Significance and meaning of Contradiction

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I ask because it seems that we throw away endless opportunity by ignoring that which we consider unlikely. The stakes involved in even one scientific advancement resultant from a highly unlikely proposition might be enormous. We might literally already be in the 27th century technologically but for those unwilling to try out the “madman’s” ideas.
That is an excellent chunk of text. I encourage you to write a title for that and post it as the beginning message of a new thread. If you don’t, then I might send you a private message sometime soon, requesting your permission for me to post it as the first message of a new thread.

I could imagine somebody having a guess about the shape of the future – or having a commitment to some ideology that includes a portrait of the future – and on the basis of that guess or ideology insisting that you are wrong. However, a policy of caution suggests that it is better to keep in mind the possibility that you are right.
For example, say one possible conclusion demands a stretch of reason, i.e., something very unlikely to happen. If we veer away from action (of whatever kind) that requires such a stretch of reason to conclusively “justify” …
Here is what seems to be the origin of Rhubarb’s disagreement with you. If we focus on the question of whether or not some very carefully specified statement is a logical consequence of some very carefully specified assumptions, then reason might be on the side of the “madman”, and “easily-made error that is very difficult to avoid making” could be a very brief description of the status quo of contemporary academic opinion.

I will go out on a limb and assert that, if we want to truly know whether or not the alleged “madman” is correct, we need to see some step-by-step argument.

Now, if you were to tell Rhubarb that you have proven the parallel postulate from the other axioms of Euclidean geometry, then Rhubarb’s first response might be to tell you that you are simply wrong, on the grounds that from your assumptions it isn’t possible to reach your conclusion. There might be no request to see your step-by-step reasoning.

This train of thought leads to something that I already posted.

It is a separate thread:
The hidden half of logic: a blind-spot in the zeitgeist of relativism?

Here is a link …
forums.catholic-questions.org/showthread.php?t=965277

The point is that Rhubarb would actually be engaged in self-contradiction if Rhubarb were to claim both of the following:
#1 Reason and logic properly understood refer to nothing but a system that allows us to obtain confirmation that, given the rules of the given system of logic, a particular attempt to provide step-by-step confirmation that Z is a logical consequence of A, B, C, … is indeed a successful attempt, and that Z does follow from those assumptions.

#2 Reason and logic properly understood also includes model-theoretic conclusions that have the following form or structure: “Z isn’t a logical consequence of A, B, C, …”

(We can discuss the technical terminology “model-theoretic.” I regret that it was necessary to use it without first introducing it.)
 
That is an excellent chunk of text. I encourage you to write a title for that and post it as the beginning message of a new thread. If you don’t, then I might send you a private message sometime soon, requesting your permission for me to post it as the first message of a new thread.

I could imagine somebody having a guess about the shape of the future – or having a commitment to some ideology that includes a portrait of the future – and on the basis of that guess or ideology insisting that you are wrong. However, a policy of caution suggests that it is better to keep in mind the possibility that you are right.

Here is what seems to be the origin of Rhubarb’s disagreement with you. If we focus on the question of whether or not some very carefully specified statement is a logical consequence of some very carefully specified assumptions, then reason might be on the side of the “madman”, and “easily-made error that is very difficult to avoid making” could be a very brief description of the status quo of contemporary academic opinion.

I will go out on a limb and assert that, if we want to truly know whether or not the alleged “madman” is correct, we need to see some step-by-step argument.

Now, if you were to tell Rhubarb that you have proven the parallel postulate from the other axioms of Euclidean geometry, then Rhubarb’s first response might be to tell you that you are simply wrong, on the grounds that from your assumptions it isn’t possible to reach your conclusion. There might be no request to see your step-by-step reasoning.

This train of thought leads to something that I already posted.

It is a separate thread:
The hidden half of logic: a blind-spot in the zeitgeist of relativism?

