Eodnhoj7 wrote: ↑Thu Jan 20, 2022 10:39 pm
Scott Mayers wrote: ↑Thu Jan 20, 2022 10:26 pm
Eodnhoj7 wrote: ↑Wed Oct 27, 2021 12:50 am
Time is a duration thus along one timeline a color may be 90% yellow and %10 brown then change to %80 yellow and 20% brown.
You cannot seperate time from a duration considering even an "instant", such as a clock hand moving a second, is a duration. Even the instant of swallowing food is a duration of time. There is no action which does not occur over a duration of time thus something may both be itself and not be itself at the same time considering time is a length.
I thought that maybe you understood the first three laws in all logics by now. The rules of logic require...
(1) some consistent rule that ASSIGNS one thing about reality to some symbolic representation. Thus the "identity" of some referent used in argument has to remain CONSTANT or you lose any means to measure anything else by. Thus, the first rule of logic regarding 'identity' demands that given some reality "A" (the meaning of something
defined) we can assign arbrarily some symbol,llike, "A", that POINTS to the reality. The expression, "A = A" is meant to merely assert that we accept that SOMETHING in any system of reasoning (logic) that we AGREE to maintain fixed. This does not mean that whatver "A" refers to in meaning is unable to change or be inconsistent. What it means is that the SIGN referencing 'equality', "=", is what is MEANT and that the left and right side coincidence of the dummy symbol, "A", is meant only to help you infer the meaning of "equality" or SAMENESS.
Then, we need to define what is "NOT EQUIVALENT" in contrast. The 'negation' symbol for this is actually a 'complementary' concept and is where we DEFINE a "contradiction" as that which allows some "A" to NEGATE what we just 'identified' in (1):
(2) Some rule exists regarding what is NOT the same (or lack a fixed identity). This is the "complement" and can either be expressed as "A ≠ Ā" or, as many do, express this as either "the law of non-contradiction" ....OR, "the law of contradiction", both that tend to imply that we cannot allow A ≠ Ā It is probably better to just assert this as the
Definition of the Complement of Identity.
The third rule that is common to all such systems is to define whether you ACCEPT the Contradiction, usually referred to as "The Exclusion of the Third (or 'middle')" and this rule is not always necessary but CAN be more specific to BINARY options, of which 'true' or 'not true' reference. There still has to be some mention of this AT LEAST for the binary minimal and why you see it there regardless. Multivariable meanings can then ADD their own rules about what is true BEYOND mere binary options. So...
(3) Some rule that excludes ALL possible solutions by some standard. If you do not have a rule to exclude somethings, then the 'logic' serves no purpose given it is meant to determine what specifically to do in contrast to some perpetually indeterminate result. [But this still includes a means to determine IF something is or is not 'determinate' if need be.'
So your concern about this is moot. You still have to have some meaning to identify something, a means to know when it is not identical and what should be accepted ABOUT contradictions (
con- means 'with';
-tra- is 'third'
diction is 'spoken rule') and is not necessarily required to DENY except for the binary minimal. Because it is
minimally required for the binary options, it is still true in SOME capacity for ALL logics. If it is not, any reason for something without these is 'paraconsistent' where it still covers all possibilities consistent SOMEWHERE. Thus, Totality itself does not require being consistent but may be 'paraconsistent' for being most inclusive of all but unable to DISCRIMINATE what is or is not 'true'
as a whole.
1. There is no consistent rule of assigning a symbol to an object. I may observe 1 cow and attach 1 to it but 1 may equivocate to hamster, car, etc. In simple assigning one symbol may equate to a variety of phenomenon thus is subject to the fallacy of equivocation.
You gave an example of interpreting a variable as a constant. I used "address" and "value" (or "content in that address"). An address acts as the name of the variable that you can 'fill' in with multiple possibilities. This
acts similar to what a contradiction stands for given it CAN hold more than one unique value. This address NAME is on the left and the VALUE is on the right. Position order matters unless said otherwise. So
"P = P" means that the left side
symbol P has the ARBITRARY meaning to refer to the
value on the right side
P as its content or meaning, AT THE LEAST! [Assignment arbitrary]; But in the logic rules, the meaning of '=' is actually misleading and is "logically equivalent" (≡ is the usual symbol). So you are confusing the assignment meaning which references its content. That is, "P = P" can be "P = 93". This is an assignment that 'equates' the value to be the content meaning of "P" as an address.
