Is modus ponens a tautology? - Mathematics Stack Exchange
2018年8月26日 · Modus ponens isn't that formula or any formula (and thus not a tautology), it's a rule. A rule tells you one way of building a proof. A rule tells you one way of building a proof. In fact, rules are part of the definition of what a proof is 1 (for a given logical system).
logic - Modus Ponens Proof - Mathematics Stack Exchange
2014年9月24日 · the Modes Ponens is this statement: (((P => Q) & P) => Q) And that statement should, at the end (i.e., in the last column of the last Q, be TRUE for all truth values of P and Q, and it will). Do the truth table for the above statement
Modus ponens as a rule of inference vs. tautology
2018年9月2日 · As I stated in my previous answer, the rule modus ponens is part of the definition of many common proof systems. Let HPC stand for Hilbert's system for classical propositional logic whose only rule of inference is modus ponens and whose axioms are listed here after Frege's. This is a well-defined mathematical object.
Modus Ponens vs implication? - Mathematics Stack Exchange
2020年8月1日 · While it is true that there is a great similarity between the first and last concepts it is perhaps best to think of modus ponens as living in the syntactic side of logic (where we deal only with strings of "meaningless" symbols), while logical implication lives on the semantic side (where we speak of truth in models).
Why is modus ponens a valid form? - Mathematics Stack Exchange
2021年6月23日 · $\begingroup$ Your example is not a correct application of the inference rule called modus ponens. So no, it does not provide a counterexample and modus ponens is completely valid and is used extensively in both formal and natural language. Please study my answer and the comments below your question more carefully. $\endgroup$ –
Dictionary Meaning of "Modus Ponens" and "Modus Tollens"
2020年2月12日 · Wikipedia says that modus ponens is Latin for "mode that by affirming affirms" and that modus tollens is Latin for "mode that by denying denies". Now, English is not my first language, but I understand it enough and these definitions still don't make sense.
Can I prove that for $c\\neq0$, if $cV=0$ then $V=0$ with modus …
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propositional calculus - Prove modus ponens for set of formulas …
It turned out that in order to talk about conditional syntactic consequence $\Gamma\vdash\psi$, we need to define $\vdash$ based on sequences of formulas that are proofs, and use a derivation rule of modus ponens $\{\psi,\psi\rightarrow\varphi\}\vdash\varphi$ which is based on the semantic consequence, especially on $\{\psi,\psi\rightarrow ...
logic - Can operations such as Modus Ponens be applied to …
2021年8月19日 · Well, for something like Modus Ponens, it turns out that yes, you can generalize it to the the following rule, which we might call 'Embedded Modus Ponens'): If you know the truth of some statement $\varphi$, and you have some other statement that contains $\varphi \to \psi$ as a component statement, then you can infer the statement that has ...
logic - Is McGee's counterexample to Modus Ponens accepted by …
It doesn't immediately follow that modus ponens is invalid (in the sense of being non-truth-preserving), but that does follow given some fairly plausible bridge principles about rationality and truth. Maybe we should give up on those principles rather than the validity of (ordinary language) modus ponens, but that's still an interesting result.