Cheng-Chih Tsai

The truth table method, natural deduction, and the truth tree method, the three validity proving methods standardly taught in an introductory logic course, are too clumsy for the battlefield of real-life. The “short truth table” test is handy at times, but it stumbles at many other times. In this paper, we set up a general method that can beat all the methods mentioned above in a contest of speed. Furthermore, the procedure can be step-by-step paraphrased in a natural language, so that, unlike the other methods, a real-life logical problem can be analyzed and explained in a real-life language too.

In this paper, we claim that Jesus’ command “Love your enemies” is compatible with the fact that (1) for a group of Cooperators and Defectors repeatedly playing the Prisoner’s Dilemma game with each other, Defection will be the dominant strategy, and (2) the Tit-For-Tat strategy, a variant of the Eye-For-Eye principle that Jesus refuted in his Sermon on the Mount, had won Robert Axelrod’s tournaments of Iterated Prisoner’s Dilemma game in the 1980s. By incorporating relevant biblical commands into an informed cooperative strategy, we find that it itself is a strong contender in a secular world of social evolution.

In response to recent debates on the need to abandon the Dead Donor Rule (DDR) to facilitate vital-organ transplantation, I claim that, through a detailed philosophical analysis of the Uniform Determination of Death Act (UDDA) and the DDR, some acts that seem to violate DDR in fact do not, thus DDR can be upheld. The paper consists of two parts. First, standard apparatuses of the philosophy of language, such as sense, referent, truth condition, and definite description are employed to show that there exists an internally consistent and coherent interpretation of UDDA which resolves the Reduction Problem and the Ambiguity Problem that allegedly threaten the UDDA framework, and as a corollary, the practice of Donation after the Circulatory Determination of Death (DCDD) does not violate DDR. Second, an interpretation of the DDR, termed ‘No Hastening Death Rule’ (NHDR), is formulated so that, given that autonomy and non-maleficence principles are observed, the waiting time for organ procurement can be further shortened without DDR being violated.

If to be is to be the value of a bound variable, then the acknowledgment and denial of the existence of chairs amounts to a serious disagreement about the range of a quantifier. However, by resorting to the intrinsic hierarchical structure of hi-world semantics, we find that the varying of domains from worlds to worlds can actually be accommodated within a unified framework. With the introduction of a universal domain D of hi-individuals and an existence predicate E that serves as a realization operator, a new semantics for quantified modal logic is proposed. It allows individual variables to range over individuals in different levels of a hi-world, and is indifferent to the ontological debate about the existence of chairs.

It is commonly held that killing is morally wrong and that the killers need to be punished, and in marginal cases where killing seems justifiable, we are advised to resort to the ethics of killing for general guidance. It is also commonly held that the notion of killing per se is accountable in terms of ‘causing death’, which is a metaphysical (or even physical) issue, having nothing to do with ethics. However, this dichotomy – between the ethics of killing and the metaphysic of killing – is questionable and we claim that the notion of killing itself presumes a social norm, which generally involves ethical considerations. This explains why there has been much debate concerning the distinction between killing and letting die. According to the account of killing that shall be proposed in this article, the distinction is based on a social norm rather than a metaphysical reality. Likewise, there is no metaphysical ground for an active-killing/passive-killing distinction. With the help of a value-time diagram that captures a key feature of a genuine act of killing, six classic scenarios in the ethics of killing are analyzed within the same framework. The prominent feature of this approach is that no physical action is an act of killing before the imposition of a social norm.

In Lowe (1995), instead of endorsing a Stalnaker/Lewis-style account of counterfactuals, E. J. Lowe claims that a variation of C. I. Lewis’s strict implication alone captures the essence of everyday conditionals and avoids the paradoxes of strict implication. However, Lowe’s approach fails to account for the validity of simple and straightforward arguments such as ‘if 2=3 then 2+1=3+1’, and Heylen & Horsten (2006) even claims that no variation of strict implication can successfully describe the logical behavior of natural language conditionals. By incorporating the German logician O. Becker’s modal intuition with the insight of Ramsey’s Test, we show that there does exist a unified, strict-conditional based account of everyday conditionals, which withstands all attacks previously raised against truth-conditional accounts of conditionals. Furthermore, a subtle distinction between autistic and realistic readings of the indexical ‘I’ involved in a conditional helps us resolve a recent debate concerning the Thomason conditionals.

In The Logical Basis of Metaphysics, Dummett argues at length that Geach has been wrong in taking the sense of a predicate to be a function that sends the sense of a proper name to that of a sentence, and claims that it should instead be a means to determine the referent of the predicate, as is suggested by Frege’s sense-determines-reference (SDR) principle. This disagreement between Dummett and Geach calls for a serious investigation into two of Frege’s sense-related principles, namely the Compositionality thesis and the SDR thesis. By making precise both theses in terms of supervenience, we pin down a preferable sense of compositionality for senses, and resolve the debate in question.

Common sense has that killing someone amounts to causing the death of someone. This makes killing a physical, biological, or, at best, metaphysical issue, and, as a consequence, the ethics of killing can be dealt with independently of the non-ethical issue of who the killer is. However, in this paper, we show that this is not the case. A physical/biological definition of death plus a metaphysical definition of causation does not exhaust the meaning of killing. Rather, the notion of killing per se generally presumes a notion of default, which often involves ethical considerations.

