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How do we derive logic?

metainfinity
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Posted 07/26/09 - 12:06 AM: Subject: How do we derive logic?	#1
A friend of mine brought up the idea that we derive logic from observation. He further went on to say that since our observation thus far is limited, we don't REALLY know whether something in the future will contradict our current logic. Aside from the fact that we defined certain fundamental principles as law(perhaps it's irrelevant), are there any holes in this reasoning? I mean, it is an appeal to absolute knowledge, but it seems perfectly valid. So do we derive logic from observation? How do you counter this "appeal to the absolute" in a rational discussion?

Kamerynn
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Posted 07/26/09 - 04:58 AM:	#2
"Logic takes care of itself; all we have to do is to look and see how it does it." "Logic is not a body of doctrine, but a mirror-image of the world. Logic is transcendental." -- Wittgenstein
When I'm working on a problem, I never think about beauty. I think only how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong. -- R. Buckminster Fuller

Postmodern Beatnik
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Posted 07/26/09 - 07:15 AM:	#3
To add to the quotes, here's A. J. Ayer's take on it: "The principles of logic and mathematics are true simply because we never allow them to be anything else." Let's take the principle of non-contradiction ("it is not the case that something can be both A and not-A in the same way at the same time") and the notion of a square circle ("something which has all the properties of a square and all the properties of a circle"). Nothing we experience could ever be a square circle. The concepts are such that we simply would not be willing to recognize anything as being both a square and a circle. Your friend seems to think that a future experience might somehow "blow our mind" in a way that causes us to reconsider this, but it seems much more likely (following Ayer) that we would simply re-evaluate the case or reconfigure our concepts until it made sense according to our a priori rules. We'd move everything else around to conform to our rules, because that's the way we think. This might seem odd, unjustified, or overly convenient, but there's a very simple reason for it: linguistic representations of the world are human inventions that facilitate understanding and communication, thus we have the authority to make language submit to logic. Our descriptions don't change anything about what's being described (unless you wish to consider how a thing is described to be one of its properties, of course). What they do is allow us to think about those things and how they relate to ourselves, to other things, and to the world in general. Logic is central to this task, thus why it would take something very serious to cause revision in its rules. But this does not yet address the question of whether we derived logic from observation to begin with. To answer this, we must consider whether or not we could ever find such rules out in the world. It's true that we will see them followed, but it is not the case that we empirically discover new rules of logic or exceptions to the existing rules. Rather, our observations may cause us to reflect on what would have been obvious had we thought about it previously. Even if empirical observations led us to revise our logical rules, it would only be because those observations had pointed us to a flaw in our previous reasoning. The two are connected in various ways, then, to be sure. But it doesn't seem they are connected in such a way as to validate the claim that we derive logic from observation. I knew there were no married bachelors long before I was aware of how many people there are in the world -- and I know it today despite the fact that I have not empirically investigated many of those people at all. Finally, it should not go unmentioned that some believe a revision of classical logic is warranted. Paradoxes, including those that supposedly arise due to quantum mechanics, have been offered as the reason, and new logics have been suggested as a result. This gets us into controversial territory, but I think two things are worth considering here: (1) Quantum mechanics in its current form is by no means a given. It has yet to be reconciled with general relativity, and how the findings supporting each will be brought together is unknown. Whatever paradoxes seem to exist now may evaporate under such a model -- though they may also remain. It is certainly worth looking into the problem in advance, even if it turns out to be purely academic. But it would be inappropriate to claim that classical logic is decidedly in trouble at this time. (2) While this is not always made clear by their practitioners (and may not always be clear to them), non-classical logics often have a different scope than classical logic. Quantum logic, for example, is about what we can say given our epistemic circumstances, not about what must be the case. That we cannot empirically support distributivity in quantum logic does not mean that it does not obtain. In other words, it doesn't change what's true, it merely means that accepting certain principles limits what we can claim to know.
"The key to being a good manager is keeping the people who hate me away from those who are still undecided." --Casey Stengel

