logical and causal possibilities and proofs

Originally posted by humy
ANYONE:

If somebody asked you "Is it true that a triangle is a shapes make of three straight sides?", and you answered "yes", are you implying that the definition of triangle has a truth value because the question started with "Is it [b]true..." followed by a definition of triangle and you just answered "yes"?[/b]

The question is basically asking 'Is this the definition of a triangle?' and the answer is 'yes'. You are not saying the definition is true, but that that definition corresponds to the standard accepted definition.

Originally posted by twhitehead
The question is basically asking 'Is this the definition of a triangle?' and the answer is 'yes'. You are not saying the definition is true, but that that definition corresponds to the standard accepted definition.

Yes, that is kind of what I thought but straggled to articulate it for myself.
So it is 'true' that that definition corresponds to the standard accepted definition.

The most common errors with definitions (usually seen in the spirituality forum) are:
1. The claim that a definition is 'wrong'. This is often involves claiming there is one true definition and sometimes the 'true definition' is claimed to differ from the commonly accepted definition. (we see this a lot with the word 'atheist' ). This is often in order to make the second error:
2. A Partial match to a definition is used to claim or imply a complete match. The arguer will try to show that x fits the definition of y using properties a and b. He will then say that y;s have property c and therefore x has property c. This leads to long drawn out arguments with people trying to show that something must be called by a certain name and rejecting all suggestions of using a different name all so that the above bad logic can be applied.

Another common question of truthiness is whether or not a scenario matches reality. The question 'Am I at home?' is not asking for a judgement on whether or not it is logically possible for me to be at home, but whether or not I am in reality at home. So the statement 'I am at home' is true if I am, in reality at home. There are situations where this confuses people about where the logic comes in, but I cannot recall a good example.

Originally posted by twhitehead
Another common question of truthiness is whether or not a scenario matches reality. The question 'Am I at home?' is not asking for a judgement on whether or not it is logically possible for me to be at home, ...[/b]

Nor causally possible (assuming we are not provided with more info or data here that logically implies it is causally impossible for you to be currently at home).

Questions about reality are often logical only insofar as they are a question as to whether or not reality matches a given description. Thus if someone says 'prove that the flower in your window is red' they are not really asking for a logical proof, but evidential proof (reliable evidence) that the description matches reality. People often confuse this with logical proof where you show a statement to be internally true. 'The flower in my window' is not internally true nor true based on definitions and logic, but true if it is an accurate description of reality.

This can be put into logic statement:
reality = description.

I see your definition for 'probability' to be close to the above logic statement which has a binary truth value. The dictionary definition of 'probability' however takes on all values except the binary ones
It is possible that your definition is asking 'what is the likelihood that such binary statements are 'true' or 'false' ? '

Originally posted by twhitehead
Questions about reality are often logical only insofar as they are a question as to whether or not reality matches a given description. Thus if someone says 'prove that the flower in your window is red' they are not really asking for a logical proof, but evidential proof (reliable evidence) that the description matches reality. People often confuse this w ...[text shortened]... finition is asking 'what is the likelihood that such binary statements are 'true' or 'false' ? '

I am not sure if I understand your question.
I don't know it this helps but:

Lets say we decide once and for all that the definition of number 4 and the only definition of number 4 is:

4 = 1+1+1+1

So now we both agree that "4 = 1+1+1+1" has no truth value and no probability and that "4 = 1+1+1+1" isn't "true by definition" but rather merely what we both agree is our definition.

Then we both agree that;

2+2 = 4

Has a truth value (and that truth value is 'true' ). Then the only disagreement you and the dictionary definition has with me is that you say "2+2 = 4" literally hasn't got a probability and it is simply 'true' while I say, because of the way I explicitly defined probability earlier, it has a probability of 1 albeit a verbally redundant and 'unnecessary' probability because you just can say it is 'true' but the probability is still defined (from my definition) nevertheless and the fact that it verbally redundant does nothing to change that.

Also, I would say 2+2=4 is 'true by definition' because it can be deduced from the definition of
4 = 1+1+1+1 (with some algebraic rules)

Originally posted by humy
I am not sure if I understand your question.

I didn't actually ask a question, I was saying your definition is a question.

Then the only disagreement you and the dictionary definition has with me is that you say "2+2 = 4" literally hasn't got a probability and it is simply 'true' while I say, because of the way I explicitly defined probability earlier, it has a probability of 1 albeit a verbally redundant and 'unnecessary' probability because you just can say it is 'true' but the probability is still defined (from my definition) nevertheless and the fact that it verbally redundant does nothing to change that.
I still don't see why you have a special definition of probability that apparently serves no purpose.

