The principle you describe is known as the law of excluded middle, and is fundamental to the classical systems of logic that has dominated thinking about (and teaching of) logic ever since the time of Aristotle (who invented logic). However, some logicians have criticized it, and there are some modern alternative logical systems that reject it.
When people are criticized for “black and white thinking” however, that does not usually mean that they are applying the law of excluded middle when they should not, but that they are applying it incorrectly. It is perfectly true (according to the law) that everything is either black or not-black, but that is very different from saying that everything is either black or white. Not only white things, but red things, and green things, and colorless things, and even very, very dark gray things are not black. Likewise, maybe it is true that everything is either good or not good, but that does not exclude the possibility, that the difference between something very good and something only a little bit good may be greater than the difference between something a little bit good and something a little bit bad. Black-and-white thinkers are people who tend to forget such facts.
“He also states it as a principle in the Metaphysics book 3, saying that it is necessary in every case to affirm or deny”
I have trouble understanding the articles on logic in Wikipedia but anyway, I think it is more accurate to “affirm or not affirm” or “deny or not deny” - similar to statistic’s Null hypothesis - Wikipedia
“A set of data can only reject a null hypothesis or fail to reject it”
In a similar way a person can agree or fail to agree with something. Failing to agree doesn’t necessarily mean they reject the statement. They might be on the fence.
“He also states it as a principle in the Metaphysics book 3, saying that it is necessary in every case to affirm or deny”
Also about atheism - “weak” atheism involves a lack of belief in god/s - it doesn’t involve explicitly denying that god/s exist.
People always forget that Schrödinger’s Cat is an exercise in reductio ad absurdum. He wasn’t saying the cat was in both states, he was pointing out how silly that would be.
That is just the sort of thing that Aristotle means. You are not disagreeing with him, just having difficulty with the rather dated language of the traditional translation. I assure you that what you said in your OP is a clear statement of the law of excluded middle, and that Aristotle is recognized as having been the first to state it (even if he did not use quite the words that later logicians would prefer).
Most of the stuff I was going to say has been said: First of all “black and white thinking” usually means things like “You’re with us or against us”, not situations of P ^ ~P
Secondly fuzzy logic.
But as a minor point to add, as a practical matter we also often need a value for “undefined” or “undetermined”. e.g. True or false: is 0/0 less than 1?
Somewhat academic point, but throwing it out there anyway.
I think that’s different to what I was talking about… I’d answer something like “agree” or “fail to agree”.
I don’t want to labour the point as undefined statements are not really relevant to what is meant by “black and white thinking”. The OP asked for exceptions to P v ~P and this is a very technical and academic one.
But “fail to agree” is just a tacit concession that the statement cannot be evaluated to true or false. And it gives the impression the statement may be evaluatable some day, when of course that is not the case.
In many of your examples, you’re talking about objective classifications of things. Shades of grey is often more applied to subjective classifications.
For example, Doug helps his neighbour John out by mowing his lawn each weekend. He does this because John is elderly and losing his eyesight and Doug doesn’t want him to get hurt or overexert himself.
Subjective observation: Doug is a good person for helping his elderly neighbour.
But, at work Doug has a reputation for correcting others all the time, even the smallest details that don’t matter to others. His colleagues have told him this is annoying, and asked him to stop, but he continues to do it.
Subjective observation: Doug is a bit of a jerk for always correcting others.
So Doug is a good person, but he’s also a bit of a jerk.
Someone with black and white thinking is going to prefer to classify Doug as either good or bad, but someone with shades of grey thinking feels quite comfortable saying that Doug is somewhere in the middle - there are good aspects to his character and not so good aspects.
See also: Cognitive dissonance
The problem with A and not-A logic is that it rests on the assumption that all things can be divided into two sets and the items in each set are all equal. This is clearly not true in real world equivalents.
Consider four items:
Item #1 is 99% A
Item #2 is 51% A
Item #3 is 49% A
Item #4 is 1% A
Using A and not-A logic, you’re going to place 1 and 2 in the A group and 3 and 4 in the non-A group. But the two items which are most similar are 2 and 3 - so why are they in separate groups? Why treat 2 as if it’s like 1 when it clearly is much more like 3?
