Beyond the Law of Noncontradiction

What is the basis for reason? And mathematics?

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Eodnhoj7
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Re: Beyond the Law of Noncontradiction

Immanuel Can wrote: Tue Sep 15, 2020 12:55 am
Eodnhoj7 wrote: Tue Sep 15, 2020 12:29 am A middle term, defined through the context of usage presented, is an assertion which underlies multiple assertions. It is an assertion which is repeated. Keep in mind I am talking about all assertions.
This is pure hogwash. You don't know what a "middle term" is.

It is that which is defined through its relationship to other words.
Both "poison" and "non poison" stem from "food is". Any noun that stands alone as singular references an "as isness" to ths phenomenon thus is implicitly followed by "is".
Not even comprehensible.
To state any singular noun is to implicitly follow it with "is" considering the noun exists for what it is as it is. "The food is not poison" and "the food is poison" both necessitate "the food is" as a middle term which is also responsible for transition to another noun.
Scott Mayers
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Re: Beyond the Law of Noncontradiction

Speakpigeon wrote: Sun Sep 13, 2020 8:39 pm
Scott Mayers wrote: Thu Sep 03, 2020 3:24 pm "Contradiction" literally comes from the etymological meaning, "with a third option asserted". ['con' with, 'tra' three, 'diction' stated thing] That something can be understood to be 'true and false' is this third of discrete possibilities.
The prefix Contra- comes from the Latin contrā, meaning against (see kom in Indo-European roots).

Contradiction litereally means "speak contrary to".

Contrary comes from the Middle English contrarie, from Anglo-Norman, from Latin contrārius, contrā, against.

So, nothing to do with "with a third option asserted" as you claim.

You would need to open a dictionary more often, but I guess you are probably not even interested in truth.
Scott Mayers wrote: Thu Sep 03, 2020 3:24 pm Does this help so far?
Not at all. This is misinformation.
EB
"con" means with, "tra" is three or third, just as I said.

Words evolve and the meaning "speak contrary", as a definition is not formally correct for logic where "contrary" is not the same as "contradicition". Both deal with some 'third' regarding an expected limitation to binary options. Your colloquial use is correctly evolved from the eymology and meaning of the original but circularly not able to establish that I am wrong.

You are welcome to disagree. The etmology helps break down the root words that hint at how the history of the terms relate to the three underlying principles of logic and helps understanding how these laws are coinciding but have different perspectives.

Note that the "law of the excluded middle" is the same as the "law of non-contradiction" but originally stated differently:

Law of Excluding the Middle: (X or not-X) means either X is true or not; you cannot permit a third option, X & not-X, where normally the 'or' is inclusive. Thus the third is excluded.

Law of non-Contradiction: not (X & not X) is identical but refers to denying this third option.

Law of Identity (Consistency): Whatever is assumed true of something, we expect it to remain true without change affecting its identity. So If X, then X. This also means that If not-Y, then not-Y remains true or becomes inconsistent (in- "undo, as of an action", con- "with", -sis- "same side or state", tence "tense")
Last edited by Scott Mayers on Tue Sep 15, 2020 2:12 am, edited 2 times in total.
wtf
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Re: Beyond the Law of Noncontradiction

RCSaunders wrote: Tue Sep 15, 2020 1:09 am
wtf wrote: Mon Sep 14, 2020 9:25 pm
RCSaunders wrote: Mon Sep 14, 2020 7:43 pm anyone who denies the law of non-contradiction is not rational.
https://plato.stanford.edu/entries/logi ... onsistent/
Why bother. Whatever it says, it's opposite is also true. If you believe that nonsense, I'll take your word for it.
Can't get more reputable than SEP. You should read the article, you might learn something. It's an interesting subject. If you refuse to click on a SEP article because you've already decided not to understand or agree or be interested in it, that reflects on you. You play a serious person on this forum. Are you trying to convince me otherwise?
Immanuel Can
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Re: Beyond the Law of Noncontradiction

Eodnhoj7 wrote: Tue Sep 15, 2020 1:13 am
Immanuel Can wrote: Tue Sep 15, 2020 12:55 am You don't know what a "middle term" is.
It is that which is defined through its relationship to other words.
No, it's not. You got that wrong, too.

