Is logic a subset of math or vice versa?

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This topic contains 24 replies, has 6 voices, and was last updated by  Unseen 5 days, 2 hours ago.

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  • #25083

    Unseen
    Participant

    To me, it’s obvious: Math is a subset of logic. You can take the math out of logic and informal/verbal fallacies remain, but you can’t take the logic out of math or you are left with nothing at all.

    • This topic was modified 1 week, 4 days ago by  Unseen.
    #25087

    _Robert_
    Participant

    Logic may end up being the result of quantum level activity in the brain… LOL…but yes in electronics mathematical calculations are the result of logic operation. For example binary multiplication by 2 is just a logical bit shift.

    0001 = 1, 0010 = 2, 0100 =4, 1000 = 8

     

    #25088

    Simon Paynton
    Participant

    You can have logic without math, but not math without logic.

    #25089

    Simon Paynton
    Participant

    Some people say that “moral facts” have the same status as logic – that they somehow exist in some external timeless fashion.  But I think that logic is grounded in the physical world, whereas morality is grounded in the human world, therefore there are no moral facts in the way that logic and math have facts.  Any moral “facts” exist in the human world, or living world at best.

    #25091

    PopeBeanie
    Moderator

    Along the same lines as what Simon’s saying, logic and math are human constructs, yet worthy of permanent usefulness because of how they can be used to help us understand the real world around us. (The “real world” being everything that exists, whether or not we exist. We merely invent common language and methods to understand the real world, and interact with it in self-serving ways.)

    Meanwhile yeah, logic is the basically lean-rule (and sometimes allowably presumptive) super-set that enables the more detailed and evolving, complex rules of math.

    #25114

    Simon Paynton
    Participant

    logic and math are human constructs

    Surely they’re abstractions rather than constructs.  I think that the roots of logic are an abstraction of physical logic.

    #25115

    Unseen
    Participant

    I think that logic is grounded in the physical world

    No, it’s grounded in the need of the human mind for things to make sense, and to think in a manner resulting in reliable and repeatable conclusions.

    #25116

    Simon Paynton
    Participant

    Yes, but the physical world has physical logic, and I think the basic laws of logic are an abstraction of that physical logic.

    #25143

    Unseen
    Participant

    Yes, but the physical world has physical logic, and I think the basic laws of logic are an abstraction of that physical logic.

    But the physical world embraces the subatomic, which isn’t logical at all by everyday standards.

    #25144

    Simon Paynton
    Participant

    the physical world

    The world of physical objects which is on a human scale, at least.

    #25145

    Simon Paynton
    Participant

    Is it possible that in other universes, the laws of logic are different?  Does everything have to have logic?  I am sure that the quantum world has a logic of its own.  Morality certainly does.

    #25147

    Simon Paynton
    Participant

    Would God have to have a logic of His own – to be internally consistent?  Or would God exist beyond of any logic?

    Existence necessarily implies reality, and reality is logical.  But since in what sense does logic exist?  As the laws of logic?  As an arrangements of logical entities and the relationships between them?

    My point is, God would not have to have a “real” existence in the sense that we ourselves understand “real” – and I claim that logic itself has the status of an abstract rather than solid existence.  However, the laws of logic apply to reality, according to the physical context and situation.

    #25148

    Simon Paynton
    Participant

    People who are moral realists say that the laws of morality (“it is wrong to murder” etc.) are a part of the fabric of the physical universe.  On the one hand, this appears ludicrous.  On the other, if morality is evolutionary in nature (i.e. in logic), which it is, then evolution is situated within the fabric of the physical universe.  Therefore, there is a link from one to the other.

    It must be true that the physical world influences everything we do.

    #25149

    Davis
    Participant

    My point is, God would not have to have a “real” existence in the sense that we ourselves understand “real”

    There are a lot of problems here. The biggest one being: assigning God qualities without any justification. You can give “God” or “the Easter Bunny” or “Tree spirits” whatever qualities you want. That’s why humans have been so creative over the centuries because they’ve created a magical realm where the laws of physics don’t apply and where weird/impossible/mysterious qualities abound. For example “God is above ethical judgement and sees not actions but a part of the human soul that defies what we would consider true morality”. And yet, I just made that up. And this argument is as convincing as “God would not have to have a “real” existence in the sense that we ourselves understand “real”. All these arguments say is: I can define some mysterious being in such a way where I give it qualities which we can never understand or even argue against (let alone prove). I keep reading this and asking myself what? why? if we didn’t take God’s existence for granted…how do you arrive at this:

    God would not have to have a “real” existence in the sense that we ourselves understand “real”

    How is this an obvious logical sentence? How would you defend this argument as opposed to the argument “God would have to have a “real existence” in the sense that we ourselves understand as “real”? And please don’t refer to fictional qualities of a being man has invented. Anyone can invent anything and give them whatever fantastical properties they like. If we had never heard of God before, how would you argue to people about God’s realness?

    #25150

    Davis
    Participant

    On the other, if morality is evolutionary in nature (i.e. in logic), which it is, then evolution is situated within the fabric of the physical universe. Therefore, there is a link from one to the other.

    I can’t really figure this out. Fabric of the universe…what exactly do you mean by that? Especially “situated within the fabric of the physical universe”? And how is evolution in nature logical? I don’t get it. Are you applying some kind of intelligence to evolution? From this point of view I see that absolutely all phenomena is logical as they all follow the rules of physics (therefore logic in your argument)…so what makes evolution a remarkable one?

    In fact, absolutely everything in the universe is situated within the fabric of the physical universe. There’s nothing in the universe that isn’t (nor anything that isn’t logical). So I don’t really how this argument tells us anything. A Beatle’s song is situated in the fabric of the universe as are cosmic rays, the accretion of sediment in river beds and the methane oceans of Titan. Those are all logical. I don’t see a difference between evolution and the build up of sand in a river. So clearly there is a connection between a Beatle’s song and the universe. Is evolution somehow more logical than the formation of a methane lake on Titan?

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