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06.05.2016

How logical are you really? – Part 1: Introduction

How logical are you really? And what does logic really mean? Is it the answer to everything? Here is a nice little quote by Einstein:

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

What the hell does he mean? Well, I have no idea what he meant – whatever that means. But here’s my take. As a programmer, the answer is straight-forward to me. To create software, I must know how the underlying system works or at least, the options it offers me for controlling it. This is, in a way, a very logical endeavor insofar as I am provided with rules under which the underlying system operates. If I follow these rules – like syntax – and make use of the available commands in a clever way, I can predictably create decent software. If I were to write ecco instead of echo, the system would report a fatal error and that would be that. Where does logic come into place? Well, to me, logic is a system by which you can use and combine axioms in order to come to new conclusions. This is a very precise art – if you will – insofar as you can easily verify the veracity of the conclusion by verifying the validity of the deduction.

Let’s take an example:

Axiom 1: All sheep are white.

Axiom 2: I have a sheep.

Conclusion: I have a white sheep.

This is the core of logic in my eyes. If axiom 1 and 2 are assumed to be certainly correct, my formed conclusion is correct as well – with absolute certainty. With logic, you can form conclusions from axioms with mathematical precision.

Here’s another example, from programming:

Axiom 1: With the command echo, you can display the result of any mathematical expression.

Axiom 2: 1 + 2 is a mathematical expression.

Conclusion: With the command echo, I can display the result of the mathematical expression 1 + 2.

This works well for programming because the environment is manufactured to be predictable and follow specified rules. If I follow those rules and know them well, I can predict the outcome with absolute certainty. I can theoretically write hundreds of lines of code without testing it even once, just to have it do exactly what I expect in the end.

Now, if I were to work with sheep in a computer program, I would first be required to define the term sheep. I would typically have to define it in terms of the memory I want to allocate for each sheep. To do this, I basically define all the variables – or properties – a sheep is supposed to have. For example, one property could be color. I could decide to store the color of a sheep as a number, a string of characters or even some more complex value – like a composite color that itself consists of the variables redblue and green.

By doing these definitions, I decide the kinds of properties a sheep can possibly have. I also decide which kinds of values each of these properties can possibly carry and also whether they can be changed or not.

At this point, I could decide to fix the color of each sheep to the string of characters white and thus make it impossible to createsheep that has any other color than white. Thus, I could say with certainty that each sheep has the color white.

Of course, a computer has no idea what either a sheep or a color is. If a computer happens to display a white color upon giving such a command, it will only be able to do this if somebody gave it specific instructions on what to do if a user enters a command to display the color white. For instance, your everyday computer will – slightly simplified of course – send equal amounts of the composite colors red, green and blue to your monitor to display whiteness. This still does not mean that the computer understands what whiteness is or how it looks or feels or whether it carries any other meaning than to do B after A happens. Any other meaning than to send an electrical current if logical conditions are met.

Now, if you were to use that program I created, you could say with confidence that every sheep is white. Alas, the sheep in this logical program have nothing to do with whatever you call sheep in the real world. In this logical program, to the computer, sheep would be nothing more than some allocated memory with some – to the computer – random content.

If you wanted to use my program to catalogue and represent real sheep, you would have to ditch it as soon as you encountered your first sheep that is not white. Or you would have to ask me to change the program.

Outside of the computer, of course, the logical quickly becomes insufficient to represent reality. Take my example with the white sheep from above. The more you start to question these axioms against reality, the more vague and imprecise they become. What is a sheep? What makes a sheep a sheep? And what is whiteness? Is a sheep still white if it is somewhat grey? What about the shades in between? And how could you even say that all sheep are white unless you have seen all sheep that ever existed?

And if you were to encounter a black sheep, would you say that it is a sheep that is black or would you call it another thing altogether, for example blacksheep? That would solve the problem of course. You could say that all sheep are white because all others are simply not sheep.

The world of labels and categories is man-made and they are usually assigned with practical concerns in mind. Different scienctific or economical disciplines use different categorizations. Thus you may still call a black sheep sheep, because – for example – it can still fuck with normal sheep.