A middle term is a prediction used rationally to connect the major and minor premises in a syllogism. It's not "defined" through that process at all. The definition of the middle term must be stable, and follow the law of identity.

And when you take basic logic, you'll know that, too.
Eodnhoj7
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Re: Beyond the Law of Noncontradiction

Immanuel Can wrote: Tue Sep 15, 2020 2:10 am
Eodnhoj7 wrote: Tue Sep 15, 2020 1:13 am
Immanuel Can wrote: Tue Sep 15, 2020 12:55 am You don't know what a "middle term" is.
It is that which is defined through its relationship to other words.
No, it's not. You got that wrong, too.

A middle term is a prediction used rationally to connect the major and minor premises in a syllogism. It's not "defined" through that process at all. The definition of the middle term must be stable, and follow the law of identity.

And when you take basic logic, you'll know that, too.
No, the manner in which "middle term" is used is defined by its relations to other words in the argument.
Immanuel Can
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Re: Beyond the Law of Noncontradiction

Eodnhoj7 wrote: Tue Sep 15, 2020 2:21 am
Immanuel Can wrote: Tue Sep 15, 2020 2:10 am
Eodnhoj7 wrote: Tue Sep 15, 2020 1:13 am
It is that which is defined through its relationship to other words.
No, it's not. You got that wrong, too.

A middle term is a prediction used rationally to connect the major and minor premises in a syllogism. It's not "defined" through that process at all. The definition of the middle term must be stable, and follow the law of identity.

And when you take basic logic, you'll know that, too.
No, the manner in which "middle term" is used is defined by its relations to other words in the argument.
No, it's not. You're just flat wrong. There's no other way to say it. That's the truth.
Eodnhoj7
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Re: Beyond the Law of Noncontradiction

Immanuel Can wrote: Tue Sep 15, 2020 2:28 am
Eodnhoj7 wrote: Tue Sep 15, 2020 2:21 am
Immanuel Can wrote: Tue Sep 15, 2020 2:10 am
No, it's not. You got that wrong, too.

A middle term is a prediction used rationally to connect the major and minor premises in a syllogism. It's not "defined" through that process at all. The definition of the middle term must be stable, and follow the law of identity.

And when you take basic logic, you'll know that, too.
No, the manner in which "middle term" is used is defined by its relations to other words in the argument.
No, it's not. You're just flat wrong. There's no other way to say it. That's the truth.
The term "middle term" derives its meaning through how it is used. Meaning is use. If memory is correct Wittgenstein observed this.
Scott Mayers
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Re: Beyond the Law of Noncontradiction

Note that the Law of Non-contradiction is specifically about a fixed claim as stated and not a rule against contradiction for other uses. That is why I expressed the etymology. When arguing, each premise STATED is defaulted to be 'true' by meaning. THIS is where the law is appropriate.

In extended logics, you can have multiple values beyond the mere binary options of a statement/proposition. As such, those values CAN have a third or more possible values. If something that is expected to stay fixed in meaning (consistent), then the statement refering to variables that can refer to whole statements/propositions require the binary values of fitness, true vs not-true. If you have a contradiction where a third option is NOT excluded, then something that leads to a contradiction FORCES you to do something else to make it 'contrary'. This action is itself the resolution to remove the contradiction by making them merely contrasting values.

For example, if given some X, then if it leads to a conclusion/subconclusion that demonstrates not-X, if we are certain both are true, then the resolution is to the contrary, "Some X and Some not-X", a third kind of possible compromised answer. But it tells us that X in this case has more than one state.
Scott Mayers
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Re: Beyond the Law of Noncontradiction

Eodnhoj7 wrote: Tue Sep 15, 2020 2:41 am
Immanuel Can wrote: Tue Sep 15, 2020 2:28 am
Eodnhoj7 wrote: Tue Sep 15, 2020 2:21 am
No, the manner in which "middle term" is used is defined by its relations to other words in the argument.
No, it's not. You're just flat wrong. There's no other way to say it. That's the truth.
The term "middle term" derives its meaning through how it is used. Meaning is use. If memory is correct Wittgenstein observed this.
I'd be cautious of interpreting the Laws excluding a third as referencing the syllogistic terms. The third being denied in not the undistributed middle fallacy, a kind of 'exclusion' of a particular type of 'middle'. The "middle' in the Law of Excluded Middle only refers to whether something presumed to require holding one meaning (one identity) and the dismissal OF contradiction can be both true and false at the same instant of discussion or argument.
Eodnhoj7
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Re: Beyond the Law of Noncontradiction

