When using natural language in a domain of a special discipline, which is fundamentally based on its use (for example, language of law), we are led on the one hand by the need for precision and unambiguity and on the other hand by the need for brevity and efficiency. A specific semantic problem for texts expressing a system of normative rules for the regulation of actions is the question of their efficient applicability in new situations. Herbert Hart came up with a suggestion on how to solve these dilemmas in the field of law and was loosely inspired by the theory of open texture of concepts. He saw the solution in an inevitable defeasibility of a rule, which, in his view, is caused by the open texture of the goal pursued by the rule. However, extensive use of the instrument of open texture of a concept or a rule can be fuel for the fire of subjectivism in semantic practice. It is necessary to distinguish the phenomenon of open texture of concepts from the polysemy of natural language expressions and the phenomenon of so-called privative modification. Applicative flexibility and effectiveness of normative theory is aided by a more appropriate generality of concepts, which is achieved, for example, by recodification of law, rather than by artificially extending the scope of concepts on the basis of their fuzziness.

The critique of logic, as it was taught on the British Isles, intensified at the beginning of the 19th century. A systematic critique of Aristotelian (syllogistic) logic was undertaken from the standpoint of common sense philosophy chiefly by Scottish philosophers, followers of T. Reid. E. Copleston of Oxford came to logic's defense. His student, R. Whately, later wrote the textbook Elements of Logic (1826), in which he replied to the objections of Scottish philosophers. The textbook correctly explains that systems of deductive logic need not suffer from the petitio principii fallacy. J. S. Mill at first wrote a positive review of the textbook, but later published his System of Logic. In it, he puts forward the contrary view when evaluating the role of Aristotelian (deductive logic), objecting to the supposedly irredeemable fallacy of petitio principii. The fallacy can be avoided, he argues, in an inductive logic proposed by him. Mill's objection to the Aristotelian syllogism was based on a misunderstanding of the analytic novelty of the knowledge contained in the conclusion of a valid argument. Mill's explication of logic is contradictory, based on an associative psychologism and sensualism. The objection against deductive logic is simply mistaken. Mill's logic and his positions were very critically appraised already by S. Jevons and the standard overviews of the history of logic fail to mention it.

Counterpossible conditionals are a special kind of conditionals whose antecedents are necessarily false (impossible). There has been a long-standing debate about their nature. According to the supporters of the orthodox view (Lewis, Stalnaker, Williamson and others), they are only trivially or vacuously true. Opponents of the orthodox view (Berto, Jago, Sendłak, Kocurek and others) do not agree with such a position, and according to them, some counterposible conditionals are true (and informative) also in a specific sense. We analyzed some "non-intuitive" arguments of classical logic as precursors to counterpossible conditionals. We demonstrated that these arguments are correct in propositional and predicate logic. Their non-intuitiveness becomes evident only when we accept the tacit assumptions that are imposed by the content of the premises and conclusions. The components of the premises and conclusions of such arguments are enthymemes of other "sub-arguments", and their non-intuitiveness is based on the factual falsity of the disjunctively connected components of the conclusions as abbreviations of two incorrect arguments. In order to explain the truth of counterfactuals and the validity of the rules of classical logic in this context, it is necessary to assume the validity of the comparative and eliminative principle of ceteris paribus. We used the same methodology for counterpossible conditionals and explained why some conceptual or mathematical counterposesible conditionals are non-trivially true and others are not. It is decided by the acceptance of tacit assumptions that are in accordance with the explicit assumptions, and the validity of the comparative and eliminative principle of ceteris paribus. Finally, we showed why logically counterpossible conditionals cannot be non-trivially true: we cannot support them with other tacit logical truths in order to make them true.

The paper starts by briefly describing the so‐called truth‐functional approach to sentential operators, typical to logic, as opposed to the more multi‐faceted approach of linguistics. The latter reflects the more complex, substantial relations between the contents of utterances, emphasizing the logico‐semantical relations and functions of sentential operators. However, as an alternative to the pragmatically inclined critique of the truth‐functional approach, the paper proposes two possible directions of explaining the specific content of sentential operators by virtue of which they transcend the role of mere truth functions. Firstly, the paper summarizes our previous investigations into the interactions between sentential operators and (1) the vector of the course of events described by a compound sentence, and (2) the direction of grammatical time captured by a compound sentence. The paper focuses on how this interaction is coordinated with the particular epistemic goal (prediction, explanation etc.) pursued when using the meaning of a complex sentence. Using the concepts of necessary and sufficient conditions, and by characterizing the vectors of condition (the if‐vector), time and relevance (dominance or the epistemic vector), the paper demarcates the rules of correspondence for conditional operators as cases of combinatorics, as described by some linguists. Secondly, based on a distinction between different constructions the same operators as truth‐functions, the paper provides a logico‐semantical explanation of the specific meaning of the else, unless and although connectives, traditionally discussed by linguists. We believe that the extensions proposed here move the camp defending a logico‐semantic approach to sentential operators at least somewhat closer to the camp of linguistic investigation.

The similarity between logic and semantics of the Stoics and Frege has long been known, and it can be explained in various ways. In 2021, Susane Bobzien published a work in which she explains this similarity rather surprisingly: she hypothesizes that Frege generously helped himself with the foundations of Stoic logic as it was published in the first volume of History of Logic in the West by Carl Prantl. However, this hypothesis encounters various problems. The key point of the whole accusation is founded on the formulation of a general proposition in language using implication and anaphora, which Frege supposedly took from the Stoics, although in Prantl's text there is only one example of a sentence with this structure. On the contrary, there are many examples of such sentences in contemporary professional (e.g. legal) texts. Many examples of semantic similarities that Bobzien presents are based only on the similarities between isolated concepts; however, that is regularly the case for such concepts with the same conceptual basis. Bobzien presents a significant number of matches only on the basis of results that could allegedly be inferred from the texts. However, this cannot be considered a proof of plagiarism. Bobzien does not consider many sources for the continuity of interpretation such as the so-called hypothetical syllogism found in available textbooks of logic. Last but not least, her claims do not consider many differences between Stoic and Frege's logic. All this leads us to the conclusion that Bobzien does not present sufficient facts and connections between them that would confirm her hypothesis about Frege's plagiarism of the Stoic logic: Frege simply was not a plagiarist.