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Is logic ultimately constructed on faith?

  1. Mar 25, 2008 #1
    To me, there is no doubt that logic cannot be constructed if it isn't initiated by a set of unprovable 'rules', axioms, to be more precise. For example, I can't prove that a statement is either true or false under any circumstances, but I do assume this is consistently true - if a statement is not false, it is necessarily true and vice-versa; there is no 'other' state. Hence one might say that logic is a product of some sort of faith, faith in the veracity of base principles. What is interesting is that logic is constructed, but also self-constructed. Namely, it possesses self-identification; it can be expanded on the basis of its own postulates. We could say logic starts as a set of rules and can then use itself to grow larger - a curious machinery. But this is only my own, isolated, analysis; I still have to develop it. I'd like to hear the opinions of other members of this forum. Are there others who are engaged in such a line of thought?
  2. jcsd
  3. Mar 25, 2008 #2
    First you should define what you mean by faith. The word is used in many contexts, some more precise than others.
    Second, you should give examples of axioms which logic is based on.

    Faith by any standard definition is: strong belief regardless of evidence.
    Logical systems are based on premises, but I'm not sure you're on such solid ground claiming logic itself is. We have developed logic based on observation, I think it would be very difficult to separate 'logic' from the human context.
  4. Mar 26, 2008 #3
    Logic is little more than language to me, the axioms in question being common agreement on meaning. For example, when I say A AND B, it means that you have A and you also have B, and if you agree with this definition of "AND" then we can communicate. If I say A IMPLIES B then it means that A requires B, so that if you don't have B then you cannot have A either, and if you agree with this definition of "IMPLIES" then we can communicate. And so on. There is no proof of these definitions, only common agreement about what the terms mean. Once you have common agreement on these terms then you can discuss intelligently and reach the same conclusions from the same premises. No magic or faith is necessary, only agreement on language.
  5. Mar 26, 2008 #4
    We can easily check some evidence for the validity of logic. For example, if logic is valid then a calculator can be designed such that, when used to add two numbers, it will give the correct sum, regardless of the two numbers.
  6. Mar 26, 2008 #5
    I agree with you. Logic is ultimately constructed on faith. Ultimately, when you analyze human society, there is nothing to be logical over. People are logical over an icon of faith upon something...whether it is the belief that god is inexistant or anything else.
    Last edited: Mar 26, 2008
  7. Mar 26, 2008 #6
    Logic is the "science of non-empirical reasoning"
    Reasoning is a mental activity called "inferring".
    To infer is to draw conclusions from true premises (e.g., data, information, facts).
    Logical reasoning always results in drawing non-contradictory conclusions from true premises.
    It is the task of logic to distinquish correct reasoning from incorrect reasoning.

    There are two ways to infer, via inductive logic or deductive logic.
    Inductive logic draws probable though fallible conclusions from true premises.
    Deductive logic results when truth of premises necessitates the truth of the conclusion.

    The truth of a premise used in logic is never based on faith, since faith does not require that one establish evidence of (data, information, facts).
  8. Apr 1, 2008 #7
    Logic is, of nessecity, predicated on a faith in the basic tenets of logic. To claim that logic can be proven true because we can either a) observe its working or b) create machines which demonstrate its working, is to use logic, specifically inductive reasoning, to demonstrate the validity of logic. Also, logic assumes the uniformity of nature, a concept which cannot be proven, but merely inferred, again based on the tenets of logic itself. At some point, one must accept the foundations of logic as true, without being able to defend their truth.
  9. Apr 1, 2008 #8
    You're really abusing a lot of well defined concepts.

    'Inductive reasoning' is based on the assumption that there is consistency in the universe. We certainly can't prove that this is so, but we can observe quite a lot of consistency, and that IS evidence for further consistency. Evidence is not proof.

    Faith is something completely indifferent to evidence and proof.
    It is 'strong belief' without the need for, or in spite of the evidence, even in spite of proof to the contrary.

    The fact something can't be proven, doesn't mean one requires faith to accept it is a reasonable assumption. The fact something can't be proven, doesn't mean there isn't quite a lot of evidence for it. The fact someone accepts something as true, because it reasonably appears to be so, doesn't mean they have faith in it.

    If all of a sudden the weight of evidence points in a different direction, then it would take faith to still believe the original direction, but believing what is supported by evidence, requires no faith.
  10. Apr 1, 2008 #9
    To the contrary you are using the very method of inductive reasoning to demonstrate inductive reasoning works. Hence, before you ever start considering its validity you have already accepted it, on faith. I am not saying Logic doesn't work, merely that one must accept its most basic tenets with no evidence whatsoever, because they cannot be evidenced. A perfect example is this: Prove 2+2=4, show your work. It cannot be done, because it is an axiomatic statement. We merely accept that 2+2=4.
  11. Apr 1, 2008 #10
    Again, you are abusing definitions. Simple belief is not faith.
    Inductive reasoning appears to work quite well. Sometimes it doesn't.
    I don't have faith that it will, it just seems like a good assumption to make. Sometimes that ends badly. I don't claim induction always works or that it must work. No one does.
    The only truth value in that statement is whether it describes reality or not. If it describes reality, then it is true, by definition. Math is a generalization based on observation. Its a rule system.
    3-4=2 is true if it describes reality, it doesn't. It is false, by definition.
    Last edited: Apr 1, 2008
  12. Apr 1, 2008 #11
    I am not abusing definititions. I never said belief was faith. I said you use inductive reasoning to support inductive reasoning. If one says, I have seen many white swans and never seen a black swan, I therefore conclude that all swans are white, he is using induction. If you say, induction has worked well for me in the past, and has rarely or never failed me, I therefore believe induction to be a valid reasoning system, you are also using induction. The problem is, the only proof of induction lies in induction. Therefore, to escape the circular logic, one must at some point assert an axiomatic statement. This statement will, of nessecity, be based on no evidence beyond its assertion.