A Leibnizian semantics proposed by Becker in 1952 for the modal operators has recently been reviewed in Copeland’s paper The Genesis of Possible World Semantics (Copeland in J Philos Logic 31:99–137, 2002 ), with a remark that “neither the binary relation nor the idea of proving completeness was present in Becker’s work”. In light of Frege’s celebrated Sense-Determines-Reference principle, we find, however, that it is Becker’s semantics, rather than Kripke’s semantics, that has captured the true spirit of Frege’s semantic program. Furthermore, for Kripke’s possible world semantics to fit in Frege’s framework of senses , worlds and referents , it will have to be thoroughly reformulated. By introducing the notion of a hi-world into the picture, we manage to keep the key ingredients of Becker’s semantics intact, while at the same time solve a fatal problem that used to shadow Becker’s original semantics—it had not been able to make sense of inhomogeneous modality. The resulting generalized Beckerian semantics provides, in effect, a Beckerian analysis of the Kripkean possible worlds. It reveals the subtle hierarchical internal structure of a Kripkean world that has not been discovered before

In his famous argument for the unreality of time, McTaggart claims that i) being past, being present, and being future are incompatible properties of an event, yet ii) every event admits all these three properties. In this paper, I examine two key concepts involved in the formulation of i) and ii), namely that of “validity” and that of “contradiction”, and for each concept I distinguish a static version and a dynamic version of it. I then arrive at three different ways of formulating McTaggart’s claims that avoid the notorious McTaggart’s Paradox. So long as we demand that McTaggart make clear use/mention and token/type distinctions in his claims, we shall find that it is indeed very difficult for him to get a genuine contradiction from i) and ii).

In ‘What Makes Killing Wrong?’ Sinnott-Armstrong and Miller make the bold claim that killing in itself is not wrong, what is wrong is totally-disabling. In ‘After-Birth Abortion: Why Should the Baby Live?’ Giubilini and Minerva argue for allowing infanticide. Both papers challenge the stigma commonly associated with killing, and emphasize that killing is not wrong at some margins of life. In this paper, we first generalize the above claims to the thesis that there is nothing morally wrong with killing per se, so long as it is instant and unannounced. Then, from the perspective of social evolution, we explain why people refrain from killing others, the general guideline being that it is unadvisable to kill someone with whom you associate a Second Person Perspective (SPP). Finally, drawing from a seminal paper of Press and Dyson on the Iterated Prisoner’s Dilemma, we stress that an SPP without an SP (Second Person), or the other way around, can both lead to unwelcome results.

It is generally believed that, for a one-off Prisoner’s Dilemma game, it is logical to defect. However, both players cooperating is apparently a better choice than both defecting, hence the dilemma. In this paper, by resorting to Ramsey’s Test, Kripke’s possible world semantics, and Stalnaker/Lewis-style account of conditionals, I show that the first horn of the Prisoner’s Dilemma is an unsound argument. It originates from failing to differentiate between a possible world and a possible set of possible worlds and failing to observe that the set of accessible possible worlds associated with a possible world in general varies from conditional to conditional. This phenomenon can also be illustrated in terms of the recently developed hi-world semantics. Moreover, a meta-argument is constructed to establish the non-existence of a logical argument for defection.

Concerning the versions of the Tenseless Theory of Time, the Old Btheory has two: the Date-analysis version and the Token-reflexive version, while the New B-theory has three: the Date-analysis, the Token-reflexive and the Sentence-type versions. Each of these five versions of the B-theory has received serious attacks from the A-theorists, some of whom even claim that the tenseless theory “though still widely held, is a theory in retreat” (Craig 1996), and that “if Quentin Smith (1993) delivered the mortal blow to the New B-Theory of Language then Laurie Paul (1997) has written its obituary” (Craig 1999). In this paper, by making more precise some key notions involved in the formulation of a tenseless theory – in particular, two notions of truth conditions, two notions of meaning and two notions of translation are distinguished – I have come up with a single B-thesis for the B-theory. When charitably interpreted, the two versions of the old theory and the three versions of the new theory can all be regarded as special ways of presenting the same B-thesis, and the various A-attacks raised against these versions can then be resolved in a systematic way.

With the advancement of bio-science and bio-technology come nasty new bioethical dilemmas, and some bioethicists have resorted to metaphysics, in particular, the notion of personal identity, to resolve them. I claim, however, that metaphysical accounts of personal identity at present are incapable of withstanding the impact of bioethical dilemmas. Bioethical issues such as criteria of death, brain transplantation, and dementia with/without advance directives invite us to deconstruct three shaky metaphysical notions concerning personal identity so that we can tackle ethical problems more freely and properly. Furthermore, policy makers are advised to be more concerned with a norm or contract that guarantees the long-term welfare of a society of individuals rather than with the pinning down of the identity of a person at the margin of life. In this way, the public can be relieved of a guilt that has been unduly haunting them — when their loved ones were in many ways gone already.