Here is a link …
forums.catholic-questions.org/showthread.php?t=965277

The point is that Rhubarb would actually be engaged in self-contradiction if Rhubarb were to claim both of the following:
#1 Reason and logic properly understood refer to nothing but a system that allows us to obtain confirmation that, given the rules of the given system of logic, a particular attempt to provide step-by-step confirmation that Z is a logical consequence of A, B, C, … is indeed a successful attempt, and that Z does follow from those assumptions.

#2 Reason and logic properly understood also includes model-theoretic conclusions that have the following form or structure: “Z isn’t a logical consequence of A, B, C, …”

(We can discuss the technical terminology “model-theoretic.” I regret that it was necessary to use it without first introducing it.)
I feel like you’re putting a great deal of words into my mouth.

Reason and formal logic are distinct things. I never said anything about what reason is. Not all reasoning involves the use of logic. Formal logic is a method of analyzing statements and arguments. Reasoning is a part of critical thinking.

And I haven’t agreed or disagreed with anything yet.
 
I feel like you’re putting a great deal of words into my mouth.
I thought that I used appropriate qualifications:
“Rhubarb’s first response might be
“Rhubarb would actually be engaged in self-contradiction if Rhubarb were to claim

Furthermore, it seems that you have something of value to contribute to the thread, and you wrote that the discussion was “dry” and for that reason might run out of steam.

However, if you prefer that I make my points in future without putting forward hypothetical scenarios about what you might or might not say, then I can change my ways.
And I haven’t agreed or disagreed with anything yet.
So the words that I put into your mouth might actually be appropriate? Let me know when you make your decision. If you disagree with something, then I stand to gain by learning a few things. After all, it’s a wide-ranging discussion and meta-discussion that includes not only logic, but also etiquette, strategy, clarity, keeping the thread alive, etc.

I see logic more as an area that requires persistent effort than as something that requires one to worry about ability or aptitude. To me, logic is like showing up on time. Everybody can do it, but not everybody is willing to arrive early and then wait.
 
Henotheism is a system where one deity is worshiped while others are accepted as existing.
Thank you Rhubarb and agnostic = “Lord help thou my unbelief” which I hope will lead me to what is in post 8!

(I’ve changed my “religion statement” several times because the earlier ones kept perplexing people!)
 
I thought that I used appropriate qualifications: … Furthermore, it seems that you have something of value to contribute to the thread, and you wrote that the discussion was “dry” and for that reason might run out of steam.

However, if you prefer that I make my points in future without putting forward hypothetical scenarios about what you might or might not say, then I can change my ways.



So the words that I put into your mouth might actually be appropriate? Let me know when you make your decision. If you disagree with something, then I stand to gain by learning a few things. After all, it’s a wide-ranging discussion and meta-discussion that includes not only logic, but also etiquette, strategy, clarity, keeping the thread alive, etc.

I see logic more as an area that requires persistent effort than as something that requires one to worry about ability or aptitude. To me, logic is like showing up on time. Everybody can do it, but not everybody is willing to arrive early and then wait.
Pseutonym, please take Rhubarb’s comments at face value.

I don’t know why talk of “madmen” has started or why it is thought helpful to Michael’s thread.

I was trying to help him on the subject of language.

I know about language. It has been a major part of my life and I know how to tell informative sources from uninformative ones.

Language uses auditory and written symbolism to allude to observed and investigatively imagined things. That’s neurological fact in human beings. (I also know neurology.)

Now, observing and knowing what one is observing for what it is, and how much one knows about it, can be known in any language. The more languages you learn, the better, also the more sciences you get into. This is the main thrust of my last few years.
 
What do you mean by the sign of contradiction of Jesus in the Eucharist?

… The subject is very dry.
Jesus is “acquainted with grief”. He says “follow Me”.

To have a trauma narrative is considered a no-no.

St Paul says “copy me” and he gave up his position in life to help his flock get a crown.

Rhubarb’s earlier remarks on logic complement what we have said about language.

I believe there are many layers to logic, e.g most of what is commonly abhorred under the label of “paradox” is a layer of logic to me. In a number of recent threads on the forum I have alluded to a mathematic basis for approximations to infinity for example (by imagining it, not being into the details enough to state them like an expert would).

