Shouldnt logic be infact the embedded logic that structures themselves allow rather than any universal binary logic or contradiction of things being either A or not A.


One can ask, "Is it light or dark". Now that depends on the time and the setting one is in.

That is, when we look into the sky at night, we observe stars and hence it is not dark but neither is it all light. it both dark and light.

Or sitting in a dark room with the door slightly open is now a setting where one is enveloped in darkness to a very large degree but through the door one can see light.

So, shouldnt we assume that structures have a certain states of being and we are trying to know the difference in their states. In which case, the more detailed a description we want of something the more we must try to find the number of states of being we can distinctly observe with the object of our attention.

The problem is that you havent really defined A tightly and therefore by implication you haven't defined not A.
You example actually states A it is 'light' and B the light is such that I can see stars. These together are not the universal set of light levels nor as you observe are they mtually exclusive.

If you defined A as a light level above X......then any light level below X is by definition not A and together they are the set of light levels.

Light or dark is not an example of A or ~A. That would be light or not light, or perhaps dark or not dark. You might need to specify what counts as dark. For instance, you might say it's dark if you can't see anything at all. Once you have a definition then either it is dark or it isn't.

Logic can't really handle vague concepts and the way we use words in everyday language is vague. Of course if you make your notion of how light it is precise, for instance by measuring luminosity, then logic will have no problems with it.

logical bob wrote:Light or dark is not an example of A or ~A. That would be light or not light, or perhaps dark or not dark. You might need to specify what counts as dark. For instance, you might say it's dark if you can't see anything at all. Once you have a definition then either it is dark or it isn't.

Logic can't really handle vague concepts and the way we use words in everyday language is vague. Of course if you make your notion of how light it is precise, for instance by measuring luminosity, then logic will have no problems with it.

Thats what I said wasn't it, more or less ?

CarlPierce wrote:

logical bob wrote:Light or dark is not an example of A or ~A. That would be light or not light, or perhaps dark or not dark. You might need to specify what counts as dark. For instance, you might say it's dark if you can't see anything at all. Once you have a definition then either it is dark or it isn't.

Logic can't really handle vague concepts and the way we use words in everyday language is vague. Of course if you make your notion of how light it is precise, for instance by measuring luminosity, then logic will have no problems with it.

Thats what I said wasn't it, more or less ?

Yes and ~Yes

CarlPierce wrote:Thats what I said wasn't it, more or less ?

Yes. We were posting at the same time and I decided not to change mine.

logical bob wrote:

CarlPierce wrote:Thats what I said wasn't it, more or less ?

Yes. We were posting at the same time and I decided not to change mine.

Twistor

Yes and ~Yes

epepke wrote:Fuzzy logic works here. There are several variants, but in the most common one, a truth value is defined as a real number between zero and one. NOT x is defined as 1 - x. x AND y is defined as MIN(x, y), and x OR y is defined as MAX(x, y). (The AND and OR definitions distinguish fuzzy from classical probability.) Note that the rules give the classical two-valued results if you constrain truth values to 0 or 1.

More interesting are the problems that, surprisingly, weren't pointed out until Bertrand Russel.

Thanks for that but one doesnt know a priori what are the values to measure and to what degree of accuracy for us to know something.

I am not sure of this but I dont think human brain works in this manner, I dont seem to remember talking to anyone in binary code.
And as twistor pointed out with some humor that we seem to cut on both sides to emphasize our approximation for example
in the above statement.

As far as the issue of vagueness is concerned, I do not necessarily consider that as a disadvantage. I infact consider that vagueness as an advantage that helps us to dynamically evaluate the values at perhaps the cost of precision.
But I also consider human language as more advanced than the many computer programs because of its ability to tie many kinds of facts and to still come out with good, coherent statements. I agree its weakness is that it is not closed and we can have many dubious non meaningful statements, however the advantages seem to be better.

I heard about fuzzy logic, this question of mine has been very old and I heard fuzzy logic just as long back. Are there any advantages or disadvantages from fuzzy logic compared to classical logic.
Infact one might start calling that as old logic rather than classical if the other ones take over.
But I am interested in my first statement. Shouldnt it be more dynamic and advantageous to concern ourselves to the level of logic as embedded by an object present in nature itself.
For example, we can have probabilistic view, we can have systems soon based on QM, also with topological flavor, we already are going to consider with DNA based logic I believe because thats a more direct approach. And we can also have different kinds of systems for computing.
your thoughts please

Also doesnt QM which so far hasnt been shown to be reducible to binary states in its nature and unlikely even if string theory takes over implies that embedded states of our most fundamental elements are different.

Which brings me to another question, most of our information theory I believe emerges from the zero and one. does multivalued logic fundamentally changes the information theory ?. When wheeler gave the idea of it from bit, are those classical bits?.
Finally what about oscillatory systems or particles, could that be a different kind of logic?

Which brings me to another question, most of our information theory I believe emerges from the zero and one. does multivalued logic fundamentally changes the information theory ?. When wheeler gave the idea of it from bit, are those classical bits?.
Finally what about oscillatory systems or particles, could that be a different kind of logic?

Yeah I'm sure there are many physical problems that don't reduce to A and ~A easily.
But binary numbers map to the set of integers 1 to 1 so binary code can easily model a system with many possible values as you simply designate each state with a multi-digit binary number.

So if something can be A, ~A or both A and ~A then call them 10, 01 and 11.

or jump into base 3 and call them 0,1,2

CarlPierce wrote:

Which brings me to another question, most of our information theory I believe emerges from the zero and one. does multivalued logic fundamentally changes the information theory ?. When wheeler gave the idea of it from bit, are those classical bits?.
Finally what about oscillatory systems or particles, could that be a different kind of logic?

