And that addresses what the QM people do - they conflate possibility with reality - "because it is possible that it is true and possible that it is false then in reality it is both true and false. And they teach that as a fact in university.
But when it comes to the issue of excluded middle, I think there is a different kind of excluded middle involved in that paradox (similar arguments have been presented to jurors in court cases).
If we exclude the middle of his narrative -
What do we get? - “Suppose that a sea-battle will not be fought tomorrow — Therefore, it is not possible that the battle will be fought.”
His conclusion is his premise. “If it is true - then it is true”
There is a name for that kind of argument.
And when it comes to statements like - “Bill will be home tomorrow” - there are always presumptions of understanding - in this case it is presumed that the listener knows that it is just a statement of high confidence - not a declaration of absolute fact (assuming it wasn’t the Pope speaking). It is a short hand language issue - not a logic issue.
Some have stopped at the state of classical logic, which, however, has long been overhauled, not completely invalid, but partial and therefore considered antiquated.
Their level of knowledge of logic is that which is based on the Aristotelian analytics (Aristotle called “analytics” what was later to be called “logic”). This logic going back to Aristotle, which I have just called “classical logic”, has had an effect until the 19th century.
They don’t know at all what a huge realm of new knowledge would open up, if they would finally start to respect and soon accept the changes within logic, mathematics, philosophy, linguistics. Throw away all ballast and notice how tiny the rational part is compared to the irrational part and that one must integrate the irrational part if the rational part is not to shrink even faster.
Classical logic includes only propositional logic and predicate logic, in which the principles of forbidden contradiction (principium contradictionis) and excluded third party (principium exclusi tertii) and, related to them, the bivalence principle (see my earlier posts) are valid.
Non-classical logics are those in which at least one of the principles of classical logic is not valid. Particularly important are those systems in which the principle of the excluded third or the bivalence principle is invalid. Such logics were developed because they were motivated by developments in mathematics (cf. for example my earlier posts about antinomy).
Non-classical logics include e.g.:
Multivalued logic (generic term for all other logics in which the bivalence principle is not valid).
I think actual logic is simply the consistency of the language - “dialectics”. What other attributes someone wants to throw in must be held that fundamental standard.
Interesting that you should bring that up - just yesterday I got the final part of my analysis - although not quite ready to explain.
I first thought I had it when I could logically prove that pi is necessarily a transfinite magnitude (without having to go through a lot of maths). But then it occurred to me that I had to prove more than that. I had to prove that the digits never repeat - that took a little more effort. But I finally got it.
I didn’t think anyone on this board would be interested.
With further scrutiny I found a problem with my analysis.
I found that I could apply the exact same theory to a rational portion of a circumference (such as 3.0) and “prove” that it was an irrational magnitude.
There are several proofs that pi is irrational but they never explain why it is irrational rather they merely mathematically prove that it must be. They do it by assuming it to be rational and then discovering a contradiction - so it cannot be rational. And that is good but it doesn’t explain WHY it is irrational. I am looking for a logical reason for why - not merely for the fact of it.
This would be a good problem for James to address because he was all into the why’s of Everything. That man could tell us Why things are the way they are not merely that they are. Religion and science are entirely based on the idea that “this is just the way it is - have faith in it”. James went beyond both of them in explaining not only “what is” but exactly WHY it is necessarily that way.
He didn’t just prove that the universe exists but why it necessarily has always existed (he could Know that the big bang theory is false - not just believe it) - why subatomic particles form - why atoms and molecules form - why light travels at that particular speed - why gravity does what it does - basically why everything is the way it is. Anyone who can do that impresses the hell out of me. And he did it through pure reasoning - pure logic - not evidence based or or assumptions of any premised existence (no - “because we know this exists then we can deduce that…”. The only time he used empirical evidence was in his final conclusion - “because my ontology requires that a universe of this exact complexity must exist and we can see that it does exist - my ontology must be true-to-reality” (my wording not his).
And that is the kind of reasoning that I am looking for - WHY pi is irrational (not able to be represented by integer ratio) - not merely whether it is irrational. I’m not certain that I can find that reasoning but it must be there. And it gives my mind something to do while waiting in traffic or sitting idle while my wife chats away with her girlfriends.
