Significance and meaning of Contradiction

[Michael19682]

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.

I just now noticed that you listed your religion as agnostic. I didn’t mean to apply scriptural analysis with someone who would prefer to stick with logic – which admittedly appears to be the purview of the agnostic viewpoint (ie., proof of …). Please clarify if I am wrong.

So what if we took any situation that involved as I proposed in another post,
mutual exclusivity. Would that be a possible definition of at least one type of contradiction, i.e.,
A contradiction is that which posits two mutually exclusive attributes inherent in the same object?
Maybe we can proceed from there? and I for my part will try to use logic.

 

[Rhubarb]

I just now noticed that you listed your religion as agnostic. I didn’t mean to apply scriptural analysis with someone who would prefer to stick with logic – which admittedly appears to be the purview of the agnostic viewpoint (ie., proof of …). Please clarify if I am wrong.

So what if we took any situation that involved as I proposed in another post,
mutual exclusivity. Would that be a possible definition of at least one type of contradiction, i.e.,
A contradiction is that which posits two mutually exclusive attributes inherent in the same object?
Maybe we can proceed from there? and I for my part will try to use logic.

Sure. You could say that mutually exclusive properties would be a contradiction.

“The chair is big and the chair is small” ascribes the object of chair the properties big and small, which seem to be mutually exclusive. In my opinion, this sentence is either ambiguous and needs more information added, or it’s just a nonsense sentence not meant to convey information. Or, simply, false.

 

[Michael19682]

Sure. You could say that mutually exclusive properties would be a contradiction.

“The chair is big and the chair is small” ascribes the object of chair the properties big and small, which seem to be mutually exclusive. In my opinion, this sentence is either ambiguous and needs more information added, or it’s just a nonsense sentence not meant to convey information. Or, simply, false.

Got it. Very nice.
Does logic define the word/semantic element “is” – an existential proposition, for example.
Take that generic chair you had in mind. Is it big or small?

 

[Rhubarb]

Got it. Very nice.
Does logic define the word/semantic element “is” – an existential proposition, for example.
Take that generic chair you had in mind. Is it big or small?

Logic, like all matters in philosophy, is hotly debated. But generally speaking dealing with ‘is’ requires a more advanced logic than the simple propositional calculus I use for examples. I’ll try to get to the point.

Is typically has two uses in logic. “There is a chair” is one way to use ‘is’, and it is used to make an an existential claim - that a chair exists. Existence/being is typically considered a quantifier in logic, not a property.

The other way is “the chair is big”. In this, ‘is’ indicates a property (big) that predicates the object (chair).

Whether the chair is big or small is really up to how we use the term. A chair can be big. But, like, it’s not bigger than my car. It can be small, if we’re thinking on stellar terms. The context matters because the logic merely analyzes the language.

 

[Michael19682]

Logic, like all matters in philosophy, is hotly debated. But generally speaking dealing with ‘is’ requires a more advanced logic than the simple propositional calculus I use for examples. I’ll try to get to the point.

Is typically has two uses in logic. “There is a chair” is one way to use ‘is’, and it is used to make an an existential claim - that a chair exists. Existence/being is typically considered a quantifier in logic, not a property.

The other way is “the chair is big”. In this, ‘is’ indicates a property (big) that predicates the object (chair).

Whether the chair is big or small is really up to how we use the term. A chair can be big. But, like, it’s not bigger than my car. It can be small, if we’re thinking on stellar terms. The context matters because the logic merely analyzes the language.

I have “quantifier” as something which indicates the scope of the term to which it is attached. Combining that notion with yours, I understand that existence is “all or none”? Thus, I can’t have partial or ephemeral existence. Just trying to understand. I’m motivated to continue the discussion because if someone says, There is a contradiction: then I say that this contradiction must be “all or none”? And you have shown how depending on how fine grained the analysis, contradictions are sometimes resolved by context. If we can resolve a contradiction into agreement (once again), then “all or none” must be provisional at best.

 

[Rhubarb]

I have “quantifier” as something which indicates the scope of the term to which it is attached. Combining that notion with yours, I understand that existence is “all or none”? Thus, I can’t have partial or ephemeral existence. Just trying to understand. I’m motivated to continue the discussion because if someone says, There is a contradiction: then I say that this contradiction must be “all or none”? And you have shown how depending on how fine grained the analysis, contradictions are sometimes resolved by context. If we can resolve a contradiction into agreement (once again), then “all or none” must be provisional at best.

Prepositional calculus analyzes relationships between sentences.

A
A->B​

B

But consider the quintessential logical syllogism. All men are mortal. Socrates is a man. Therefore, Socrates is mortal. Using PC, we get

A
B​

C

This tells us nothing. The logical relationships in these sentences sub-sentential. So we use first-order logic. First-order logic examines the relationships within sentences. It adds quantifiers to sentences to symbolize sentences like the syllogism above. The universal quantifier in “all men are mortal” helps break apart the relationships in the sentence. Quantifiers can range over certain variables and sentences depending on how they’re written. First-order logic using these quantifiers have their own rules (patterns of inference) that let you infer information from given assumptions or premises. And then you can find contradictions.

For instance, if we have these premises…

1. All men are mortal
2. Socrates is a man.
3. Socrates is not mortal.

The conclusion we can derive would be a contradiction. The various quantifiers have their own rules about what can be inferred depending on how they’re used. The universal quantifier (usually signified by saying “all Ps are Qs” is contradicted any time there is a P that is not a Q. (But curiously, it is NOT contradicted if there are no Ps at all)

 

[Michael19682]

Prepositional calculus analyzes relationships between sentences.

A
A->B​

B

But consider the quintessential logical syllogism. All men are mortal. Socrates is a man. Therefore, Socrates is mortal. Using PC, we get

A
B​

C

This tells us nothing. The logical relationships in these sentences sub-sentential. So we use first-order logic. First-order logic examines the relationships within sentences. It adds quantifiers to sentences to symbolize sentences like the syllogism above. The universal quantifier in “all men are mortal” helps break apart the relationships in the sentence. Quantifiers can range over certain variables and sentences depending on how they’re written. First-order logic using these quantifiers have their own rules (patterns of inference) that let you infer information from given assumptions or premises. And then you can find contradictions.

For instance, if we have these premises…

1. All men are mortal
2. Socrates is a man.
3. Socrates is not mortal.

The conclusion we can derive would be a contradiction. The various quantifiers have their own rules about what can be inferred depending on how they’re used. The universal quantifier (usually signified by saying “all Ps are Qs” is contradicted any time there is a P that is not a Q. (But curiously, it is NOT contradicted if there are no Ps at all)

A very challenging answer.
Right now I streamed my thoughts
, Given the syllogism as above, 1.2.3., there is a reasonable theory of “logical” contradiction that can’t be resolved by means of the given context. A lot like a law, but not exactly so.
In a fuller context, all can be resolved.
E.g. 2a. “mortal” and “not mortal” are opposites, but not necessarily contradictory
That substitution can easily fulfill the logical context of any rhetorical syllogism, or enthymeme.
Now, if it be that context can sometimes/even always resolve contradictions, then again how to understand the statement/conclusion:
“There is a contradiction”
It signifies different things to different people.
E.g., Logical contradictions are in certain contexts unyielding.
Contradictions inspire some to preserve them for arguments sake, yet some of them inspire people to eradicate the premises that preserve them.
E.g. All toys are balls.
All balls bounce.
All toys bounce.
Not a contradiction according to the logic of the premises. But very annoying unless it means nothing. Better to not create contradictions that we are not motivated to resolve by filling in the context, and better to not create truisms that are irksome.