Identity law is more properly,
P ≡ P
But when writing we assume the context and can forget this. So let's use the double equals (==) for (≡). Then the rule is
P == P
but
P = P would assign whatever it contains, even the name 'P' itself as just such a possibility.
Whatever something is, it represents the most PERFECT
symbol (or model) of itself. So
P == P can be a way of saying that you can assign 'P' like this,
P = P, then add that this is also reversible. That is, if the Right side P is anything, its best representative of its meaning would be just itself. So P == P means that the literal 'P' will always at least represent itself, for whatever meaning it is given. The MEANING here stays CONSTANT.
A memory in the computer can have ROM (fixed memory data) that contains some fixed value, like zero or one. In RAM, these can be
assigned constant which means that nothing in the running program could change it. ALL others are
variable (can 'vary' in value or content).
2. "Some rule existing for that which is not the same always" is not always the same as the variables may equivocate to anything. Dually, I can argue "myself" is not the same to "myself" as there may be multiple selves; however the multiple selves equate as 1 self thus a contradiction occurs as there are both one and many selves.
You need to get a good book on set theory because you are missing out that they use the word, "equals" differently than "equivalent". "Equivalence" [equal valence] references sets that have the same number of content rather than mean that they are 'equal'. For instance,
{Scott, Eodnhoj7, 935.9, "Tah dah",} is 'equivalent' to {John, 305, 9, why?}. Scott is not 'equal' to John or any other concept in the other. It just contains the same NUMBER of variables. A single constant can be understood as {Scott} ≡ {P}.
If you understand this, it suffices to cover all possible logic systems, even paraconsistent, or relatively non-sense systems. [Where you can flip some meaning of something in a non-sense world arbitrarily, in our worlds, we DEFINE 'logic' to refer to the consistent systems.
3. "A rule that excludes all possible solutions by some standard" would have to require universal observation as not everything is observable. Not everything is observable and we know this because of change. A change occurs and what was once not observed is now observed therefore implying a non observed state existing beyond the current state. Because not everything is observable we cannot make any "all" statements.
The Axiomatic Set theory is normally taught after one gets familiar with the meanings of terms. Most of it is definitions of terms that need to be made 'comfortable' with before getting to the actual details. Your concern here is covered in the advanced Set theory studies. But here is one example: Normally even in math, there is an assumption of context that matters, not just the literal expressions. As such, the most general means of teaching universals like 'all' refers to some
assumed universal set even where not mentioned. As such, a "-P", might better be expressed as "U - P", and means "given the Universe, U, without P; or the Complement in the set, 'U' of some 'P'.
Even if you think you understand by some particular book you may be using, it is best to look at multiple different authors of Set theory (or any subject) so that you can be sure to learn what one author may miss or explain things in different ways that might be more understanding. Either way, I believe that you need more study of what HAS been learned. You may think you are unique in understanding something on this but those before us have covered a lot of ground and are absurdly picky to be PRECISE and so do NOT miss your concerns. Much of it is just about communication misinterpretations.
4. The assigning of a symbol to some aspect of reality observes the reverse as well given reality represents itself through symbols. Reality justifies symbols. Given the A=A implies the same time and two distinct things can occur at the same time, A=A is moot as it may equate to A=-A as well. An example of this is the moment of swallowing food, the food is both in position A and position B during this same moment as the moment encompasses a variety of movements.
Dually all points of change observe both A and -A (or B) simultaneously. This can be further observed in the state of potentiality where two different or opposing things exist at the same time. Potentiality is a time as potentiality exists within a duration of time; i.e.. A occurs, B and -B is the actual state of being potential (multiple conflicting states exist under the time span of potentiality). An example of this is Schrodinger's cat.
