Socrates

.a modus ponens argument with all true premises valid but not sound strong but not cogent sound cogent invalid

A modus ponens argument, with all true premises, is indeed a valid one. Validity in logic refers to the structure of an argument, where the conclusion follows necessarily from the premises. However, validity alone does not guarantee the truth of the conclusion, which brings us to the distinction between validity and soundness. Soundness requires not only a valid argument but also that all premises are true. In this case, a modus ponens argument with all true premises would be both valid and sound, thus fulfilling the criteria for a strong and cogent argument. However, it is essential to recognize that strength and cogency are not synonymous. A strong argument is one where the premises provide strong support for the conclusion, while a cogent argument goes further by also ensuring that the premises are true. Thus, a valid argument can be strong but not cogent if the premises are not true. In conclusion, the distinction between validity, soundness, strength, and cogency highlights the complexities and nuances of constructing a logically sound and persuasive argument."