    A math equation can never describe reality. Simpyl put show me a "real life" exampel of 2+2=4. You can't because 2's and 4's are not found in nature. Objects are found in nature to which we ascribe symbols. Having created a self consistent language for manipulating those symbols we impose that language on the natural order and it works. But your 2 could jsut as easily have been a 010 or a * or any other convenient symbol so long as the system is self consistent.
  13. Apr 2, 2008 #12
    No, the problem is there is 'no proof' at all with regards to induction. Inductive reasoning doesn't prove anything, not even itself. Inductive reasoning is useful, nothing more. You may have faith in it, you may believe it works even when it doesn't, but induction doesn't demand faith. All it demands is that one accept an assumption, even tentatively. People do this all the time without believing that thing is true.
    Sure it can, just not with complete accuracy.... because math is, by definition, a generalization. To expect math to be able to describe reality in its entirety is simply misundertanding math.

    To describe something in its entirety, you would literally have to recreate it. I see no reason to do that, and math is useful mainly because its a very precise form of 'shorthand'.
  14. Apr 2, 2008 #13
    So to believe in induction, without proof, demands an act of faith, no matter how tentative.
  15. Apr 2, 2008 #14
    No it doesn't.


    You are equivocating.

    If I let a ball go from my hand a thousand times and every time it falls to the ground, I can use that as evidence that balls fall to the ground when I let them go.

    It is however induction.
    Last edited: Apr 2, 2008
  16. Apr 2, 2008 #15
    You just committed the fallacy of affirming the consequent while trying to defend logic.

    But in response to the OP, the only faith that you really need to have to affirm logic is faith in the principle of non-contradiction. Faith in predicate calculus wouldn’t hurt, but even that probably isn’t necessary.
  17. Apr 2, 2008 #16
    You are completely correct to say the induction isn't proof its evidence. We are arguing over the meaning of the word evidence it seems. I have been using proof and evidence interchangeable which is my mistake. Let me rephrase my point. The only evidence one can find for logic depends on induction. Therefore, without assuming the validity of inductive reasoning, we can have no evidence to support logic.

    "Faith is something completely indifferent to evidence and proof.
    It is 'strong belief' without the need for, or in spite of the evidenc"

    Since all evidence for logic depends on induction, one must start from a point of belief int he absence of evidence. This is not nessecarily a bad thing, and faith is not a dirty word. Nor does it mean I reject logic or its implications. It just means that one must accept certain axioms based on faith. Or if you prefer Descartes term, "The Light of Reason".
  18. Apr 2, 2008 #17
    No. One starts with observation. From the evidence of observation, one can see that induction has worked in the past. Whether it will continue to work is an open question.

    We know however, that induction has worked. Induction works. There is evidence that induction works. And we know for a fact that it has worked often, and for a long time.
    There is evidence that induction works. Since it has worked for a long time, it is a reasonable assumption, its probable, it seems likely, based on the evidence of the past, that it will continue. No proof, mind you.

    The problem of induction is not about what is likely, or probable. Its not about not being able to make a decision based on the evidence of the past. The problem of induction is about 'certainty'. Its about skepticism in the face of that uncertainty.

    And if you refer to Descartes, you probably know, there were people being burned at the stake in his time for heresy. Faith is pretending ignorance is a virtue.
    Last edited: Apr 3, 2008
  19. Apr 2, 2008 #18
    Induction is the argument that because something has happened in the past it is probable to continue happening. That is what inductive reasoning means. You are using inductive reason to support its validity. When you say induction has worked and probably will, thats i inductive reasoning. It is totally valid reasoning, completely logical. And thats the point.There is no point from outside of logic which is a starting point for an examination of logic.

    Your statement about Descartes time period is as meaningless as me refuting Relativity by telling you that in Einstein's day they burned people for being Jewish.

    Your definition of faith is arrogant, ignorant, and offensive.
  20. Apr 2, 2008 #19

    Math Is Hard

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    None of the above. You should not attack people who are trying to help you by pointing out problems in your argument. In fact, you should thank them.
  21. Apr 3, 2008 #20
    LOL! na logic would dictate that it is not constructed on faith,
    Which came first the chicken or the egg?
    1.Chicken's come from egg's=True
    2.Egg's come from chicken's=True

    So by these two things we know that are true, and do not need faith to know that there true.

    The only logical answers to which came first a chicken or an egg, would have to be the chicken, because the chicken most have not allways laid egg's because #1&2 are true.

    3.a chicken didnt allways lay egg's because #1&2 and true=true

    so that would logicaly mean that at one point a chicken had the reproduction of a (A)-sexual, which then logicaly at one point it's DNA must of had a genitical mutation, for a chicken to lay egg's. And that would be logic thats not ultimately constructed on faith.

    But #3&4&5 would be false if you belived in >.< i wont dare to say it I,m sure everyone here know's that answer...
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