Ravages‘ post about god and religion (trackbacked to my previous post) has attracted a lot of debate. The one most interesting to me was about logic. It is amusing how engineering, scientists swear by logic like it was the holy grail of truth and knowledge. I used to be one of them, till I read the Robert Persig book ‘Zen and the art of motorcycle maintainence’. In that book Phaedrus questions and challenges rationality itself. That got me thinking about logic and its validity. How logical is logic itself?
Fortunately for me, I am a computer science student, and I have the technical background to take a crack at this question. I know, a student of philsophy would be better equipped than I am, but when you are dealing with computational theory the lines get blurred, exteremly blurred. One of the assistant professors in computer science did his bachelors in philosophy and while pursuing his masters, specialized logic and stumbled upon computer science, going on to do a PhD in it. One of the best teachers I have taken a course under.
What is logic? Unfortunately we enounter a stumbling block at the very begining here. There no universally accepted definition for logic. The most general one I could come across was in MSN Encarta. It says “Logic is a science dealing with the principles of valid reasoning and argument. The study of logic is the effort to determine the conditions under which one is justified in passing from given statements, called premises, to a conclusion that is claimed to follow from them.” This is a fairly generic definition that includes most, but not all, of what logic is. This also gives me enough ammo to attack it with.
Traditionally, logic is bivariate. That is to say that there can be only two values to a statement, viz., ‘true’ and ‘false’. Logic also says all that is not false is true. It works well when you are dealing with the limited universe as defined by your premises. But the real question is, how valid can this be in reality? Not very. Consider the statement ‘It will rain tomorrow’, is it true? It is possible, but we cannot say it is true. This is not allowed in traditional logic. A statment can either be true or false, nothing else. How are we to try and understand the world, the natural, the supernatural or the divine with something as limited as this?
Granted, that we can do better than this. We do have multi-valued logic systems. But they fail too. They cant take you very far without stumbling on the rules that they created themselves. To illustrate one such example with bivariate logic, consider the statement ‘This statement is false’. Its simply a statement talking about itself. Can we assign a truth value to it? Just try and you will realize that it is not possible. You will run into contradictions either way. How useful is a tool that isnt powerful enough to talk about itself?
One might argue that is indeed the nature of all tools and intelligence. We havent been able to figure out how our own brain works, and logic is an invention of man, how can u expect logic to be able to explain itself? Going by that argument, our quest for Truth is an excercise in futility because the Truth is much bigger and more profound that ourselves, and if we arent powerful enough to understand how we work, then how can we be expected to understand Truth?
Going back to the definition, logic as a system can be employed only under the existance of premises, i.e., statements that are assumed to be true. In mathematics, they are refered to as axioms. What if we dont have any assumptions? What we seek is the ultimate truth, the truth above and beyond all truth. We wish to gain the knowledge that will explain the universe we live in, starting from nothing, void, no assumptions. Call it what you wish, enlightenment, nirvana, Truth, God. You choice of the name is your choice of the path that you wish to follow to get to the destination. How do you employ logic here? It isnt even valid anymore.
The natural question to ask is, how does logic work so well for science, if it fails miserably trying to explain nature? After all, isnt science a quest for understanding nature? Logic does remarkably well for science and engineering simply because the language and universe of science and engineering is mathematics. It is a severly limited universe, and one invented by man. My math professor said it best when he explained “What are numbers? Numbers are things you do arthmetic with. What is arthmetic? Arthmetic is what you do with numbers.” That’s how math starts off. Those are its assumptions – existance of numbers and arthmetic.
This makes me question science as a tool to understanding the unverse. It is such an adhoc, weak and approximate means. It isnt even consistent with itself. In fact Godel, one of the most influential logicians of the twentieth century, proved that any self-consistent recursive axiomatic system powerful enough to describe integer arithmetic will allow for “true” propositions about integers that can not be proven from the axioms. So science cannot be right about things simply because the logic system that it relies on is not consistent, is flawed. Science was always a quest for explainations, never the truth anyway.
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I totally agree with your opinion.
ur talking abt the best and purest part of CS … but i digress. will come back to read the whole post, just read the starting
have a good weekend,
prero.
Interesting post! By the way, I like your new page format! Well, to my point here. Logic is good, but definately not the be all-end all. Rationality must be balanced with intuition and just plain ol’ gfaith! The trick is to know which to use is all, and that’s the big one!
I do enjoy your post and debating with you about religion. Science came up with the Darwin theory without a bone to prove anything they decided to call it fact and teach it in schools. Where was the science there and the logic?
Indeed we have original sin, you don’t have to teach a two year old to grab their own toy and say mine, you have to teach them to share.
Organized religion takes care of the poor, the needy, the Aids victims etc.. all over the world because we care about human life. That is what the tithes and offerings are for.
While society needs scientists and the curious, look at what has happenned to our schools since we added Darwin and took out prayer and the ten commandments. I am in high school ministry and the kids are in a war zone every day at school under pressure of the worst kinds.
Organized religion brings them a family of people who love them and accept them exactly as they are not perfect just people.