dirksen7
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Posted 07/26/09 - 12:13 PM:	#4
It´s a difficult question, but even though there is something wrong with this question. The thesis is that we derrive logic from our observation - meaning hopefully sense experience in the end. But is this so? Or is it the other way around. That we actually observ things in a mathematical view - meaning that because of our being-in-the-world (to use a concept from Heidegger) we look at things in a special way. When you hear a car go by, you don´t hear a sound - and then afterwards conclude that this is a car. No you hear it as a car. That´s why we look at patterns in our environment as mathematical. (Well the argument is a lot longer - but read Being and time or better the german version Sein und Zeit.) Logic is and will always be logic - meaning there will always be contradictions like a=not-a or tautologies a=a, but this is because logic speaks it own language (as Wittgenstein find out in philosophical investigations)

MagicalTree
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Posted 07/28/09 - 03:43 PM:	#5
Kamerynn wrote: "Logic takes care of itself; all we have to do is to look and see how it does it." I like this quote because it pretty much sums up any further discussions on logic. Humans as a whole decide what is logical and what isn't logical. We have to agree at a certain point on the most basic things, or else we wouldn't be able to function at all. Every mathematical concept is seen as logical (unless being argued), because humans have created this system to attune with our own natural perception of the universe.
"Except our own thoughts, there is nothing absolutely in our power." -Rene Descartes

Doug Shaver
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Posted 08/03/09 - 05:58 AM:	#6
metainfinity wrote: So do we derive logic from observation? No, we derive it from necessity. We can't think without it.

Jurist
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Posted 08/04/09 - 09:05 AM:	#7
Doug Shaver wrote: No, we derive it from necessity. We can't think without it. I just sat here for 30 seconds and thought of a sunny beach.
Just because I'm a lawyer doesn't mean I'm always wrong. -- Me

Doug Shaver
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Posted 08/07/09 - 12:47 PM:	#8
Jurist wrote: I just sat here for 30 seconds and thought of a sunny beach. What did you think about that beach? Whatever your response to that question, how do you make sense of it if what you say could be both truth and false?

aufbau87
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Posted 08/07/09 - 06:22 PM:	#9
metainfinity wrote: A friend of mine brought up the idea that we derive logic from observation. He further went on to say that since our observation thus far is limited, we don't REALLY know whether something in the future will contradict our current logic. Aside from the fact that we defined certain fundamental principles as law(perhaps it's irrelevant), are there any holes in this reasoning? I mean, it is an appeal to absolute knowledge, but it seems perfectly valid. So do we derive logic from observation? How do you counter this "appeal to the absolute" in a rational discussion? To ourselves, learning logic, observation plays a key role. But aside from this descriptive epistemological point, if someone's refutes something like 'Pv~P', then they mean something else than we do by 'v' and '~', and the arrangement of the signs in the sentence (its syntax). We change the meanings of the terms, not the laws' truth-values. I don't know if it significant to ask 'where do the laws derive from?' just as it would be ludicrous to ask 'What events took place before time existed?' Perhaps it is significant, but an answer other than 'none' or 'nothing' would be self-contradictory, at best. Ask your friend this: do we TEST the laws of logic? Our understanding of testability comes from obviously empirical theories, e.g. Einstein's general theory of relativity. How could we even, in principle, devise a test against the law of excluded middle in a similar, if not more obvious, way? At least with our exemplar cases of testable assertions (or empirically testable problems), it is known what the world would be like if they (or either of the rival hypotheses in question) were true. What would the world be like if 'Pv~P' were false? What observations would we expect to transpire?

deepthought
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Posted 08/08/09 - 08:31 PM:	#10
metainfinity wrote: A friend of mine brought up the idea that we derive logic from observation. He further went on to say that since our observation thus far is limited, we don't REALLY know whether something in the future will contradict our current logic. Aside from the fact that we defined certain fundamental principles as law(perhaps it's irrelevant), are there any holes in this reasoning? I mean, it is an appeal to absolute knowledge, but it seems perfectly valid. So do we derive logic from observation? How do you counter this "appeal to the absolute" in a rational discussion? I would suggest to your friend that we derive logic from perceptions that are inherently flawed by the imperfection of our understanding.

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