I don’t think he’s employing circular logic. He’s merely deducing that if something is going to happen in the future that it is impossible for that thing to not happen in the future. His conclusion and his premise are basically one and the same statement expressed differently but I am pretty sure that’s not a sufficient condition for something to qualify as a circular argument. In mathematics, people often start with a premise such as (X = 40 \times (632 + 1004) \div 3) only to end up with a conclusion such as (X = 5453.3\dot3). Does that amount to circular logic given that the conclusion is basically the initial premise stated differently? I don’t think so. Circular logic is less of a logical mistake – I would go so far as to say that, strictly speaking, it’s not a logical mistake at all – and more of an ineffective debate tactic (or a tactic that is effective but in a deceptive way.)
I think the mistake Aristotle made is that of equivocation. His argument is basically a non-sequitur that is not immediately obvious thanks to the fact that he uses one and the same word in two different ways.
His argument basically goes something like this:
To say that a man had free-will at some point in the past is to say that it was possible for him to make a different decision than the one he made at that point in time. If it wasn’t possible for him to make a different decision then he had no free-will at that point in time.
If it was true on Monday that Joe will make the decision that he made on Tuesday then it was also true on Monday that it was not possible for him to make any other decision .
It was true on Monday that Joe will make the decision that he made on Tuesday.
Thus, Joe did not have free will on Monday.
That’s a non-sequitur hidden by the fact that it employs one and and the same word in two different ways – that word being “possibile”. Its premises are true but its conclusion simply does not follow. And although more or less obvious to me, it isn’t quite easy to explain in simple words.
I think what happened back then is that, failing to see the mistake that he made, Aristotle had no choice but to reject one of the three premises. And since his belief that humans have free-will was among the stronger, it was either premise #2 or premise #3 that had to be shot down. For some reason, premise #2 looked more convincingly true to him, so he decided to reject the third one. And so he concluded that the law of excluded middle, albeit true in most cases, is not true when it comes to statements about the future. Statements such as “I will go for a walk tomorrow”, he thought, are neither true nor false. Rather, they become true or false once they are actualized. But before they are actualized, they are neither true nor false. Sounds kind of like QM. As far as I know, he didn’t go on to replace his binary logic with some kind of ternary logic. We had to wait more than a thousand years for that to happen.
Fuzzy logicians say that most concepts are factually fuzzy in the sense that they can apply to different objects to different degrees. The fuzzy logicians are right. Whether or not a particular term applies to an object is often not a matter of a simple yes or no, but often a matter of degree. In fuzzy logic, one specifies the degree to which a term applies to a particular object by a number from the continuum between 0 and 1: If an object does not fall under a certain term at all, the term in degree 0 applies to it; if it falls completely under it, the term in degree1 applies to it; and if it falls only more or less under it, the term in degree g with 0<g<1 applies to it. For a term one has to specify a function which determines under which circumstances it applies to an object and in which degree. (This function determines a fuzzy set.) For example, one can specify that the predicate “x is a tall man” applies to men up to 1.60m in degree 0, to men from 1.90m in degree 1, and to men between 1.60m and 1.90m in certain (with height increasing) degrees between 0 and 1; a 1.75m tall man may be tall in degree 0.5, for example.
Since the 1980s, fuzzy logic has increasingly found its way into technical applications under the keyword “fuzzy control”, especially where exact mathematical calculations of the processes to be controlled are complicated, lengthy or hardly possible due to the many and unmanageable influencing variables. In this case, precise measured variables are first translated into fuzzy terms such as “quite fast”, “quite close to the target”, etc. (“fuzzification” is the word for this), which then form the basis for simple rules that are easily accessible to human intuition: “If the car is quite fast and quite close to the target, then brake quite hard”. The “outputs” of these rules are then transformed back into precise control instructions according to specific procedures. This procedure allows control on an “intuitive” basis without the availability of an exact mathematical model of the process to be controlled. Fuzzy control has found its way, for example, into the control of video cameras, washing machines, elevators and even subways.
If you know what the term means and if you know what the thing you’re trying to label constitutes of, then it’s a simple “yes”, “no” or “not defined”. No need for fuzziness. Not that fuzzy logic is wrong or useless, it’s just that it’s not in opposition to binary logic.
The words rational, irrational and integrate have DIFFERENT meanings outside maths.
SO this thread is just a confusion of terms.
S even if philosophy can “integrate the irrational,” (WTF that is supposed to mean), you would need to know where and with what it is being integrated, and philosophy would not be using a method remotely similar to the one used by maths, so the answer is NO on several counts.
You are then saying that only does so in the same way as maths, which makes the question meaningless.
According to you the question is “Can philosophy integrate the irrational as philosophy can?”
