Is logic a subset of math or vice versa?
January 12, 2019 at 4:53 am #25083
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.
January 12, 2019 at 2:17 pm #25087
- This topic was modified 2 months, 1 week ago by Unseen.
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 = 8January 12, 2019 at 4:58 pm #25088
You can have logic without math, but not math without logic.January 12, 2019 at 9:41 pm #25089
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.January 12, 2019 at 11:37 pm #25091
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.January 14, 2019 at 2:02 pm #25114
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.January 14, 2019 at 5:03 pm #25115
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.January 14, 2019 at 5:24 pm #25116
Yes, but the physical world has physical logic, and I think the basic laws of logic are an abstraction of that physical logic.January 16, 2019 at 6:54 pm #25143
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.January 16, 2019 at 6:59 pm #25144
the physical world
The world of physical objects which is on a human scale, at least.January 16, 2019 at 7:04 pm #25145
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.January 16, 2019 at 8:40 pm #25147
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.January 16, 2019 at 8:50 pm #25148
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.January 16, 2019 at 9:13 pm #25149
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?January 16, 2019 at 9:26 pm #25150
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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