I’ve been told my thinking is more “black and white” than normal…
I based some of my reasoning on a principle of logic that says that things are either “A” or “not A”. (I forget the exact details)
I wonder if there are any exceptions…? Maybe quantum physics or the world of human emotions? I suspect that I would think that many of those so-called exceptions are just not thought about in the right way…
For any given X and Y, you can probably figure out a way to characterize them so that one is “A” and the other is “not A”. For any given “A” and “not A,” however, there will be things that don’t fit neatly into the two boxes.
Take a lion-tiger hybrid. Is it a lion or a tiger? For “lion,” it’s both “A” and “not A”. For “tiger,” it’s also both “A” and “not A”. For “feline,” however, it’s clearly just “A”, and a penguin is clearly “not A.”
So: are your “A” and “not A” a priori categories, or a posteriori?
Nothing can be A or not A ***at the same time and in the same respect. ***A lion-tiger hybrid is not A, whether A is a lion or a tiger. Your “logic” would say that a square is both A and not A, whether A is a triangle or a pentagon. It doesn’t work that way.
Of course, if an animal is 1/16 lion and 15/16 tiger, we have to more accurately define lion-ness and tiger-ness, and if any lion characteristics remain, it’s neither a lion nor a tiger. And the “in the same respect” qualifer is important.
There’s “fuzzy logic,” where you can assign relative measures of truth to propositional statements. “Jack is a Thief” might be 78% true for the fellow who climbed the beanstalk, but only 4% true for John F. Kennedy. In each case, the proposition is somewhat true and somewhat false.
This, of course, plays a bit of hob with our classical and intuitive notion of “true.” But if you treat it as a kind of variety of probability, it produces some useful results.
Classically, no, a proposition is either true or false, nothing in between, and never both at the same time. Imagine a jury reporting to the court, “We find the defendant guilty and not guilty.”
Well, the exact details in Formal Logic, (although other approaches to logic differ in description) are:
Contradictory Opposition: the opposition of being and non-being as such.
Man vs Not Man.
Privative Opposition: the opposition of being and non-being within a subject.*
Manly vs Unmanly.
Contrary Opposition: the opposition of being and non-being within the same subject.
Man vs Brute.
Relative Opposition: the opposition of two positive terms which mutually refer to one another in the same subject.
Man vs Boy.
= = =
So, while it is true that one may identify and discuss objects in Contradictory Opposition, it is not true that logic insists that Contradictory Opposition is the only manner in which one may approach any particular discussion. In fact, for many discussions, Contradictory Opposition would be an illogical method of examination.
At at very low level of logic all “things” must be or not be, and can’t be something else. But not all “things” are actually that limited. However, because most of what we can observe can be reduced to terms of “A” or “Not A”, we assume that as the normal, and all other cases as exceptions. Schroedenger’s Cat is an example where in all senses (hypotheically) a cat can be both alive and not alive. Within the framework of conventional thought that would be a noted exception.
Almost everything is an exception, the world is mostly gray.
You can play a language game where you take “A or not A” as an inviolable principle.
You can also play a language game where you don’t. [Not just to stubbornly prove a point about the caprice of language, but actually for useful reasons; for example, there is a form of logic called intuitionistic logic which does not validate “A or not A” in general, but is very convenient for phrasing certain kinds of reasoning]
It depends on how you want to use the words “or” and “not”, and what sorts of things you would put in place of “A”, and under what conditions you would assert such propositions as would result… One person might say putting “Sherlock Holmes has blood type AB-”, or “The Godfather is the best movie of all time”, or “Bargledysnob”, in place of “A” yields a counterexample, and another might not, having different logical semantics in mind.
Very much a post teenage realization for me. JohnClay, may I ask how old you are?
I think of that this way: is the cat fully alive or is it not fully alive? Has the cat turned out to be alive, or has it turned out to not be alive, or has the viewing event not yet happened?
I’m in my thirties.
Well I consider moral dilemmas and our values to be gray… though when you compare the values intuitively at any particular point in time one value seems more attractive or perhaps they are approximately equal.
I’m not sure I understand you. But anyway it isn’t specific enough in what way it is the “best” and also “of all time” can imply that it also includes all future movies.
