logical and causal possibilities and proofs

Originally posted by twhitehead
I stick with the textbook definition:

Given a set of possible outcomes that occur at specific frequencies, the probability is a measure of those frequencies.

Or in the words of Wikipedia:
[quote]Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibili ...[text shortened]... hereas a 50/50 result is fantastic under my definition it is unsatisfactory failure under yours.

I stick with the textbook definition:

What if the textbook definition isn't what someone would most naturally mean by probability? Then he would have an incentive to make his own definition. That is what I did.

Note that it is not clear in the above sentence but I would add that 1 and 0 are exclusive. ie a probability lies in the open set (0,1)

What if I disagree with the textbook definition that this is what I mean by probability and I have created a perfectly self-consistent alternative definition that many people would intuitively agree with and prefer to the one in the text book?
Why would that definition be any less valid than that of the textbook?

I note that your definition is 'applied probability'. Your probability is to mathematical probability

not sure what you mean by 'applied probability' in this context.

When I see something happens at a frequency of 90% you will only ask 'how sure are we that it will happen'?

you have completely lost me with this "you will only ask 'how sure are we that it will happen'? " With my definition, why would I not give a probability of 90% given me knowing the evidence for 90% ?
I may only fail to give 90% if I didn't know that evidence; but my definition covers that. That kind of probability depends on what we know.

Originally posted by humy
My current definition of probability (which may keep on evolving just as it has been slowly evolving over time and I hadn't bothered to try and write it down before so me exactly choice of words below are improvised and likely very far from perfect )
is:

1, Given all what you know, if there there exists a most rational degree of certainty for something wit ...[text shortened]... ere, none of those problems ever arise.

What is your definition? I am very eager to compare.

My above definition of probability that allows definable probabilities for 'deductive assertions' ( I define 'deductive assertion' here as meaning an assertion with a truth value that can be deduced using just pure deductive logic alone i.e. without empirical evidence), such a 1+1=2, goes against conventional definitions of probability and many if not the vast majority of philosophers and statisticians would thus strongly disagree with my definition of probability, although I would hope to change their mind about that. And the definable probabilities to most (I say 'most' and not 'all' because I know of a trivial exception which I am not willing to discuss here ) deductive assertions can only take on the values of 0 or 1 that makes them rather redundant and pointless from any likely practical point of view because we can validly not mention probabilities of deductive assertions but rather just talk about assertions being either 'true' or 'false' corresponding to that said '1' and '0' of probability thus rendering even mentioning the probability of those deductive assertions totally superfluous and I wouldn't recommend using them.

But, nevertheless, I insist, redundant as they are, they are still real for deductive assertions, simply because the way I define probability implies they must be real. And the fact that they are redundant is irrelevant to whether they are real according to the way I define probability

Originally posted by humy
What if the textbook definition isn't what someone would most naturally mean by probability? Then he would have an incentive to make his own definition. That is what I did.

My stance on definitions is that you are free to make up your own as long as you clearly state them whenever you enter a conversation using them and with the realization that non-standard definitions may lead to confusion and miscommunication.
I am also somewhat surprised by what you would most naturally mean by probability as it is far from common usage and would explain the immense confusion in the other thread. We were obviously discussing different subjects and not realising it.

What if I disagree with the textbook definition that this is what I mean by probability and I have created a perfectly self-consistent alternative definition that many people would intuitively agree with and prefer to the one in the text book? [b]
As above, feel free to make up your own definition, but I would be surprised if you can find anyone else intuitively agreeing with it.

[b]Why would that definition be any less valid than that of the textbook?
Definitions hold no truth value. They are for communication purposes only. All definitions are equally valid. (assuming they are not incoherent) . However, to aid communication it helps to be consistent and in this case you will cause immense confusion by using a non-standard definition and you would do better to make up a new word. You were more than happy to expand the vocabulary for a new type of mode. I suggest doing the same with probability. Or even better consider the word 'likelihood' which has some precedence in that area although I can see it too causing some confusion as it is, in standard English, a synonym for probability.

not sure what you mean by 'applied probability' in this context.
You have taken probability theory and applied it to the universe and human knowledge and then only considered the extremes ( 0 and 1 ). You are using probability theory to make a judgement about the likelihood of a rule about events consistently holding.

Originally posted by twhitehead
My stance on definitions is that you are free to make up your own as long as you clearly state them whenever you enter a conversation using them and with the realization that non-standard definitions may lead to confusion and miscommunication.
I am also somewhat surprised by what you would most naturally mean by probability as it is far from common usage ...[text shortened]... ity theory to make a judgement about the likelihood of a rule about events consistently holding.

Definitions hold no truth value

Correct; and, as far as I can recall, I never said they did.
Nevertheless, something can be true by definition.

Example;

A triangle has 3 sides by definition of triangle.

Deciding that the definition of triangle being a shape with 3 straight sides has no truth value but, at least according to Hume, "A triangle has 3 sides" (when not presented as a definition ) does.

I found a reference to Hume claiming that anything that is "true by definition" has "truth values" but the link doesn't allow me to copy and paste it here but you could view on page 281 at:

https://books.google.co.uk/[WORD TOO LONG]

If only I could be permitted to show the whole link address here, which I can't.

Originally posted by humy
Correct; and, as far as I can recall, I never said they did.