Scott Mayers wrote: Tue Sep 15, 2020 2:52 am
Eodnhoj7 wrote: Tue Sep 15, 2020 2:41 am
Immanuel Can wrote: Tue Sep 15, 2020 2:28 am
No, it's not. You're just flat wrong. There's no other way to say it. That's the truth.
The term "middle term" derives its meaning through how it is used. Meaning is use. If memory is correct Wittgenstein observed this.
I'd be cautious of interpreting the Laws excluding a third as referencing the syllogistic terms. The third being denied in not the undistributed middle fallacy, a kind of 'exclusion' of a particular type of 'middle'. The "middle' in the Law of Excluded Middle only refers to whether something presumed to require holding one meaning (one identity) and the dismissal OF contradiction can be both true and false at the same instant of discussion or argument.
The laws of excluded middle can refer to both "=" and "=/=" where both equality and not equality revert to P and -P.
RCSaunders
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Re: Beyond the Law of Noncontradiction

Eodnhoj7 wrote: Tue Sep 15, 2020 2:41 am
Immanuel Can wrote: Tue Sep 15, 2020 2:28 am
Eodnhoj7 wrote: Tue Sep 15, 2020 2:21 am
No, the manner in which "middle term" is used is defined by its relations to other words in the argument.
No, it's not. You're just flat wrong. There's no other way to say it. That's the truth.
The term "middle term" derives its meaning through how it is used. Meaning is use. If memory is correct Wittgenstein observed this.
"Men love Wittgenstein rather than Aristotle because their deeds are evil."
RCSaunders
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Re: Beyond the Law of Noncontradiction

wtf wrote: Tue Sep 15, 2020 1:58 am
RCSaunders wrote: Tue Sep 15, 2020 1:09 am
Why bother. Whatever it says, it's opposite is also true. If you believe that nonsense, I'll take your word for it.
Can't get more reputable than SEP. You should read the article, you might learn something. It's an interesting subject. If you refuse to click on a SEP article because you've already decided not to understand or agree or be interested in it, that reflects on you. You play a serious person on this forum. Are you trying to convince me otherwise?
I read the article twenty year ago. The update in 2018 did not fix anything. The problem is that logic after Abelard was beginning to be destroyed by divorcing reason from that to which reason pertained, actual concepts of existents, until finally it was destroyed by the logical positivists and linguistic analysis to nothing more than the manipulation of symbols. One simple juvenile mistake destroyed logic, the confusion of the word true (meaning a proposition that describes some aspect of reality correctly) and true (meaning the operation or manipulation of symbols was done correctly). Boolean true only describes a symbolic relationship which has nothing to do with true logic.

Kant confusing meaning (that which a concept refers to) with a definition opened the door to the destruction of reason.
Scott Mayers
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Re: Beyond the Law of Noncontradiction

RCSaunders wrote: Tue Sep 15, 2020 8:33 pm
wtf wrote: Tue Sep 15, 2020 1:58 am
RCSaunders wrote: Tue Sep 15, 2020 1:09 am Why bother. Whatever it says, it's opposite is also true. If you believe that nonsense, I'll take your word for it.
Can't get more reputable than SEP. You should read the article, you might learn something. It's an interesting subject. If you refuse to click on a SEP article because you've already decided not to understand or agree or be interested in it, that reflects on you. You play a serious person on this forum. Are you trying to convince me otherwise?
I read the article twenty year ago. The update in 2018 did not fix anything. The problem is that logic after Abelard was beginning to be destroyed by divorcing reason from that to which reason pertained, actual concepts of existents, until finally it was destroyed by the logical positivists and linguistic analysis to nothing more than the manipulation of symbols. One simple juvenile mistake destroyed logic, the confusion of the word true (meaning a proposition that describes some aspect of reality correctly) and true (meaning the operation or manipulation of symbols was done correctly). Boolean true only describes a symbolic relationship which has nothing to do with true logic.

