How to prove that our logic applies universally to all things we come across

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BenSinner

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Here is the scenario:

SKEPTIC: “Our logic isn’t trustworthy and paints an untrue picture of reality”

REALIST: "But we would be using our logic to affirm that statement, though. So that means our logic IS trustworthy.

SKEPTIC: “How do you know you are using your logic to assess my statement?”

How do you know you are using your logic to assess my statement?

How would the REALIST know that he is using his logic? How could he answer the SKEPTIC?
 
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How do you know you are using your logic to assess my statement?

How would the REALIST know that he is using his logic? How could he answer the SKEPTIC?
How can I know I am using logic? This question has several sub questions we need to answer first

What is logic?

noun: logic
  1. reasoning conducted or assessed according to strict principles of validity.
What is reasoning?

noun: reasoning; plural noun: reasonings
  1. the action of thinking about something in a logical, sensible way.
What is logical?

adjective: logical
  1. of or according to the rules of logic or formal argument.
Rule 1 of the formal rules of logic
(1) for all propositions p, it is impossible for both p and not p to be true

The skeptics statement violates this law.

We have used our logic to asses his statment
 
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Here is the scenario:

SKEPTIC: “Our logic isn’t trustworthy and paints an untrue picture of reality”

REALIST: "But we would be using our logic to affirm that statement, though. So that means our logic IS trustworthy.

SKEPTIC: “How do you know you are using your logic to assess my statement?”

How do you know you are using your logic to assess my statement?

How would the REALIST know that he is using his logic? How could he answer the SKEPTIC?
I would ask the skeptic how does he know that he is asking me something, or stating something. I would like to see how he answers.
 
What if the skeptic were to say:

“The ‘logic’ you used to find truth in my statement is not the same as the logic you used to refute my statement. It only appears to be the same logic according to your misconceptions”

So basically how could we prevent the skeptic from accusing all arguments against his to be "misguided logic’ and all arguments that support his as ‘true logic that one will misinterpret as the misguided logic’???
 
What if the skeptic were to say:

“The ‘logic’ you used to find truth in my statement is not the same as the logic you used to refute my statement. It only appears to be the same logic according to your misconceptions”

So basically how could we prevent the skeptic from accusing all arguments against his to be "misguided logic’ and all arguments that support his as ‘true logic that one will misinterpret as the misguided logic’???
Then, I would ask him: How do you know that “the logic’ I used to find truth in your statement is not the same as the logic I used to refute your statement.”?
 
We cannot demonstrate our logic to be reliable, since we would have to use our logic in order to do that.
 
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