Michael, the kind of shame I was referring to was when people have been told to stop their hobby, or that they were too stupid to know about things. Some family members get this kind of put down. Some people have had it from teachers.
 
Pseutonym, please take Rhubarb’s comments at face value.
Which comments? Before I posted anything in this thread, Rhubarb posted the following (not directed at me, obviously, since I was not participating, and I wasn’t named, and there was no allusion to me that I could discern):
“Logic” is used colloquially to mean “rational, makes sense, thoughtful, etc.” but that is not the proper use. Logic isn’t what Mr. Spock would have us believe what it is.
That looks like scolding (again, directed at somebody else, not at me).

It was followed by what looks like a kind of lecturing:

“Logic is nothing more than a formal language.”
Okay, but if we take that literally then we cannot say that logic is a method, unless we can identify a language with a method and identify a method with a language.

“To use logic properly all the rules of the language have to be stated up-front.”
Okay, but then a manuscript that fails to use logic properly may be of great value in helping people to eventually learn to use logic properly. I have in mind Pasch’s postulate, which is AWOL in Euclid’s most famous scroll. On the other hand, I wouldn’t be offended by somebody who claims that the diagrams in Euclid are part of the logic, and that what was eventually discovered was a way to do logic without relying upon diagrams. However, we then run into a bit of trouble unless Euclid stated up-front his rules for the logic of diagrams. Did he? Is it in the book? Here’s a starting point for a conversation.

If I’m thinking, and posting my thoughts, then somebody should do some fact-checking, or demonstrate that I am confused and that no fact-checking is needed.

Now, take me at face value. When I ask a clear question that ends with a question mark, I am hoping for a reply that acknowledges that I asked a question, and that attempts to actually either answer the question or provide some kind of explanation that is not an evasion of the difficulty. Acknowledging that it is difficult, and providing an initial train of thought as you attempt to discover an answer is okay. Everybody can learn from that. We can think aloud, so to speak, and help each other reformulate our thoughts to make everything clear.

I don’t see the value in scolding immediately followed by lecturing that answers questions that weren’t asked.
 
I thought it inappropriate to name a hypothetical participant in a dialogue or monologue after a thread participant and so did the latter apparently. That’s all. 🙂

Michael, I don’t know who these “madmen” are and I don’t like the sound of them.

I think not enough account is made of approximations to infinity and the phenomena of spectrums which solve a lot of so-called dilemmas more apparent than real.

Logic is far far bigger than usually made out as far I can see.

Michael, I think what we call randomness merely approximates to random. This is because there appears to be a huge amount of pattern everywhere. Some cycles will only come round in the long term.

From my tertiary reading (digests of digests) I think Hume began to intuit approximations and spectrums but fluffed it. Godel apparently got into it a bit. Because of Hume’s “sympathies” he was tempted astray.

Did you originally have some parables in mind in regard to which to ask about how to resolve or analyse specific misunderstandings? It’s always easier to work with real life examples.

Human affairs and those of the universe are so incredibly multi-layered, it is impossible to do them justice with infant school level logic as some (who haven’t joined in this thread yet 😉 ) often try.

Natural languages have huge vocabularies with myriad connotations and near infinite nuances hence are good tools for it.

Language is auditory and written symbolism for what is already symbols processed by the central nervous system. Language is also allusive, and not water-tight as “fundamentalists” allege. We should say what we mean and mean what we say. If we put it various ways they confirm each other’s meaning. Don’t use a Bible without marginal references and pursue lifelong mutual catechesis in groups. Leon-Dufour is a good dictionary of the Bible.

Languages engage the brain which is our ultimate tool. We have it already and we have always had it. The public is told not to use them. Abilities mustn’t be harnessed. “Primitive” man was brilliant.

I have never claimed anything I say is anything other than allusive.