Also, I would say 2+2=4 is 'true by definition' because it can be deduced from the definition of 4 = 1+1+1+1 (with some algebraic rules)
That I disagree with.
True by definition means something trivially follows from or matches the definition. The moment any amount of 'deduction' or 'algebraic rules' come into play then it is true by argument not by definition.2+2=4 makes use of other definitions (such as what '2' means) and thus cannot rightly be said to be 'true by definition'.

Originally posted by twhitehead
...
I still don't see why you have a special definition of probability that apparently serves no purpose.

Surely a definition of probability (not sure what you mean by 'special definition' here. Unconventional? ) will serve deductive purposes?
I assume the whole of modern conventional science of statistics and probability theory is based on some kind of rigorous definition of probability (which I am not sure if I ever seen yet ) ?
Doesn't an explicit definition serve a purpose there?
Surely neither science of statistics or probability theory can be truly rigorous unless there is a clearly definition of probability?
Before I even talk about probability, I should state exactly what I mean by probability else it is unclear what exactly is it that I am talking about -hence my definition.

Note my definition of probability makes no direct statement of whether analytic propositions have probabilities and the definition isn't there to say analytic propositions can have probabilities but rather it is there to just define what I mean probability, nothing else. And the fact that my definition just happens to logically imply that analytic propositions have a probabilities is merely an accidental consequence of what I mean by probability.

( I only have just learned about the technical terms 'analytic propositions' and 'synthetic propositions' ;

https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction

And what I previously called 'deductive statements' were actually 'analytic propositions' and I will try and remember to only call them that for now on )

Originally posted by humy
Surely a definition of probability (not sure what you mean by 'special definition' here. Unconventional? ) will serve deductive purposes?

Yes, I meant unconventional.

I assume the whole of modern conventional science of statistics and probability theory is based on some kind of rigorous definition of probability (which I am not sure if I ever seen yet ) ?
The textbooks all seem quite rigorous and consistent to me.

Doesn't an explicit definition serve a purpose there?
Yes, those definitions serve a purpose. I understand that purpose. I do not understand the purpose of yours.
Are you saying: 'its got a purpose because everyone else has a purpose for their definitions' ?

Before I even talk about probability, I should state exactly what I mean by probability else it is unclear what exactly is it that I am talking about -hence my definition.
I fully agree that you should define terms before using them in certain contexts. What I am failing to understand is why you have chosen to use a word that typically means something else and dropped the terms that are typically used for what you wish to say. I can understand the use of 0 and 1 for 'false' and 'true'. Us programmers have been using them for decades. I can't understand a reason for doing that in mathematics, or for renaming it 'probability'. What is wrong with 'boolean'?

Note my definition of probability makes no direct statement of whether analytic propositions have probabilities and the definition isn't there to say analytic propositions can have probabilities but rather it is there to just define what I mean probability, nothing else. And the fact that my definition just happens to logically imply that analytic propositions have a probabilities is merely an accidental consequence of what I mean by probability.
Well now you are making a bit of sense. After all the speech about 'definitions have a purpose' you admit that when applied to analytic propositions it did not have a purpose.

So, it has a purpose when applied to synthetic propositions? What is that purpose? And I am not asking 'why have a definition?' I am asking 'why borrow a word that is typically used to mean something different? '

And also why assign a numeric value to a binary position?

Originally posted by twhitehead
Yes, I meant unconventional.

[b]I assume the whole of modern conventional science of statistics and probability theory is based on some kind of rigorous definition of probability (which I am not sure if I ever seen yet ) ?
The textbooks all seem quite rigorous and consistent to me.

Doesn't an explicit definition serve a purpose there?
Y ...[text shortened]... used to mean something different? '

And also why assign a numeric value to a binary position?[/b]

Are you saying: 'its got a purpose because everyone else has a purpose for their definitions' ?

No, I am saying 'my definitions has a purpose' (to define what I mean by probability ) .
I mistakenly thought you might be suggesting there is no point of a definition for probability which is why I pointed out the conventional definition for it has a purpose.

And also why assign a numeric value to a binary position?

You mean to a truth value? I think I have already answered that with "...my definition just happens to logically imply that analytic propositions have a probabilities is merely an accidental consequence of what I mean by probability."

And I am not asking 'why have a definition?' I am asking 'why borrow a word that is typically used to mean something different? '

Because what it more typically means is very nearly but not exactly what I mean by it and I simply cannot get my head around that exact convention meaning. I am simply incapable of forcing myself to think of probability in such a way as to reject the idea as truth values being equivalent to probabilities -

If you were to ask me my 'degree of certainty' that 1+1=2 and that I haven't make a mathematical mistake, I would both think and say "total certainty" i.e. I assign that 'degree of certainty', which I believe to be totally rational and therefore a true probability according to what I always naturally mean by probability, a probability of 1 (even though I wouldn't naturally explicitly say the superfluous comment of "It has a probability of 1" after I just said "total certainty" ) I find any other way of thinking about it too unnatural for my mind and, to my mind, even if/though not to other minds, perverse.

