faith.

Aquinas went on to give natural reason three roles in relation to theology: (1) To demonstrate the “preambles of faith”–such as God exists, God is one, etc.; (2) To help explain the faith by analogies; (3) To reftue “assertions contrary to the faith, either by showing them false or lacking in necessity.” Also, he saw two errors in relation to reason and theology: (1) To admit nothing in the faith but what was given by reason; (2) To set the faith wholly outside reason.

David

 

[Liberian]

Atheos Sum,

The best logic, if your assumptions are incorrect, will lead you to incorrect conclusions. Atheists begin with certain (incorrect) assumptions and wind up with atheism. Theists begin with other assumptions and wind up with theism. The logic isn’t biased; it’s just not being applied correctly.

That said, most of the logic that I have heard from atheists takes the form of “I’m right and you’re wrong” and “That can’t be true so it isn’t true.”

• Liberian

 

[Catholic2003]

atheos_sum:

The breadth of your knowledge about systems of logic is impressive.

Thanks. I have to confess that I work with the logics of program verification (e.g., Hoare logic) for a living. I’ve taken graduate courses in both philosophical and mathematical logic.

atheos_sum:

So, you’re saying that the intuitionist critique of excluded middle goes like this: Unless we can prove “A” or “not A” then how can we be sure whether “A or (not A)” is correct?

Shouldn’t we try plugging in values?

If A is “God does exist”, then how do you plug in values? Intuitionists/constructivists do accept “A or (not A)” for those cases when plugging in values will work.

The concept that constructivists most directly have trouble with is proof by contradiction. They feel that deriving a contradiction from the assumption of (not A) isn’t at all the same thing as a direct proof of A. It turns out that proof by contradiction is related to the law of the excluded middle, because if “A or (not A)” is true, and (not A) leads to a contradiction, then the only remaining possible alternative is that A is true. Thus constructivists reject the law of the excluded middle as well.

atheos_sum:

I was not aware of the intuitionist denial of excluded middle, although i feel as though I should, seeing how i am entering my second year as a philosophy and economics student.

I came across it in computer science because it is possible to extract a program/algorithm from a constructive proof, but this is not the case with non-constructive classical proofs.

atheos_sum:

But let’s get back to the discussion of God and atheism and logical systems, and suppose we ask a different question.

Which logical system should be used in the discussion over the existence of God?

In mathematics, you generally use the weakest logical system possible to establish your result, so that it is most widely applicable. Since constructive logic is a subset of classical logic, in that all constructive proofs are also valid classical proofs, it is better to use constructive logic if possible.

For example, if you have a direct proof of God’s existence, use constructive logic. If you only have an indirect proof, in that assuming God’s non-existence leads to a contradiction, then your proof is only valid in classical logic.

 

[Steve_Andersen]

atheos_sum:

… “Well, who made up the rules of logic? The atheists did …

well the pagans actually
athos_sum:

…

Now, either my “logic” is correct or incorrect, but I don’t think it can be “biased” unless, of course, I’m using incorrectly—which would bring us back to that second alternative, namely, “incorrect.” So the question I have is if we are actually using different methods of “logic.” But how can two different forms of logic coexist and be true?..

logic is just a reasoning tool
it most basic set up is given A and B we can say C

Logic says nothing about the truth of A or B merely the relationshp between them and C
so a logical arguement that includes God as one of its givens can be just as valid as one that assumes no God

 

[Bobby_A.Greene]

There are also modal logicians in favor of God.

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.

 

[Bobby_A.Greene]

atheos_sum:

Then I’m confused as to why you introduced mathematical logics into a discussion concerning philosophical logics

.

**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!

 

[Bobby_A.Greene]

Liberian:

Atheos Sum,

The best logic, if your assumptions are incorrect, will lead you to incorrect conclusions. Atheists begin with certain (incorrect) assumptions and wind up with atheism. Theists begin with other assumptions and wind up with theism. The logic isn’t biased; it’s just not being applied correctly.

That said, most of the logic that I have heard from atheists takes the form of “I’m right and you’re wrong” and “That can’t be true so it isn’t true.”

• Liberian

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.

 

[atheos_sum]

Catholic2003:

If A is “God does exist”, then how do you plug in values?

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

Catholic2003:

Intuitionists/constructivists do accept “A or (not A)” for those cases when plugging in values will work.

You are much more knowledgeable than i am. What would it look like if plugging in values didn’t work?

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?

Catholic2003:

The concept that constructivists most directly have trouble with is proof by contradiction. They feel that deriving a contradiction from the assumption of (not A) isn’t at all the same thing as a direct proof of A. It turns out that proof by contradiction is related to the law of the excluded middle, because if “A or (not A)” is true, and (not A) leads to a contradiction, then the only remaining possible alternative is that A is true. Thus constructivists reject the law of the excluded middle as well.

That makes sense. Intuitionism, then, is more demanding in cases where it can be applied. It wants direct proofs of the proposition.

So wouldn’t this entail that the burden of proof is the same for both a theist and an atheist to make positive arguments for their own positions, insteading of pointing out contradictions in one another? Then, i would ask, wouldn’t this become more difficult for the atheist, Since, the atheist has to show that (not God) whereas the theist has to show that (God)?

Catholic2003:

In mathematics, you generally use the weakest logical system possible to establish your result, so that it is most widely applicable. Since constructive logic is a subset of classical logic, in that all constructive proofs are also valid classical proofs, it is better to use constructive logic if possible.

For example, if you have a direct proof of God’s existence, use constructive logic. If you only have an indirect proof, in that assuming God’s non-existence leads to a contradiction, then your proof is only valid in classical logic.

But isn’t it more difficult to have direct proof of something’s non-existence? Is it even possible in the discussion of God? Somewhat like Anselm, however, i’m not asking if (proof of God’s existence) exists in reality, but whether (proof of God’s existence) exists in the mind: is a direct proof of God’s non-existence even possible in theory?

There is a famous article by Antony Flew on this called “Theology and Falsification”.

 

[Contarini]

atheos_sum:

What they have in mind is summed up by what someone told me yesterday. “Well, who made up the rules of logic? The atheists did and it’s no wonder then why it’s in their favor. You made up the rules and did not include God in them, so it’s not wonder he can’t win.”

I can see why a poorly educated Christian would make such an argument when faced with a clever atheist. But it is of course a silly argument, unless you are in fact using rules of logic that not everyone would accept as self-evidently true. Without seeing an example of the kind of thing you’re talking about, we can’t have a meaningful discussion about it. Maybe the person was being defensive because they weren’t up to answering your arguments. Or maybe you really were claiming that something was a “rule of logic” when it wasn’t. Fallible human beings are quite prone to do this.

In other words, of course rules of logic themselves are not biased. But the way people use logic is always biased, and if you’re more familiar with logical argument than your opponents it would be easy to bamboozle and frustrate them.

Edwin

 

[atheos_sum]

Contarini:

I can see why a poorly educated Christian would make such an argument when faced with a clever atheist. But it is of course a silly argument, unless you are in fact using rules of logic that not everyone would accept as self-evidently true. Without seeing an example of the kind of thing you’re talking about, we can’t have a meaningful discussion about it. Maybe the person was being defensive because they weren’t up to answering your arguments. Or maybe you really were claiming that something was a “rule of logic” when it wasn’t. Fallible human beings are quite prone to do this.

In other words, of course rules of logic themselves are not biased. But the way people use logic is always biased, and if you’re more familiar with logical argument than your opponents it would be easy to bamboozle and frustrate them.

Edwin

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.