If you need recommended particular books, let me know. But what you are speaking above is a multivalued logic. You can use the trinary, {0, 1, 2}. The "complement" is the maximum minus whatever is being complemented. For instance, -0 is 2; -2 = 0; -1 = 1. Any system greater than the binary (true/false) values LACKS the excluded middle rule and/or its complement.
So this too is covered in the formal systems BASED ON ONLY THOSE three general rule [the first two, Identity and Complement (or its 'contradiction' if binary). I can handle many valued logics personally but am still always learning more. But you should not think that Set theory has missed out on what you are particularly saying. The rules for multivalued systems do not overrule the binary systems. The whole binary systems have to be 'true' in order to define the latter systems. Given the binary system is also included in the multivalued systems, it still 'happens' to be true that when given only 2 values, P + -P is true and P*-P is false, the meanings of which 'true and false' themselves are defined IN necessarily.
[If you like the quantum theory issues, you should join in on discussions about the latest. Some of this is related with regards to reality and math/logic:
viewtopic.php?f=12&t=34156
5. I am not speaking of binary options. The law of contradiction is not binary as both +P and -P share the same medial form of P. An example of this would be a square peg and a square hole equating through the square shape. In reference to the OP the third medial term would be "duration" or "point of change"; multiple phenomenon can occur during a duration while dually a point of change observes 2 elements occur at a single point.
"Con-tra-diction" == with three/third dictum, other than the two exclusive options, "true" and "not-true". If you are wanting to use this in binary, it is not assigned outside of the two. Thus, if you get something as "true and false (of the same concept)", this third possibility is called the "contradiction" which demands we assign this as 'false' or the lowest value of the two values. So {0, 1} is limited to the "contradiction". The term was often meant in context to imply the emotional distaste of this with regards to truth values. As such, something that is NOT {0, 1}, like {0, 1, 2}, for instance, enables access to use 3 or more dimensions. Then the term, "contradiction" is no longer meaningful in those dimensions [Adding a value is 'dimensioning' in the same way a space is.]
6. I am not arguing for the existence of logic. Logic may require descrimination yet this discrimination first requires sameness thus P=P and P=-P. Where there is universal sameness there is nothing; I am arguing logic is nothing.
[my underlined for emphasis]
That last sentence is very ambiguous.
"Logic" comes from "log-related" as in something logged formally and analysed symbolically. They are the 'accountants' of the Greek times that combined their skill of record keeping and its means of using ONLY the symbols they can record to determine something from it about reality. The term "log" in math relates to this as they used the logs to multiply two numbers by turning them into something using logarithms. (log-arithm(etic) == use addition of the logs) [We probably get the English, "look" from this "log" or vice versa too.]
Logic is like a game that requires rules. The particular use of a game by players is what represents the 'contents' at the time of play. The 'conclusion' is the end of the game. What preceded it determined the "validity" of it as a fair game completed without difficulty. If there is a problem with the players at the particular game due to one of them NOT willing to follow the agreed-to rules, they should not play the game. Likewise, logic is like a very simplistic game with the least rules that can assign a token to each player. They really aren't so dumb as to confuse their 'equivalence' to the tokens as meaning they ARE the tokens! The tokens will have to represent the reality but the determination of the winner will require the players are the same way from the beginning. Then the winner becomes the conclusion, if all the rules were played, the token used that becomes a part of the conclusion refers to back to the reality
where the game maps back to reality.
Logic does not require being 'true' of the whole. When the conclusion is based 'validly concluded', we mean the fitness within the confines of the game's rules are correct and IF we assume the inputs to the argument 'true', the conclusion the MUST be 'true'. That the conclusion when remapped to reality should be 'true' requires the logic being used is limited to a well-defined
domain(s). When the argument is 'valid' AND 'true' using real referents assumed 'true', the argument is then, "sound". Think, "
if everyone played and survived their game playing fair, they are 'sound' players and it was a sound game".
So logic doesn't have to be the 'reality' of Totality. But Totality DOES contain its right to adopt patterns of reality based upon consistent rules. We are a Universe within Totality that has patterns, even though Totality contains ALL that is true, false, true-and-false, etc.