But reality does not really care about these labels. Shit is fluid. Look at the sexes. In our minds, there is basically just men and women. Penis or vagina. But these are just labels we assign to something we observe. No penis is exactly the same as another. No vagina is. And then there are the rare confusing cases where it is not exactly clear which sex it is – or the ones that do not identify with the sex they are born with.

Now I am not advocating for the idea that it is oppressive to assign labels. The mind is what it is and it simply works this way. If you feel that you want to overcome labels, the reasonable way is not to create a new label for whatever specific thing you think you are and demand everyone to adapt to your new labeling. The problem is that you want to label yourself something and then identify with that label. You are creating this pain for yourself.

Labels serve a purpose. They make communication easy. If one always wanted to call each thing exactly what it is, one could not call it anything at all. One would just look at it and say: It is what it is. And as far as I understand it, this is one key aspect of meditation. I love it.

The key is not to make the mind fair, to make labels super precise. The key is, I think, to realize that labels are not the thing they describe, and to use them with this caveat in the back of your head. To see a man and call him a man without seeing him as nothing more than a generic instance of the label man.

Labels are tools. They are not precise by nature. And this is the big challenge for logic. You can play around with labels and axioms and make logically sound deductions. But a logically sound deduction does not take into account the imprecision of the underlying axioms insofar as they relate to reality.

And at this point I think it becomes clearer what Albert Einstein might have meant with the quote that I cited above. Within a man-made system like mathematics and logic, absolute certainty can exist. But reality is not man-made and reality’s underlying rules can only be approximated through empirical means – that is, observation.

To round this up, here’s another mindfuck for your pleasure: Have you understood gravity just because you can mathematically predict it? Does it become less magical and crazy if we have words and numbers for it? Or is it a mystery that can best be appreciated in the absence of labels? Can you understand a sheep by classifying it? Or by simply seeing it?

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  • Smokingjacket

    Axiom 1: All sheep are white.

    Axiom 2: I have a sheep.

    Conclusion: I have a white sheep.

    An alien spaceship lands in the woods outside Munich. You’re out strolling when you encounter the strange inhabitants who are apparently stopping off as they’ve been assigned the important task of capturing a sheep to bring back to their masters in Sirius B system. They tell you all of this telepathically of course….and you jump and hop around the with joy telling them you have one just in the next field.

    You and your two new alien friends approach the wall and you shout “there! there! this what your’re after my friends” as you point at two docile four legged white sheep chewing peacefully away……the aliens look startled and perplexed which you cannot understand until they say to you.

    Axiom 1: All sheep are black.

    Axiom 2: I have a sheep.

    Therefore I have a black sheep.

    You then in horror look at the picture they show you of sheep from they’re system. Their sheep are indeed black, 4 legged, but exactly resemble canines on our planet.

    You all scratch your collective heads together and wonder is not all logic, even logic derived from a non-human perspective related back merely to the language we use to describe our own unique worlds? In essence, would not two different species fail to understand each other, not because of logic, but rather despite it, right within the language we use when we logically think our world ought to be a certain way?

    • Haha, nice one. Not sure if I understand your last paragraph correctly, but yeah, logic can play around with ‘truths’. But truths are only as valid as your usage of language is uncannily precise and pedantic – which is impractical in everyday life. For everyday life, our usage of the term sheep is perfectly satusfactory – despite not being 100 % ‘logical’. Even with the aliens, you would probably quickly decide to make a distinction between earthsheep and uranussheep. With more encounters, inconsistency would come into play and then likely some interplanetary commission would introduce official scientific names. The normal folks, of course, would keep calling them simply sheep and say: What do I care for those aliens? In fact, there are, across Englishspeaking countries, various species with the same names. The only way to distinguish them through language is to use scientific vocabukary or perhaps mention of the country you are referring to.

      • Smokingjacket

        Logic is simply the approximation of predictable rules that the human mind uses in order to navigate a path through a reality that will always be intrinsically alien to it.