Namaste Matt,
thank you for the post.
The problem I have with this statement:
"Further, this definition is somewhat different in the various philosophical disciplines."
Is that it is basically an escape route.
it is, however, simply a statement indicating that various philosophical schools have a different understanding and criteria for what they consider "proof". that these philosophical view points have different views is not my doing
That you may in fact be defining "proof" and "prove" wrong but since you said the definition is "different" to different "philisophical disciplines" you have an escape to being wrong.
whilst this may seem to be the case it actually is not. in terms of the sort of "proof" that i am talking about, there are several different understandings depending on ones point of view. from the Popperian model, it is clear that only intersubjective evidence can ever be considered as valid evidence. it is from this point of view that my views of evidence are derived.
To me this is worse than saying a falsehood unintentionally. It's the same as saying something but refusing to admit it may in fact be incorrect. If you don't allow yourself open for being incorrect then you truly don't allow yourself to be correct.
strange point of view, but if it works for you
Just like you can't truly beleive something unless you challenge it, otherwise that is simply acceptance. You are trying to protect your "view" and deeming that there are different definitions of the same terms. The problem with that concept is if there are different definitions (that is definitions that can contradict) then the language we are using is failing at being a language... when I looked "proof" up on dictionary.com it says this (here are the first 8):
there are, however, different definitions for the same word. I'll give you a wonderful example. what does the word "boot" mean?
In
mathematics, a
proof is a demonstration that, assuming certain
axioms, some statement is necessarily true. A proof is a
logical argument, not an
empirical one. That is, one must demonstrate that a proposition is true in all cases before it is considered a
theorem of mathematics. An unproven proposition for which there is some sort of empirical evidence is known as a
conjecture. In virtually all branches of mathematics, the assumed axioms are
ZFC (Zermelo–Fraenkel set theory, with the axiom of choice), unless indicated otherwise. ZFC formalizes mathematical intuition about
set theory, and set theory suffices to describe contemporary
algebra and
analysis.
Proofs employ
logic but usually include some amount of
natural language which usually admits some ambiguity. In fact, the vast majority of proofs in written mathematics can be considered as applications of
informal logic. Purely formal proofs are considered in
proof theory. The distinction between formal and informal proofs has led to much examination of current and historical
mathematical practice,
quasi-empiricism in mathematics, and so-called
folk mathematics (in both senses of that term). The
philosophy of mathematics is concerned with the role of language and logic in proofs, and
mathematics as a language.
Regardless of one's attitude to formalism, the result that is proved to be true is a theorem; in a completely formal proof it would be the final line, and the complete proof shows how it follows from the axioms alone. Once a theorem is proved, it can be used as the basis to prove further statements. The so-called
foundations of mathematics are those statements one cannot, or need not, prove. These were once the primary study of philosophers of mathematics. Today focus is more on
practice, i.e. acceptable techniques.
Mathematical proof - Wikipedia, the free encyclopedia
Now "evidence" is used quite a bit in the more common of these definitions.
Evidence - Wikipedia, the free encyclopedia
After reviewing the "evidence" I would have to say that that statement of yours is in fact false.
perhaps you should continue to review the evidence, espeically the parts where i've indicated that my view comes from
The overwhelming evidence shows that proof is merely a collection of evidence, enough evidence to make you accept the subject as true. Instead of using escape route statements, such as "in my view", maybe you should face the possibility that your definition of the word proof is incorrect.
since i was quite specific in my useage of the term and, subsequently, see that my useage was correct, perhaps you would like to consider the possibility that there is more than one understanding of the term "proof"?
If you do so then you must accept your arguments against proof may be incorrect as well since you possibly had defined it incorrectly.
my argument against proof is that i want evidence as evidence and proof are not the same thing. Proof is, also, a measure of the % of alcohol in an alcoholoic beverage.
Don't get me wrong... I respect that you like to say "in my view" also as a way to seem less threatening. To not imply that your fiew is definately correct but that it is simply your view. I agree with that, because in truth all I say and all you say is just in our own "view" or its what we "think" is true.
then i fail to understand why you would chide me on this statement.