Kant confusing meaning (that which a concept refers to) with a definition opened the door to the destruction of reason.
From that link, it says:
Paraconsistent logic is defined negatively: any logic is paraconsistent as long as it is not explosive. This means there is no single set of open problems or programs in paraconsistent logic. As such, this entry is not a complete survey of paraconsistent logic. The aim is to describe some philosophically salient features of a diverse field.
This is itself confusing. Normally, anything 'explosive' is dismissed in traditional logic. Yet this falsely asserts that this stance (paraconsistent logic) is a system that agrees with this here, when it is the opposite: that they accept contradiction by permitting an alternate place (a para-llel place) that permits resolution of the contradiction. As such, that article appears to be written by non-paraconsistent supporter because it falsely implies they accept ONLY logic that is NOT explosive....thus, not contradictory. Thus, this article cannot be trusted for it being contradictory in expressing it.

Many times an outsider of some philosophy may misinterpret the intentional meaning. This definitely demonstrates SOME misinterpretation or simply poor writing skills. If this was intentional, then it was set up to purposely make this view contradictory. It is possible that those originating the stance ARE lacking rational capacity. However, the class of those people who may support the LABEL, would be more likely to be supporting a system of reasoning that permits the resolution of a contradiction by allowing for consistency 'elsewhere' even if it is not consistent locally. IF this is what was intended fairly, this perspective DOES have validity.

It is definitely not relevant to 'logical posivists' as you falsely presume. You may be taking a political interpretation with some bias.

This is a debate about whether nature originates as abstractions that manifest into reality versus reality as being independent of abstract representations. For instance, you might discover a 'pattern' scientifically and guess some logic applies. But given most of science cannot precisely assure what is specifically true for being induced by stats that are not extreme (0% or 100%, or, possibly by some, 50%). The view by a logical positivist might then argue that given formal logic is itself artificially VARIABLE, like how you can use different languages to express the same thing, then the actual reality may not map onto any PARTICULAR system. As such, all you can assume valid of any one system of reasoning via 'logic formalism', is that the systems are defined by symbolic representations only and that while it may be universally true about what the reasoning represents, another system can use another language to prove what couldn't be proven by another.

An example: the rules of a given game, like Monopoly, is it's relative 'logic' system. Following the logic of the game's written rules is relatively arbitrary to that game though. That is, you can only use the rules of Monopoly for Monopoly, not some other game. So, the rules of games are relatively arbitrary and thus are only relatively true of the DOMAIN of the system's rules.

This has no relevant connection unless you interpret 'para-consistency' as referencing the nature of games themselves to be like different universes, which they are relative to our use. The question of whether there is a universal system of reasoning by those labelled as 'posivists' today looking back on others (that label was not created by those labelled as such but by outsiders trying to classify where they think those people fit into. For instance, Bertrand Russell, by some, is interpreted as being a 'logical positivist'. But is he, by context of how some interpret the meaning of 'logical posivists'? Bertrand actually believed that there IS a universal 'logic' but would still likely agree to separate the reasoning from meaning that you can have a priori statements. Rather, they would argue that logic cannot speak of whether the very first premises in any logical discourse can be interpreted as true BY THE SYSTEM itself. Then, all that could be interpreted about a logical argument is that you have POSTULATES that we pretend are true a posteriori and then treat these statements as symbols when developing a system of logic.

This is absolutely rational and would be likened to that example of Monopoly as having rules that are 'formulated' consistently but does not speak about whether the particular players are real or not. This is because there may be no players willing to play. But the fact of whether the players exist is irrelevant to the consistency of the created rules. Then 'player' is a SYMBOL because it is VARIABLE and you don't require defining the qualities of whomever they are themselves. The game can be played by Chinese person IF THEY CAN UNDERSTAND THE RULES. But the rules then are also then just symbols unless or until they are interpreted.

THIS is the essence of the logical posivists. Note that Godel became an 'intuitionist' based upon his "Incompleteness Theorem". Because it proves that you cannot have a perfect logic that covers all possible reasoning YET, we trust that nature IS 'reasonable' still, the meaning of one's INTUITION is what defines this nature of trust because you cannot use one complete logic to solve all problems assumed to still exist.
raw_thought
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Re: Beyond the Law of Noncontradiction

Your OP has given me much to think about. I will ponder, but right now it seems deep.