Yeah I'm sure there are many physical problems that don't reduce to A and ~A easily.
But binary numbers map to the set of integers 1 to 1 so binary code can easily model a system with many possible values as you simply designate each state with a multi-digit binary number.

So if something can be A, ~A or both A and ~A then call them 10, 01 and 11.

or jump into base 3 and call them 0,1,2

but you are missing something immediately. efficiency, from mapping one could at best show that both formalisms are ultimately the same, it however physically i.e. computationally differs. We dont have infinite time or resources.

Second, I am not sure also of the formalism equivalence. It once again depends on the kinds of sets one constructs perhaps??.
and taking other considerations, perhaps dimensions, topology???

cavarka9 wrote:I am not sure of this but I dont think human brain works in this manner, I dont seem to remember talking to anyone in binary code.

Our common binary codes are "True" and "False". In some cases we can interprete "Yes" and "No" as codes...

But I am interested in my first statement. Shouldnt it be more dynamic and advantageous to concern ourselves to the level of logic as embedded by an object present in nature itself.

True. I mean Yes.

Living in our natural environment, we have learned to distinguish objects which are useful to us. When we need to identify a single object, that's all we do - we don't care to create scales or taxonomies or logic in cases we don't need them.

Regarding your original example, light and dark, we don't need anything else if distinguishing light from dark satisfies our need. When we need what's between them, we have 'twilight'. For more precise needs, we have 'civil twilight' when we still see most of object by plain eyes, 'nautical twilight' when we see both horizon and many stars (and can measure the angle between them), ... etc

Rilx wrote:

cavarka9 wrote:I am not sure of this but I dont think human brain works in this manner, I dont seem to remember talking to anyone in binary code.

Our common binary codes are "True" and "False". In some cases we can interprete "Yes" and "No" as codes...

But I am interested in my first statement. Shouldnt it be more dynamic and advantageous to concern ourselves to the level of logic as embedded by an object present in nature itself.

True. I mean Yes.

Living in our natural environment, we have learned to distinguish objects which are useful to us. When we need to identify a single object, that's all we do - we don't care to create scales or taxonomies or logic in cases we don't need them.

Regarding your original example, light and dark, we don't need anything else if distinguishing light from dark satisfies our need. When we need what's between them, we have 'twilight'. For more precise needs, we have 'civil twilight' when we still see most of object by plain eyes, 'nautical twilight' when we see both horizon and many stars (and can measure the angle between them), ... etc

thanks and welcome.

cavarka9 wrote:thanks and welcome.

Thank you, I wish you welcome too! I've been a Ratskep member almost from the beginning, but I'm not a frequent poster.

epepke wrote:

cavarka9 wrote:Which brings me to another question, most of our information theory I believe emerges from the zero and one. does multivalued logic fundamentally changes the information theory ?.

Honestly, no, it doesn't, at least not theoretically. To an arbitrary precision, you can do everything with bits.

However, there are also practical considerations. A mathematical argument has to be not only accurate but understandable. You can model all of mathematics with second-order predicate language or a Turing machine, and you can do a hell of a lot with Peano arithmetic. Nobody does, though, because it's just too damn hard to write down all the steps and figure out what they're doing on a large scale.

As Richard Feynman pointed out, mathematics is largely the quest for better notation.

thanks, any sources for proofs? I would be interested in that. I agree that from a physicist point of view of calling mathematics as a quest for better notation, I think it is more than that. Combinotrics is not about notation entirely. There is some truth to mathematics, truth interms of it being useful for the real world at least.

I am interested in proofs and physical consideration.
What I mean is, in QM it is True, false, true and false. But in classical logic, it is 1,0 1or 0, except "or" in classical logic comes from two bits. In QM every bit can start of in "or". second is the issue of randomness. How does one inculcate randomness?.
As I said, I am interested if you have any more information. Could one dream a set of all sets?. Thanks again but will really appreciate if you can come up with proofs.In any case, interesting thought if nothing else.

epepke wrote:

cavarka9 wrote:thanks, any sources for proofs? I would be interested in that.

Google is your friend. What do you want proofs of? There are tens of thousands, probably. You can probably find most of what you want by starting with Wikipedia and branching out. Also college texts. But I don't know exactly if you want, and I don't have an encyclopedic knowledge of books.

What I mean is, in QM it is True, false, true and false. But in classical logic, it is 1,0 1or 0, except "or" in classical logic comes from two bits. In QM every bit can start of in "or".

I can't figure out what you are trying to say here.

second is the issue of randomness. How does one inculcate randomness?.

AFAIK, there is no finite algorithm that can generate a truly random sequence, if "truly random" is used in the Knuth sense, which seems to be what is required to model QM. Of course, some QM interpretations don't require randomness, but they cause other problems with an algorithmic approach.

Could one dream a set of all sets?.

Ah, when you get into the set of all sets, then you get into those other problems that Russell started to point out.

Consider the set of all English words, including hyphenated terms. Now, consider whether the term is self-descriptive or not. The term "short" is, assuming we think that five letters is a short word. The term "polysyllabic" is, because it has more than one syllable. Most terms, such as "potato" or "green" or "monosyllabic" are not self-descriptive.

Now consider the term "not-self-descriptive." Well, it cannot be self-descriptive, because if it is, then it is not-self-descriptive. Nor can it be not-self-descriptive, because if it is, then it's self-descriptive. A contradiction. How about "self-descriptive"? it can be either, because if it is it is, and if it isn't it isn't. It's undecidable.

For more on this sort of stuff, see Douglas Hofstadter or the originals, Gödel, Turning, and Church.

Thanks, in QM everybit is both 1 and 0 untill we measure. In classical logic, you will need 2 bits for an "or" operation.