Thursday, May 6, 2010


To Understand, to Have Understanding, to Know

What does it mean when we say "I understand"?

Like everybody else - or at least I think everybody else - I used to take it for granted. I thought that I knew what it meant.

Now that I'm getting to know more about what goes on in whatever it is I call my mind, I'm pretty sure I was wrong.

Here's what I've figured out so far.


First of all, we seem to think that we think.

Some of us think we think "rationally", but most of us have no idea what that actually means.

It seems to me that we - as a species - have been working at understanding what 'thinking' is for a very long time. At least since the Greek philosophers and the Chinese sages. Probably longer than that - at least 2,500 years or more.

Somehow we've latched on to 'logic' as 'real thinking' and everything else as some sort of minor annoyance.

I don't agree that 'logic' and 'rational thinking' are the real kings and queens of all 'mental processes' and that the rest of whatever goes on in our minds is at most second rate.

And here's why:

Logic - a Necessary Digression

We've studied the hell out of Logic. We've formalized it and we know what it is. Well, those of us who've taken the trouble to study it a little know what it is.

First, what it isn't.

Logic is not sticking 'because' in the middle of sentences. It's not making up 'reasons' for things. And it's not asking and then answering 'why'?

Logic is a rigorous, formal method of evaluating the Truth or Falseness of sentences which are constructed according to specific rules.

First of all, what is a sentence?

In 'Logic' it's a string of symbols consisting of 'propositions' and 'logical connectives'. The 'propositions' are just blobs or words that can have any structure and may or may not mean anything. For the logician, the only thing that matters is that they are either True or False. In fact, for the logician, it doesn't matter at all what True and False mean - only that they are different and only that there are only two possibilities.

The 'logical connectives' are special words which can be used to 'connect' two propositions or sentences. When stuck in between two of these things, the three of them form a new 'sentence'. That 'sentence' is either True or False and the value strictly depends on (1) the values of the two things on each side of the connective and (2) the rules of the connective.

Let's get formal:
  • P, Q, and R are all propositions or sentences - which means they have truth values.
  • * AND, OR, and IMPLIES are connectives
  • Let's add in NOT, which isn't a connective, but it's useful. It's 'logical negation' - which means that if P is True, thenNOT P is False - and vice versa.
So we build sentences by writing P AND Q, Q OR R, P IMPLIES R and things like that. We evaluate these sentences according to the rules:
  • if P and Q are both True, then P AND Q is True, otherwise it's False
  • if P and Q are both False, then P OR Q is False, otherwise it's True
  • if P is True and Q is True or if P is False, then P IMPLIES Q is True, otherwise it's False
  • if P is True, then NOT P is False and if P is False, then NOT P is True.
If we add in some Parentheses, we can get really wild and use sentences for propositions and write things like:


We could also write the same thing without the parentheses, but we wouldn't know what it means without using some special rules. Why? Because we wouldn't know if
means (P AND (Q OR (NOT R)) ) OR (S IMPLIES Z) or the thing I wrote above.

But that's for really studying 'Propositional Logic' - which you can find in a book. For now, it's not really important.

The important thing is this:

The Truth of the sentence depends completely on the Truth of the basic propositions - that is, the propositions which don't contain any 'logical connectives'. These are the 'Axioms'. It's what you start from.

Everything you write using Logic can be traced back to and completely depends on the Axioms - the Propositions you write down and start from.

This means that Logic only transforms the shape of the original propositions. It can't add anything new.

Working with Logic is like walking around a house and looking at it from different sides. No matter what you do, it's still the same house. Nothing is ever added or subtracted from what it was to start with.

There's more Logic - for example, First Order logic adds 'quantifiers' to the Propositional Logic we've just outline. It adds exactly two: the Universal Quantifier and the Existential Quantifier.

This lets us write richer sentences because we can then write things like: All P is True and At Least One P is True.

Having quantifiers makes is easy to tell when someone is saying something stupid. For example, if somebody says "All cats are mean", you can tell they don't know what they are talking about if you've ever met a cat that wasn't. So you object, and then they say you're being picky and that they really meant "most cats are mean". That is supposed to make it better, but it really
means that they don't really know, but want to think of it that way. So, it's better to keep your mouth shut and just know that they say stupid things.

Also, it helps tell what you can know for sure. For example, when somebody says "you can't do that", but you think it would be a good idea to "do that", all you need to do to prove that
it's possible to "do that" is to find one example where it worked. Then you can ignore them. This is a great help when starting a business, because most everyone will tell you it "won't work", but if you can find an example of when "it worked", you can ignore them because you know it's possible.

There are a lot of things like that.

So Why Logic?

Well, if I want to do something AND I can figure out enough things which are True, then I can use Logic to figure out if the thing I want to do will work.

Or, I can take the thing I want to do and I can see if it's Logically Consistent with a bunch of other things that I have to do or something like that.

Or maybe the thing I want to do has to have something which I can't do. If I can figure that out, then I can avoid trying to do something which won't work.

Logic can keep us out of trouble. It can help us predict if something will work or if it won't.

