Are the inference rules of propositional calculus tautologies?

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SUMMARY

The discussion centers on whether the inference rules of propositional calculus, specifically Modus Ponens, are considered tautologies. Participants assert that Modus Ponens is a ternary relation on formulas and not a formula itself, thus not a tautology. However, references from "Introduction to Logic" by Irving Copi and "Introduction to Logic" by Patrick Suppes are cited, which classify Modus Ponens as a tautology. The debate highlights the distinction between inference rules and tautologies, emphasizing that while Modus Ponens is a well-formed formula, it is not categorized as a tautology.

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  • #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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