Proof is less safe ground than hypothesis. It’s essential to always have many hypotheses otherwise one doesn’t see things. An insect has 1,000 eyes each side, “all the better to see you with”! 😉

My multi-theory hypothesis or multi-hypothesis theory might be a bit like the quantum things I’ve started to read perhaps? Whilst we don’t know “what’s what” we must come out of the closet about the huge amount we really do know about the whats. A False Falsification Principle is used like the Wimbledon Tournament or the US Primaries - only one hypothesis is allowed and once alleged to be eliminated it is never allowed to exist. The mantra is always, “there’s no evidence” when there is rather a lot of evidence.

On top of that, “absence of evidence” either yet found, or yet come across by an individual writer, is not the same as “evidence of absence”. “Archaeology disproves”, I keep hearing when scarcely a speck of the earth has been dug - now that’s a contradiction!!!

Like an irate mother wanting all the jigsaw pieces swept off the table to set tea. That’s no way to carry on building up a jigsaw more and more and more.
 
That is an excellent chunk of text. I encourage you to write a title for that and post it as the beginning message of a new thread. If you don’t, then I might send you a private message sometime soon, requesting your permission for me to post it as the first message of a new thread.

I could imagine somebody having a guess about the shape of the future – or having a commitment to some ideology that includes a portrait of the future – and on the basis of that guess or ideology insisting that you are wrong. However, a policy of caution suggests that it is better to keep in mind the possibility that you are right.

Here is what seems to be the origin of Rhubarb’s disagreement with you. If we focus on the question of whether or not some very carefully specified statement is a logical consequence of some very carefully specified assumptions, then reason might be on the side of the “madman”, and “easily-made error that is very difficult to avoid making” could be a very brief description of the status quo of contemporary academic opinion.

I will go out on a limb and assert that, if we want to truly know whether or not the alleged “madman” is correct, we need to see some step-by-step argument.

Now, if you were to tell Rhubarb that you have proven the parallel postulate from the other axioms of Euclidean geometry, then Rhubarb’s first response might be to tell you that you are simply wrong, on the grounds that from your assumptions it isn’t possible to reach your conclusion. There might be no request to see your step-by-step reasoning.

This train of thought leads to something that I already posted.

It is a separate thread:
The hidden half of logic: a blind-spot in the zeitgeist of relativism?

Here is a link …
forums.catholic-questions.org/showthread.php?t=965277

The point is that Rhubarb would actually be engaged in self-contradiction if Rhubarb were to claim both of the following:
#1 Reason and logic properly understood refer to nothing but a system that allows us to obtain confirmation that, given the rules of the given system of logic, a particular attempt to provide step-by-step confirmation that Z is a logical consequence of A, B, C, … is indeed a successful attempt, and that Z does follow from those assumptions.

#2 Reason and logic properly understood also includes model-theoretic conclusions that have the following form or structure: “Z isn’t a logical consequence of A, B, C, …”

(We can discuss the technical terminology “model-theoretic.” I regret that it was necessary to use it without first introducing it.)
By all means start a new thread as proposed. By the time I can harvest the responses, it will be the 27th century. Blessings to rhubarb, vic, you PsueTonym and all who have contributed more passiively to the thread also. Good this gave rise to something useful for others.
 
For any one curious, not that it matters to the about to be born new thread but rhiubard was perceived as not disagreeing per se, but as an agent of compassionate instruction employing disagreement tangentially to illustrate his point on formal logic.
Also, as a background, PsueTonym, my entire understanding of randomness and the madman’s coincidence results from my experience with mental illness diagnoses. I find that once the examiners get it in their heads that certain thought patterns are always indicative of faulty brainwork, they assign the pills and therapies with such arrogance of certainty that it is seldom in the consdieration of their ideas that the lunacy might be correct.
Example would be that a person is traumatized by a menacing dog and the result is massive fear and anxiety, which then becomes like obsessive compulsive disorder (just a random example nothing to do with me). The examiners say it is lunacy and that a dog does not cause a person to check for their keys 200 times before leaving the house everyday.
Yet in reality, who is to say?
Theories abound everywhere, but if the missing tungsten filament had never been discovered, we would all be in the dark on the literal level – 🙂
 
I think that there are a lot of contradictions in the Bible and in Catholicism. Oftentimes, I see a contradiction explained by saying that it was to be interpreted metaphorically or that what was written was not what was meant literally. Or if it is a Catholic teaching, one way of getting around the contradiction is to say that it was not an infallible teaching but was something that developed over time across cultures.
 
