MHB Are the inference rules of propositional calculus tautologies?

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The discussion centers on whether the inference rules of propositional calculus, specifically Modus Ponens, can be classified as tautologies. It is established that inference rules are relations on formulas, while tautologies are specific formulas, leading to the conclusion that Modus Ponens is not a tautology. However, some participants argue that Modus Ponens can be represented as a well-formed formula (wwf) and is considered a tautology in various logic textbooks. The conversation also touches on the definitions of inference rules and tautologies, highlighting differences in interpretations across different logic texts. Ultimately, the distinction between inference rules and tautologies remains a point of contention in the discussion.
  • #31
solakis said:
I hope you realize if we say 3+5=7 the whole of mathematics collapses
I think saying Mathematics "collapses" is a bit too strong a statement. After all we don't know everything. Your example is oversimplified but it has often happened that someone has made a statement that has been accepted for centuries only to have it be disproven later on. (Admittedly I don't know of any examples of this in Mathematics...I primarily do Physics.) A false statement obviously needs to be fixed but if we don't know it's false the structure of Mathematics remains.

-Dan
 
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  • #32
No rules the Universe-PYTHAGORAS 26 centuries ago
God gave us the Nos everything else is human invension- KRONECKER nearly 130 years ago
 
  • #33
solakis said:
No rules the Universe-PYTHAGORAS 26 centuries ago
God gave us the Nos everything else is human invension- KRONECKER nearly 130 years ago
Do you have a point?

-Dan
 
  • #34
No is ashort writing for Number
Sorry i don't get your question
I simply mentioned famous sayings about Nos
 

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