By using mathmatics please explain how in the Old Testament there were 300 predictions on Who the Messiah would be and how He would come. Jesus performed all 300 miracles. That’s about 1 in a trillion and then some.
Good Job, Semantic! Doctor Logic (you can find him on the right side of my site)is always debating logic and metaphysics and the such in his site!
Semantic, I really enjoyed the way you have opened yourself up to truths and logic and philosophy.
Keep searching and with God’s help you will learn the truth!
And annonymous, I disagree with you on organized religion (to a certain point). Yes, organized religion is ‘supposed’ to take the money from the coffers to help those in need, but is that the case? I have seen organized religion in particular sects and found it to be more hungry for implements other than the welfare of the human race.
But as I have said prior, not all organized religion, just those who have become much like the church of Ephesus (left their first love), Pergamos (worship idols and their children have learned and commit fornication) Thyatira (ditto Pergamos), Sardis (forgotten), Laodiceans (sit on the fence).
Rev 2:1-29, Rev 3:1-22
Peg, thank you for your comment. Paul was writing to those churches to warn them of where they were straying and we have the same issues to this day. However, even though you know it is a personal relationship with Jesus and by His blood, grace we are saved, we are still to be a part of the Body of Christ. I am sorry you have had a bad experience with organized religion but God is of order not chaos.
Kristen
semantic overload,
I had to chime in on this post. :)
IMNSHO, logic is a tool for consistency checking. More broadly, mathematics is an enumeration of all self-consistent structures. If nature is self-consistent (e.g., events either happen or don’t happen, but not both), then nature has to be isomorphic to a mathematical system. In that case, the scientific method is the only way to study nature.
We create theories about the logical structure of nature and then seek to validate or falsify those theories empirically. Similarly, we create theories about the meaning of language propositions in each context in which they are used. We merely require that the uncertainty in our theories of physics and language be reducible to some small enough level to achieve a given task, e.g., to build a airplane, teach a concept, or cook from a recipe.
Thus, to give up on science one must sacrifice either logic or the consistency of nature. Yet, if you give these things up, you cannot know anything (at least not anything expressable as a logical proposition) nor make any predictions.
Let me put it another way. Without logic, “France is in Europe” and “France is not in Europe” could not be shown to be inconsistent. Thus, without logic, we could trust both with equal confidence. Without logic, there is no knowledge.
Finally, Gödel’s Incompleteness Theorem does not say that certain mathematical systems are inconsistent, but rather that they are incomplete if consistent. That is, there are truths in those systems that cannot be proven in a finite number of steps. For example, the Goldbach Conjecture (every even integer greater than 2 can be written as the sum of two primes) has never been proven, but has been true in all tested cases. The Conjecture may be an example of a proposition that cannot be proven, but which is true nonetheless. I really don’t see this as a problem for either logic or mathematics.
The axioms of logic simply reflect its consistency. If the universe is not consistent, then we can’t know anything about it anyway.
Q: If it is dark outside, and you get to your front door, and find you don’t have your keys, where do you search?
A: Under the street light. It is the only place you will possible find your keys in the dark.
that is why we have metaphysics.. :)
Inconsistency Queen of Science 1850-2007
When you introduce a falsehood in physical science you cannot remove the respective truth from your theory. Rather, explicit falsehood and implicit truth form a powerful couple able to produce virtually any result you need. The following quotation is based on formal logic and is an exaggeration with respect to physical theories; nevertheless it is quite instructive:
W. H. Newton-Smith, The Rationality of Science, Routledge, London, 1981, p. 229: “A theory ought to be internally consistent. The grounds for including this factor are a priori. For given a realist construal of theories, our concern is with verisimilitude, and if a theory is inconsistent it will contain every sentence of the language, as the following simple argument shows. Let ‘q’ be an arbitrary sentence of the language and suppose that the theory is inconsistent. This means that we can derive the sentence ‘p and not-p’. From this ‘p’ follows. And from ‘p’ it follows that ‘p or q’ (if ‘p’ is true then ‘p or q’ will be true no matter whether ‘q’ is true or not). Equally, it follows from ‘p and not-p’ that ‘not-p’. But ‘not-p’ together with ‘p or q’ entails ‘q’. Thus once we admit an inconsistency into our theory we have to admit everything. And no theory of verisimilitude would be acceptable that did not give the lowest degree of verisimilitude to a theory which contained each sentence of the theory’s language and its negation.”
As soon as you introduce the magic contradictory couple rationality starts disappearing and you do not need valid arguments anymore. Invalid arguments increase the power of your theory additionally: whether “Reversible heat engines working between the same two temperatures have the same efficiency” does or does not really follow from “Heat never flows spontaneously from cold to hot” is a question brothers scientists would never ask.
The falsehood enables you to demonstrate miracles and become a divinity; the respective truth enables you to predict verifiable results. Einstein’s false principle of constancy of the speed of light produces miracles such as time dilation, length contraction, Minkowski’s space-time, time travel etc. Einstein’s (rather, Newton’s) true principle of variability of the speed of light gives correct predictions such as the gravitational redshift factor.
Pentcho Valev
pvalev@yahoo.com