Knowing things like that saves a lot of time, money, anguish, and other things we want to save. It helps us be successful - whatever that means to each of us.

Logic is reliable.

Why is logic so reliable?

Not magic: Logic is a bunch of rules for figuring out if things will work based on thousands of years of experience.

So Logic is the Answer!




Where do the Propositions come from?

Remember, the Logic just transforms our propositions - our axioms - our guesses of what is right or wrong.

If our Propositions are crap - then all the Logical Reasoning in the world won't make them smell good. It will only be looking at the crap from different points of view.

Crap is still Crap.

One place our Propositions don't come from is 'reason' or 'logic'. We get them by following some other rules.

Scientific Propositions

One set of rules are the ones used in Science: a fact is an independently, verifiable experimental result.

Let's take that apart:
  • a result is something which can be measured. This means that there is a mechanical method which transforms something which happens into a number. The mechanical method must be reliable. For example, the diameter of an object. If it's a hard sphere, then that's easy to do; if it's a rectangular solid, then we need more rules (for example, measure each width on a line normal to each face and compute the average of the three measurements); if it's a bag of gas, then we're screwed because we can't reliably measure the diameter.
  • an experimental result is a _result_ measured from an activity which can be described precisely. The precision must be sufficient to compute the accuracy with which measurements
  • a verifiable experiment is one which can be performed again. In order to do this, the activity of the experiment must be completely described in enough detail that the activity can be performed with the same precision.
  • an independent experiment is an experiment performed by a different experimenter, using different equipment at a different time and place from the original experiment. This depends on the precision and completeness of the description and removes any bias the experimenter, location, and time of the first experiment may have introduced into the results.
This is pretty restrictive. It's also pretty slow and pretty expensive. It's also pretty good at building reliable knowledge.

So that's one way of getting propositions. We design experiments and do them to see what happens. We verify them to make sure that we know what to expect. Then we try to figure out rules which describe what we've observed and then test them using Logic to look at the results from different angles - so to speak.

How else can we come up with a Proposition?


How about we just guess?

Guessing is good. We do it all the time. Most of the time it doesn't work though.

But often, it's all we have.

Say it's election time and you decide to vote. Who are you going to vote for? You know both of them want to get elected and that both of them will say about anything they think you want to hear. In other words, most of what they say are lies. So you guess. You say "I think this one is more likely to do what I want" and then you pull the vote lever.

Now if you were being "logical", you'd do something else because you know both of them are lying. So maybe you wouldn't waste your time voting. Maybe you'd logic yourself into making a lot of money so you could just bribe whoever won. That would be more 'rational', if you want to get a politician to do what you want.

Emotional Propositions

How about we just claim something we want to be trueactually is?

As far as 'Logic' and 'Reason' goes, this is just fine.Remember, 'Logic' starts after you've got the propositions - it doesn't care where you found them. And inasmuch as 'Logic' is formalized 'Reason', well, the same can be said for 'Reason' as well.

When we do that and use 'Logic', we call that 'Rationalizing'.

We're 'just making up reasons for what we want to do'.

This is how a lot of real disasters are created.

Take starting a war.

Does it really make sense to rip everything apart, destroy somebody else's hard work, their lives, etc etc?

Sure - if you're willing to cause that much pain and you want their stuff.

Or maybe you think you need to think they're evil and that you're so right that you have to stamp out the evil.

But enough of this

Back to Thinking

I think you'll agree that - looked at this way - rational thought isn't really much 'higher' than any other form of 'thought'.

We're really just kidding ourselves.

So what is all this 'thinking' and 'understanding'.

What I 'think' about 'understanding'

When I'm really honest with myself, I say that I understand something when I have a feeling of comfort and confidence that I know what that 'something' will be like the next time it comes up.

If it's a freight train moving along - I 'understand' that it will stay on the tracks and I can control whether or not it squashes me.

Of if I'm trying to sell somebody something - I 'understand' that if I get the price right and am patient enough and advertise it enough, somebody will come along and buy it.

Sounds pretty good - doesn't it.

What Happens if things happen like I Predict?

When things happen the way I predict - then I think I'm pretty smart, I get more confident, and I 'lean on' my 'understanding' even more.

Does that mean that I can make accurate predictions?

Experience says: Well, Maybe. It all depends.

What Happens if things don't happen like I expect?

Well, lots of things.

Mostly I used to ask Why?

Then I'd come up with some Propositions to use to build a logical argument explaining how what I understood should have happened, but didn't.

This would usually involve finding somebody to blame. (If they'd only listen to me or do the right thing or weren't so self centered or . . .)

Then I'd can feel comfortable again because I'd 'know why it happened that way'.

In other words, I'd 'understand'.

(I know you would never do anything like this. You understand things a lot better than I do - don't you?)

And So, . . .

It's just one big circle of self delusion.

If you believe this stuff, you probably feel uncomfortable.

So even if you know it's true, you won't feel that you 'understand' it and will want to try.

See the trap?

(c) Copyright 2010 Mike Howard. All Rights Reserved.