But you did ask if they could be 'less valid'. My response is that unless it is incoherent, then any definition is valid. The only concern is whether it is wise to have a definition that will cause confusion.

The text book definition is obviously the one most people will go to when reading anything about probability in a mathematical context.

Originally posted by humy
you have completely lost me with this "you will only ask 'how sure are we that it will happen'? " With my definition, why would I not give a probability of 90% given me knowing the evidence for 90% ?
I may only fail to give 90% if I didn't know that evidence; but my definition covers that. That kind of probability depends on what we know.

Under your definition, you would say that the scientific finding is that events probably take place with a frequency of 90%. You will say that the probability is 1 (or as good as 1) that events take place with a frequency of 90%. Whereas I will say that events take place with a probability of 90%.
Your probability is the probability of probabilities as correctly identified by DeepThought and for which there is already a standard term 'likelihood'.

Originally posted by humy

Definitions hold no truth value

Correct; and, as far as I can recall, I never said they did.
Nevertheless, something can be true by definition.

Example;

A triangle has 3 sides by definition of triangle.

Deciding that the definition of triangle being a shape with 3 straight sides has no truth value but, at least according to Hume ...[text shortened]... n%22&f=false

If only I could be permitted to show the whole link address here, which I can't.

If it is in An Enquiry Concerning Human Understanding then you can get to it here:

http://infidels.org/library/historical/david_hume/human_understanding.html

Note that they'll get you to agree not to email them to try to contact the author with questions, which apparently people do do. 😀

Originally posted by humy
If only I could be permitted to show the whole link address here, which I can't.

Reply and quote gave me a long url, but I wasn't allowed to view the book.
Next time you want to post long URLs use a service like https://goo.gl/ or http://tinyurl.com/
In this case, don't bother as I don't think we are in disagreement.

Originally posted by DeepThought
...

Note that they'll get you to agree not to email them to try to contact the author with questions, which apparently people do do. 😀

I find that pretty funny.

They say:

" All of the Historical Library authors are dead--and in many cases have been so for several decades. ... any email addressed to these authors will be ignored. "

So I take it that some people would try to contact the dead author to ask them about something?
I will see if I can contact David Hume to ask him if he would be kind enough to clear up some of the confusion here -wish me good luck on that one?

ANYONE:

Is the probability that I would succeed (to persuade the dead David Hume to talk to us here) exactly zero, nearly zero, or undefined?

Originally posted by humy
Is the probability that I would succeed exactly zero, nearly zero, or undefined?

Nearly zero. You cannot know for sure that he is dead.

Originally posted by twhitehead
Nearly zero. You cannot know for sure that he is dead.

I agree. Although, in everyday language, I would say "I am sure" he is dead, I am not 'sure' in an absolute sense.

ANYONE

I am pretty sure that, according to strictly conventional terminology (as opposed to mine) for probability, a statement such as "1+1=2" or "1+1=7" doesn't have a 'probability' but merely has a 'truth value', but, can someone give me a web link that clearly and irrefutably explicitly asserts that with absolutely no room for interpreting it different?
-because I have been trying to find such a link to make absolutely sure I have got my facts absolutely straight but got nowhere.

twhitehead

Just out of curiosity, I have a question for you:

are the two statements

4=2+2, 4=1+1+2

definitions, because the both define what 4 is, thus have no truth value, or propositions, because they make an assertion, thus have truth values?
Or does it just simply depend on whether you 'present' them as definitions or propositions i.e. you are allowed to have the very same statement expressed in the very same form as either a definition or a proposition thus blurring the distinction between the two for the same given statement because it just depends on the context of that same statement?
So the statement "4=2+2" has not truth value in the context of "I define number four as 4=2+2" but "4=2+2" has a truth value in the context of "I believe 4=2+2"?

Originally posted by humy
are the two statements
4=2+2, 4=1+1+2
definitions, because the both define what 4 is, thus have no truth value, or propositions, because they make an assertion, thus have truth values?

In the absence of explicitly saying they are definitions, I would take them as equations based on known definitions.
I don't think you can present them both simultaneously and say they are both definitions, unless you give more explanation. Dual definitions tend not to work.

Or does it just simply depend on whether you 'present' them as definitions or propositions
Yes, context is everything.

i.e. you are allowed to have the very same statement expressed in the very same form as either a definition or a proposition thus blurring the distinction between the two for the same given statement because it just depends on the context of that same statement?
I don't think it blurs the distinction at all. It is just a recognition that symbols can be used for different things. The '+' sign can mean something other than numerical adding (and in set theory, almost always does). In fact, in set theory, adding numbers with the '+' operator is just an example used for illustration of a set operation. The same symbol may be used for adding matrices, vectors, and many other types of things via different operations. You can even define what we typically call multiplication to be '+'.
And the equality symbol has even more uses. And when we come to programming, both symbols may mean something totally different.

But it is usually clear based on context when you are defining and when you are testing for truthiness so I do not think there is any the blurring of the two and only rarely confusion as to which is which.

... and no real connection to probability.

[edit]
If I recall correctly, in set theory a 'group' can be shown to be isomorphic to a subset of the real numbers and the standard mathematical operations.

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 true..." followed by a definition of triangle and you just answered "yes"?

According to conventional formal logic, definitions don't have truth values.