I think that there are a lot of contradictions in the Bible and in Catholicism. Oftentimes, I see a contradiction explained by saying that it was to be interpreted metaphorically or that what was written was not what was meant literally. Or if it is a Catholic teaching, one way of getting around the contradiction is to say that it was not an infallible teaching but was something that developed over time across cultures.
What does a contradiction signify?
What do contradictions mean to you?
 
What does a contradiction signify?
What do contradictions mean to you?
One way of getting a contradiction is to violate the law of non-contradiction. The law of non-contradiction states that a thing cannot be both A and not-A at the same time and in the same sense. All knowledge depends on the rule that A =/= ~A.
The law of non-contradiction is one of the basic laws of logical thought. I don’t see how you could have rational discourse without it.
 
One way of getting a contradiction is to violate the law of non-contradiction. The law of non-contradiction states that a thing cannot be both A and not-A at the same time and in the same sense. All knowledge depends on the rule that A =/= ~A.
The law of non-contradiction is one of the basic laws of logical thought. I don’t see how you could have rational discourse without it.
Man is God?
 
So, forgive the lecture I guess?

Man is God is not a contradiction, as such. Though you might be able to explicate the sentence into a few sentences to get a contradiction.

A contradiction, in a formal sense, is when you have a premise, and the negation of the same premise. “Man is God and Man is not God” is a contradiction because from that one sentence you can derive:
  1. Man is God
  2. Man is not God.
If we adhere to the rule of non-contradiction, as Tomdstone said, a contradiction can tell us some things about an argument - namely it allows us to utilize a pattern of inference called reductio ad absurdum. Logicians use a reductio in their proof to demonstrate what can’t be the case. If a premise lets you derive a contradiction, you have proven the negation of that premise.

For example: We think it’s raining outside. We also think that if it’s raining outside, our car will be wet. We an write these premises like so: [the bold indicates why I chose the variable I did]
  1. R (it is RAINING outside)
  2. R⊃C (if it is RAINING outside, then the CARis wet)
However, we look outside and see that the car is, in fact, not wet. So we’re adding another premise.
  1. ~C (It’s not the case that the car is wet)
From 1 and 2, we can derive a conclusion. We can conclude that
  1. C (The car is wet)
So our final proof looks like this:
  1. R (it is RAINING outside)
  2. R⊃C (if it is RAININGoutside, then the CARis wet)
  3. ~C (It’s not the case that the car is wet)

  1. C (the car is wet) (from 1 and 2)
However, now we can clearly see that 3. and 4. is a contradiction. So we know a few things about the situation, now. Logic is “truth-preserving” so we know that if we use all true premises and proper logic, our conclusions must be true. But our conclusion lead to a contradiction. By the law of non-contradiction we know that cannot be. So, we know that either we did our logic wrong, or, a premise is false. The logic is valid (modus ponens) so we must have a premise that is false. But we know that 3 is true because we looked outside and verified it. So, that leaves either 1 or 2 as our false premise. 1 can be false, and it’s just not raining. 2 could be false, and our car is in our garage as it rains outside.

To me, a contradiction indicates bad thinking, or, bad information. I think my example explains why I think that. Our thought by necessity uses our language. And our languages have rules that structure the thoughts they convey. Sometimes contradictions arise from examples above. Sometimes they arise from ambiguity or imprecise language. Or simply bad reasoning.
 
So, forgive the lecture I guess?

Man is God is not a contradiction, as such. Though you might be able to explicate the sentence into a few sentences to get a contradiction.