Though abusing a mentality like that can cause one to fail to look at things objectively at times and realize that there are such things as truths, some things are truths despite our personal views (what you consider our internal
i do not presume to be objective
i am, as are most beings that i've met, quite subjective given that my experience of anything is coloured by my past experience, intellectual grasp of the subject and so forth. i would never advocate that my views are objective, i'll leave that for others.
I find this interesting since we can use mathematic to communicate.
the only reason that this is so is due to the formalized nature of maths as they fit within their framework and, to understand the nomenclature, we have to be operating within the framework.
For example in another thread you mentioned binary... binary is a number system. When you use binary with something such as mathematics you can see mathemetatics as a language.
i suppose that one could if they were so inclinded.
In fact how could would deny it is a language when the computer you are typing on uses the language of mathematics to communicate the information you type to the web server, which then uses another language based on mathematics to translate it to a human readable language.
i do not speak assembly nor do i speak machine code.
How is mathematics different than english and binary different than the english alphabet.
Mathematics and
computer science use artificial entities called formal languages (including
programming languages and
markup languages, but also some that are far more theoretical in nature). These often take the form of
character strings, produced by some combination of
formal grammar and semantics of arbitrary complexity.
I don't misunderstand. I strongly beleive Logic is a tool... not a formal system.
In
logic and
mathematics, a
formal system consists of two components, a
formal language plus a set of
inference rules or
transformation rules. A
formal system may be formulated purely abstractly, for its own sake, or it may be intended to serve as a description of some domain of real phenomena or some aspect of objective reality.
In mathematics, formal proofs are the product of formal systems, consisting of
axioms and rules of deduction. Theorems are then recognized as the possible 'last lines' of formal proofs. The point of view that this sums up all there is to mathematics is often called
formalism, but is more properly referred to
finitism.
David Hilbert founded
metamathematics as a discipline for discussing formal systems.
Any language that one uses to talk about a formal system is called a
metalanguage. The metalanguage may be nothing more than ordinary natural language, or it may be partially formalized itself, but it is generally less completely formalized than the formal language component of the formal system under examination, which is then called the
object language, that is, the object of the discussion in question.
I beleive these two sum it up nicely. Which is why I beleive logic is a tool.
that something is classified as one thing does not mean that it cannot, also, be classified as something else. to wit, the defintion provided above.
To me (based on the general definitions of proof) this would mean that you are saying certain concepts aren't subject to "proof" because it is impossible to gather enough evidence to be estabilshed as proof.
that is correct.
To me this sounds like avoiding the possibility that you could be proved wrong.
really? how much evidence is "sufficient" for one to be pursuaded? nevertheless, one can provide a copious amount of evidence that i am incorrect in my views, which is not the same as proof.
Not it isn't... at least not the general definition. To deny the general definition would serve no purpose to safeguard your own pride. What you say is in fact the general definition of proof...
i think that you are projecting a great amount of your own views unto me and then arguing with them. i am interested in gathering evidence and determing what that evidence indicates, regardless of my personal views on the subject.
would you speculate that since the informal defintion of theory is not accepted by the scientific process, that all scientists are engaged in protecting their ego?
However, I do not beleive the same. In fact Objectivism is defined in the dictionary as:....
I beleive the same.
you have thorougly confused me now... do you or do you not hold to an Objectivism view point?
I don't beleive in two realities... one inside and outside of us. I beleive there is in fact just one reality and it is external (as you say).
that is not my view. it is quite clear that beings can experience a reality that is entirely subjective and within their own sense perceptions and has little correspondence with external reality. one only need see some severely mentally imparied beings to observe this, in my opinion.
To me, saying there is two realities is a contradiction. Since a reaity is something that is real... whereas if we have two realities that can and possibly do conflict then there is indeed really only one reality.
why is that so? there is more than one dimension to this ontological universe, correct? how have you determined that multiple dimensions in the ontological universe are ok but multiple experiences of said universe are not?
metta,
~v