So, it has a purpose when applied to synthetic propositions?

It has no purpose applied to synthetic propositions. It is merely a matter of deduction from my definition of probability that is applies to synthetic propositions, whether I like it or not.
Does the conclusion of a logical deduction have to have a purpose to be flawless and correct?

Having said all that, You make me think I better not put into my book the definition of what exactly I always naturally mean by the word probability but rather make both my explicit definition of probability I put in my book and everything else I say in my book contrived to comply to the exact conventional meaning -I really don't like that! But cannot risk the repetition of my book being tarnished by heavy criticism of going against conventional wisdom -not worth the risk no matter how I look at it.

So I think I should explicitly state an extra criterion to my definition of probability I explicitly gave earlier in this thread that goes something like:
...
...
4, a probability cannot take on a value of exactly 1 or 0. One consequence of this is that no synthetic propositions can ever have probabilities, only analytic propositions can have probabilities.

One complication of that is that some philosophers consider the distinction between synthetic propositions and analytic propositions blurred and possibly meaningless. I will have to look into that matter later.

Originally posted by twhitehead
Yes, I meant unconventional.

[b]I assume the whole of modern conventional science of statistics and probability theory is based on some kind of rigorous definition of probability (which I am not sure if I ever seen yet ) ?
The textbooks all seem quite rigorous and consistent to me.

Doesn't an explicit definition serve a purpose there?
Y ...[text shortened]... used to mean something different? '

And also why assign a numeric value to a binary position?[/b]

There is a problem with the definition of probability. The probability of some outcome is the number of times that outcome arises divided by the number of trials, in the limit that the number of trials goes to infinity. While this doesn't create practical problems there is a philosophical problem with a definition that involves doing an infinite number of experiments.

twhitehead

At this forum:

http://forum.philosophynow.org/viewforum.php?f=21

I started two new threads

One of them was:

Does 1+1=2 have a "probability"?

http://forum.philosophynow.org/viewtopic.php?f=21&t=18593

where, to my surprise, the replies all indicate that they think definitions DO have probabilities.

and the other thread was:

Do definitions have truth values?

http://forum.philosophynow.org/viewtopic.php?f=21&t=18596

where, to my surprise, the replies all indicate that they think definitions DO have truth values.

It could be they are all non-experts and don't know what they are talking about at least when it comes to conventional probability theory and philosophy. But it seems to me, judging purely from their responses, they would be in general agreement with my definition of probability. And, perhaps this indicates that most of the human population, at least those that are not experts in philosophy or probability theory, would also be in general agreement with my definition of probability. I asked one of my brothers (not the one who is an expert in philosophy ) about this and he also thinks a truth value also is a probability (of either 1 or 0) AND that a definition can be 'true', at least if most people are in general agreement with it. So I see evidence that it could be that what most people, at least most laypeople, mean by probability is more in agreement with my meaning than yours.

So perhaps I shouldn't modify my definition of probability in my book to dismiss truth values as also being probabilities after all? After all, I had to actually ADD an extra criterion (the 4th one ) to my definition just purely for the purpose of dismissing truth values as also being probabilities (purely because I assume that is conventional wisdom in standard philosophy ) thus making my definition arguably unnecessarily extra complicated with that extra and apparently superfluous criterion! Can you give me a good reason why I shouldn't simplify my definition of probability in my book by simply leaving out that apparently superfluous criterion so that the definition is more in agreement with what most people mean by probability?

I will try my best to contact the bother of mine that is REAL expert on philosophy and see if I can persuade him to clear up some of this confusion.
-I have just right now e-mailed him; now I can only wait and see.

Originally posted by humy
...
...
Does 1+1=2 have a "probability"?

http://forum.philosophynow.org/viewtopic.php?f=21&t=18593

where, to my surprise, the replies all indicate that they think definitions DO have probabilities.
...

edit error;

That should have been:

"...the replies all indicate that they think truth values DO have probabilities.
...

Originally posted by humy
[b]twhitehead

At this forum:

http://forum.philosophynow.org/viewforum.php?f=21
...
...the replies all indicate that they think definitions DO have truth values. .

oh I spoke too soon:

They now seems to be agreeing much more with your definitions.
Looks to me like this issue of what people usually mean will soon be resolved once and for all; but I wait and see.