A contradiction, in a formal sense, is when you have a premise, and the negation of the same premise. “Man is God and Man is not God” is a contradiction because from that one sentence you can derive:
  1. Man is God
  2. Man is not God.
If we adhere to the rule of non-contradiction, as Tomdstone said, a contradiction can tell us some things about an argument - namely it allows us to utilize a pattern of inference called reductio ad absurdum. Logicians use a reductio in their proof to demonstrate what can’t be the case. If a premise lets you derive a contradiction, you have proven the negation of that premise.

For example: We think it’s raining outside. We also think that if it’s raining outside, our car will be wet. We an write these premises like so: [the bold indicates why I chose the variable I did]
  1. R (it is RAINING outside)
  2. R⊃C (if it is RAINING outside, then the CARis wet)
However, we look outside and see that the car is, in fact, not wet. So we’re adding another premise.
  1. ~C (It’s not the case that the car is wet)
From 1 and 2, we can derive a conclusion. We can conclude that
  1. C (The car is wet)
So our final proof looks like this:
  1. R (it is RAINING outside)
  2. R⊃C (if it is RAININGoutside, then the CARis wet)
  3. ~C (It’s not the case that the car is wet)

  1. C (the car is wet) (from 1 and 2)
However, now we can clearly see that 3. and 4. is a contradiction. So we know a few things about the situation, now. Logic is “truth-preserving” so we know that if we use all true premises and proper logic, our conclusions must be true. But our conclusion lead to a contradiction. By the law of non-contradiction we know that cannot be. So, we know that either we did our logic wrong, or, a premise is false. The logic is valid (modus ponens) so we must have a premise that is false. But we know that 3 is true because we looked outside and verified it. So, that leaves either 1 or 2 as our false premise. 1 can be false, and it’s just not raining. 2 could be false, and our car is in our garage as it rains outside.

To me, a contradiction indicates bad thinking, or, bad information. I think my example explains why I think that. Our thought by necessity uses our language. And our languages have rules that structure the thoughts they convey. Sometimes contradictions arise from examples above. Sometimes they arise from ambiguity or imprecise language. Or simply bad reasoning.
Don’t worry. Still friends, Rhubarb, and a lecture every now and then is good.
You say you can explicate the sentence in a few sentences to get a contradiction. What does that mean. Please explicate.
To answer a much earlier question of yours about my saying there is a contradiction in his Presence in the Eucharist: He is God, he who we receive. He makes us God by his intermingling with with our spirit, yet we are men still. Man is God and Man is not God. A contraction you claim, by reductio ad absurdum. Yet it is the experience we appear to be intended to have, at least for as long as the Peace of Grace lasts. To claim this is a contradiction in inalterable and absolute terms is to disclaim, or contradict the Scriptures, which tell us that God can do whatever he wants, and whenever?
 
One way of getting a contradiction is to violate the law of non-contradiction. The law of non-contradiction states that a thing cannot be both A and not-A at the same time and in the same sense. All knowledge depends on the rule that A =/= ~A.
The law of non-contradiction is one of the basic laws of logical thought. I don’t see how you could have rational discourse without it.
This I think presumes an inherent Unity and indissoluble nature to things. Or that certain privileged human categorical designations (attributes) are primary and immutable according to those notions we may call average and mutually exclusive.
E.g.
Proposition: Mulberries are good food because they can be eaten.

Well, I’m allergic to them.

But my guess is that at least some creatures in nature would thrive on them.
Which of these is the inherent attribute of a mulberry?

Should I prefer my human logic coupled with my allergy, or rather be “bird brained”
and eat the mulberry?
 
You say you can explicate the sentence in a few sentences to get a contradiction. What does that mean
Well, logic is for analyzing sentences, and sentences carry information. So we have a sentence “it is hot” that expresses information. But someone could reply “no it isn’t, the AC is on.” So we clarify. “It is hot outside.” And then maybe “It is hot outside when you’re not in the shade.” Or. “It is hot outside when you’re not in the shade from 10 to 2.”

So. Perhaps there’s more to the sentence “Man is God” that we can expand upon and then analyze.
 
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