Mostofa Nazmul Mansur

'Paradoxes of material implication' is a significant topic in modern symbolic and mathematical logic. Various attempts have been taken to resolve these paradoxes. Thus, a number of schools of logic have been developed in this regard. In our present paper we examine three of the main schools of modern logic which deal with these paradoxes: many valued logic, modal logic and relevance logic. Three-valued logic, which is a kind of many-valued logic, fails to show any promise in resolving these paradoxes as it adopts the entire truth table based on traditional bivalence. Five-valued logic, another kind of many-valued logic, shows some promises in resolving these paradoxes. But it destroys the system of propositional calculus and the process of judging the validity/invalidity of arguments. So it is difficult to accept this solution with such a price. Modal logic, the second approach discussed in this paper, resolves these paradoxes by introducing the device of strict implication. But the problem is that it creates some new paradoxes, namely paradoxes of strict implication, which are analogous to the paradoxes of material implication. Hence modal logic is also not adequate. Relevance logic, however, resolves these paradoxes without creating any new paradox. It does not destroy the system of propositional calculus or the process of judging the validity/invalidity of arguments. Hence, relevance logic solves the problems of the logic of implication. Although there are some minor difficulties in relevance logic, we hope that more work in this area will resolve these problems soon, so that relevance logic will provide a fully adequate logic of implication.

This paper examines Emmanuel Levinas’ ethics of responsibility, grounded in his concepts of Otherness and the face-to-face relation, and compares it with Alain Badiou’s critique and alternative ethical vision. For Levinas, ethics does not arise from universal principles or intentional consciousness, but from the asymmetrical demand of the Other—whose face calls us to an infinite responsibility that comes before thought or choice. The ethical subject (the Same) is not autonomous, but is summoned into responsibility by the undeniable presence of the Other’s vulnerability. Badiou, however, challenges this view. He sees Levinas’ ethics as overly focused on passive victimhood and as lacking engagement with historical truth and action. For Badiou, ethics comes not from compassion but from fidelity to truth-events—disruptive acts that break with the existing order and call for active participation in creating change. In his view, the ethical Same becomes a subject of history by doing good through commitment to truth, not by simply witnessing suffering. This paper explores the strengths and limitations of both thinkers, arguing that while Levinas highlights the deep ethical demand of the Other, Badiou presents a more activist and dynamic vision of ethical agency. The paper suggests that Badiou’s approach may be more effective when confronting injustice or striving to build a more just world.

Hard incompatibilism is a view which asserts that determinism and free will are inconsistent and given the facts of our best sciences determinism is true; and hence, free will does not exist. Not only that, it also claims that if the world were indeterministic and our actions were caused by states or events, still we would lack free will. In this way, it denies the truth of any libertarian account of free will based on event causation. In that sense, this is a hard position. Regarding moral responsibility, this hard incompatibilism claims that human agents are not morally responsible for their actions, unless they are the ultimate originators (agent-causes) of the actions in question. Derk Pereboom has offered an argument in favor of his hard incompatibilism, aka hard determinism, in which he shows four different hypothetical situations (thought experiments, indeed) each of which is aimed to prove that we are not morally responsible for what we do. The argument is, thus, known as four-case argument. In the present paper, Pereboom’s four-case argument is examined and defended. It has been shown here that Pereboom is quite correct, if we consider the true sense of the term ‘moral responsibility.’ This ‘true sense’ of the term “moral responsibility” is considered as the strong sense of moral responsibility in this paper. However, a weak sense of the term “moral responsibility” has also been proposed in this paper. This proposed weak sense of “moral responsibility” can accommodate most of the socially-approved ways of ascriptions of responsibility. And finally, it has been claimed that our general intuition that every event has a cause and we are not the ultimate sources of our actions is true from the strong sense of moral responsibility; and our commonsense intuition that as human beings we are inherently free and responsible for our actions is true from the weak sense of moral responsibility.

Defenders of the Kantian maxim, i.e. ‘ought’ implies ‘can’, defend the maxim taking the term “implication” in the sense of ‘entailment’. But if it is granted that “implication” means entailment, then it can be shown that the Kantian maxim that ‘ought’ implies ‘can’ is false. Sinnott-Armstrong attempts to prove the falsity of the maxim by his argument from Self-Imposed Impossibility in which he offers his famous example of Adams. But Sinnott-Armstrong’s example of Adams appears to be not strong enough to prove the falsity of the maxim; it is a subject to be captured by a version of the maxim, namely the Maxim-KT. That is why two new examples of the argument from Self-Imposed Impossibility are presented in this paper which are stronger and are able to prove the falsity of the Kantian maxim.

Despite its enormous popularity, Russell’s theory of definite descriptions has received various criticisms. Two of the most important objections against this theory are those arising from the Argument from Incompleteness and the Argument from Donnellan’s Distinction. According to the former although a speaker may say something true by assertively uttering a sentence containing an incomplete description , on the Russellian analysis such a sentence expresses a false proposition; so, Russell’s theory cannot adequately deal with such sentences. According to the latter objection a descriptive sentence is actually ambiguous—it expresses a general proposition when the description contained in it is used attributively, and a singular proposition when the description in question is used referentially; Russell’s theory is inadequate as it fails to capture this ambiguity and offers an analysis according to which a descriptive sentence expresses only a general proposition. These objections are examined in the present dissertation. It is shown here that these objections arise from: (i) ignoring the distinction between the meaning of a sentence and the assertions made by using it, (ii) the failure to distinguish between the semantic meaning of a sentence and the pragmatic meaning with which it is used on a particular occasion. To make the distinction mentioned in (i), a significant part of Scott Soames’ theory concerning meaning and assertions has been adopted in this dissertation; and, to make the distinction mentioned in (ii), a test, namely the cancellability test, and two Distinguishing Criteria, namely DC-1 and DC-2, have been developed here. It has been argued here that if we properly make the relevant distinctions, then we will find that: (a) the phenomenon cited by the Argument from Incompleteness can be well explained keeping the Russellian analysis of descriptive sentences intact, (b) the phenomenon arising from the Argument from Donnellan’s Distinction raises an issue of pragmatics and is irrelevant to Russell’s semantic analysis of descriptive sentences. So, none of the above criticisms poses a genuine threat to Russell’s theory of definite descriptions; his theory actually provides, to a large extent, a correct semantic analysis of descriptive sentences.