It seems that you’re saying that the criteria is “Is the item mostly A”? And that is exactly the outcome for #1 and #2 (“yes”) and #3 and #4 (“no”).
It’s a bit like there being two identical twins and someone completely different… say the criteria is “what’s your favorite color?” and one twin said “red”, another said “green” and the completely different person said “red”. According to the criteria of favorite color, one twin and the other person are in the same category, yet the twins are otherwise the two most similar people…
“Why treat 2 as if it’s like 1 when it clearly is much more like 3?”
It’s like saying “why treat twin 1 like the other person when clearly twin 1 is clearly much more like twin 2”? Well how they are alike is based on a specific criteria (“favorite color” or “is the item mostly A”) rather than considering other aspects.
I have seen some failed logic that asserts that two things are similar because they are both “not-A”…
A silly example would be:
Neither bats, nor coffee grinders are fish, so they DO have that in common!
Many of the real life examples I can think of involve politics and strange bedfellows…You have climate change deniers identifying with the devout, and all huddling inside the “conservative” tent, because neither are liberals.
How else if an A and not-A system going to work? That’s the foundation of the system. It says “There’s a group A. You are either a member of that group or you are not.”
My point was that membership is usually a lot fuzzier than this system takes into account. Whatever quality defines A is probably going to be present in varying amounts.
The problem with some of these examples is that a thing is not necessarily a member of only one group. Something may be A and B. That doesn’t make it Not A. It is A and it is also B.
The OP makes me think irresistably of Alfred Korzybski and his General Semantics movement. Get yourself a copy of Martin Gardners Fads and Fallacies in the Name of Science, which devotes an entire chapter to Korzybski. The man was famous for lambasting “two valued logic”, and insisted that looking at the world in terms of A and Not A resulted in literal mental instability. According to Gardner, he taught his students to answer questions “Yes” or “No” or “et cetera”, the last of which was an answer besides “A” and “not A” that included all other possibilities. The General Semantics magazine was entitled “ETC.”
General Semantics was a big influence on Science Fiction Writer os the 1940s and 1950s, including Robert Heinlein (who explicitly mentions him more than once), L. Ron Hubbard (who, it’s claimed, lifted some of Dianetics/Scientology from General Semantics) and A.E. Van Vogt, who was a member of both General Semantics and Scientology. He significantly wrote a book entitled The World of Null A (“Null A” wasrepresented by a letter A with a bar over the top), where this indicated a world where non-Aristotelian two-valued logic held sway.
Gardner criticized the General Semantics movement in Fads and Fallacies and in other of his works (asuch as The Whys of a Philosophical Scrivener). SF Critic Damon Knight did such a devastating critique of Van Vogt’s book (in his book In Search of Wonder, which devotes a chapter to it) that he rewrote it. Van Vogt later wrote two sequels.
I just noticed that this sentence is missing two significant words:
Changes the meaning. And it’s a form of IS. What would Korzybski (“IS-ness is Insanity!”) say?
In terms of classification, related to the above mentioned fuzzy logic:
http://en.wikipedia.org/wiki/Paradox_of_the_heap
I always took this principle to mean something very simple and tautological: a thing is what it is, and it cannot simultaneously be what it is not.
Even the controversy over the nature of light (wave vs. particle) does not obviate this principle. Light is what it is (wave or particle or somehow both) but it is not, at the same time, something else.
The heap of sand is what it is, at every stage of the process (i.e. a progressively smaller heap). The word “heap” is just what we call it, and that so-called paradox is just a question of when do we stop calling it that. That’s just because words like “heap” have vague meanings.
The Shrodinger’s Cat thing, I thought, is supposed to be based on the Heisenberg Uncertainty Principle, which is about what we can observe and how our observations can affect the status or existence of (at least some) things. There is nothing in either of those that contradicts this principle.
This principle may seem trivial and uninteresting, stated like that, but for me it is just a way of grounding some discussions in reality, and to help rule out magical thinking.
Roddy
Like the Big Bang and the Chinese Room, the metaphor has more use against the intent of the originator than it does for him!