Like I said, some people would take “The Godfather is the best movie of all time” as the sort of thing which is a counterexample to “Either A or not A”. Others will disagree and say that’s not the sort of thing that gets to go in place of A, as you did. But it’s not that one of you is correct and the other is wrong. You’re just playing different language games. You can always twist your interpretation of things to support either position; English is an informal language, not a formal one, so debating a point this fine is just semantic quibbling. It’s all in how you formalize it.
It’s all hypothetical. But the the theory is that the cat is both alive and not alive at the same time. So it’s both A and Not A. But it’s an exceptional circumstance. People tend to think the cat is either alive or not alive anyway, and not in both states simultaneously. But it’s certainly possible to define a system where things can have an uncertain definition.
What about this - the cat is alive in one parallel universe and not alive in another - then eventually one of those realities merges with our own… apparently a large proportion of theoretical physicists believe in parallel universes.
Why don’t you try doing it then? Your initial attempt wasn’t very satisfactory.
It is to me. I’m not claiming I can twist things so that YOU will be forced to analyze language the same way I do…
I’m perfectly happy to say that many declarative sentences in ordinary language are not to be taken as the sort of thing which evaluates to a boolean (one of {TRUE, FALSE}). And for me, “The Godfather is the best movie of all time”, or “Sherlock Holmes has blood type AB-”, or “50 is a big number”, or “You’re welcome”, or “I christen thee David”, or “There is a string of 100 consecutive 7s in the decimal expansion of pi”, or such things, in certain moods, are examples of sentences I would not normally want to analyze in terms of some artificially overformalized rules for assigning them a value among {TRUE, FALSE} [for different reasons, in the different examples]. Such rules will often have little to do with the use which those strings of words actually play in my speech-life.
Of course, someone else who wanted to straitjacket everything into such a Boolean form of analysis could nonetheless formalize such Booleanizing rules, and I might even care about those rules in other moods. And so I could never force anyone to stray from their perspective that everything is either TRUE or FALSE, should they want to formalize everything that way. But to me, that’s no different from claiming that every sentence evaluates to one of {RED, BLUE, GREEN}, or a number between 0 and 20, or what have you, by certain rules… I could make up rules which did so, but they’re not of any particular significance for the use to which I ordinarily put my language.
If, for you, a “proposition” means “something which evaluates to either TRUE or FALSE”, then, trivially, all “propositions” will evaluate to either TRUE or FALSE. But then, as I see it, there are a number of utterances in ordinary language which are not usefully analyzed as “propositions”, in this sense.
[I would not even want to say that, for every meaningful proposition P, there also a meaningful proposition NOT P. Just because there is some rules in our language for when we are warranted to claim P does not mean there are also some corresponding rules in our language for when we are warranted to claim NOT P. But this is an abstract point which I suspect there is little use in my harping on in this thread…]
I’m talking about there being a property and that something either fully has that property or it doesn’t fully have that property.
e.g.
“The Godfather is the best movie of all time”
The property is “the best movie of all time”… so either The Godfather is “the best movie of all time” or it is not “the best movie of all time”.
“Sherlock Holmes has blood type AB-”
The property is “blood type AB-”
“50 is a big number”
The property is “a big number”.
That property needs to be pretty clearly defined e.g. In a given context, “a big number” means equal or greater than 100.
Well actually in most situations you’d want to know if you agree or not. e.g. either you explicitly agree or you don’t explicitly agree. (completely agreeing or copmletely disagreeing is a false dichotomy) I don’t consider being able to explicitly agree or not explicitly agree to involve “some artificially overformalized rules”.
I’m not that knowledgeable about these kinds of things though.
It’s like statistics “reject the null hypothesis” or “do not reject the null hypothesis”.
Or an explicit “yes” vs. a lack of an explicit “yes”.
So you could ask someone if 50 is a big number. Their answer should either be yes or not yes. “Not yes” covers “I don’t know” and “perhaps”.
If “clearly defined” means “it has to be defined in such a way that everything either clearly has or clearly does not have the property”, then, tautologically, yes, for any object and any clearly defined property, the object either clearly has or clearly does not have the property. If we restrict our attention to such predicates, there’s no question left.