Final answer:
The statement is false, as it is possible for two sentences to have the same truth value without being logically contradictory, making them jointly satisfiable. The noncontradiction principle and the evaluation of propositions and evaluative sentences play a role in assessing statements' truth values. Joint satisfiability focuses on logical compatibility rather than having identical truth values.
Step-by-step explanation:
The claim that if there is no valuation for two sentences on which both sentences have the same truth value, then these sentences are not jointly satisfiable, is false. It is possible for two sentences to have the same truth value and still be satisfiable in some valuation. For instance, the sentences “Snow is white” and “The sky is blue” can both be true independently of one another, making them jointly satisfiable. The crucial factor is whether the sentences contain a logical contradiction. The principle of noncontradiction states that contradictory statements cannot both be true in the same sense at the same time.
Sentences that express propositions are claims that we judge to be true or false based on knowledge we acquire through various means. Evaluative sentences, which express an evaluator's opinions, are different in that they do not simply have truth values unaffected by human thought. Here, the concern is over the quality or value of something rather than factual accuracy.
In philosophy, particularly in the study of knowledge and logic, we often assess the validity of claims based on certain rules. For example, the no false premises rule means a valid conclusion cannot be derived from false premises. However, the original statement conflates two distinct scenarios: same truth values and joint satisfiability. The latter requires compatibility in a logical sense, not necessarily identical truth values.