Logic and Elements. (Premises and Conclusions: Symbolic Logic for Legal Analysis).

We may happily agree with Holmes that logic is not the life of the law\u27 and yet contend that logic should play a significant role in legal discourse. Logic cannot demonstrate the truth of premises, and so by itself it cannot demonstrate the merits of a legal argument. Moreover, even given the premises, it may be that a leap of faith, or intuition, has an irreducible role at least in some good legal arguments.2 But at least a sound legal argument will not be an illogical one. An argument will not be persuasive if it appears to violate basic principles of logic. If the enunciation of a principle of law is to have any hope of stability it must be capable of consistent application in situations that are materially similar, and if the articulation is not logically coherent this condition is unlikely to prevail. In this paper, I will explore the use of symbolic logic in discussing the notion of elements of a claim or a defense. I will use the term claim in a general sense, referring not only to the grounds underlying an action-what is asserted in a complaint or charging instrument- but also to any demand forjudicial relief. Thus, I will speak of a claim for preliminary relief or for discovery sanctions. In Part I, I will suggest that the attempt to state a legal argument by setting out the elements of the claim or the defense symbolically can often assist the quest for clarity. In Part U, I will explore some of the limits of this technique, showing that in some cases the very notion of the elements of a claim or a defense breaks down. In Part Im, I will suggest the outlines of a logic for legal argument that operates defeasibly and so is significantly different from the classical logic presented vividly and engagingly in a wonderful new text, Premises and Conclusions, by Robert Rodes and Howard Pospesel.

Logic and Elements. (Premises and Conclusions: Symbolic Logic for Legal Analysis).

We may happily agree with Holmes that logic is not the life of the law\u27 and yet contend that logic should play a significant role in legal discourse. Logic cannot demonstrate the truth of premises, and so by itself it cannot demonstrate the merits of a legal argument. Moreover, even given the premises, it may be that a leap of faith, or intuition, has an irreducible role at least in some good legal arguments.2 But at least a sound legal argument will not be an illogical one. An argument will not be persuasive if it appears to violate basic principles of logic. If the enunciation of a principle of law is to have any hope of stability it must be capable of consistent application in situations that are materially similar, and if the articulation is not logically coherent this condition is unlikely to prevail. In this paper, I will explore the use of symbolic logic in discussing the notion of elements of a claim or a defense. I will use the term claim in a general sense, referring not only to the grounds underlying an action-what is asserted in a complaint or charging instrument- but also to any demand forjudicial relief. Thus, I will speak of a claim for preliminary relief or for discovery sanctions. In Part I, I will suggest that the attempt to state a legal argument by setting out the elements of the claim or the defense symbolically can often assist the quest for clarity. In Part U, I will explore some of the limits of this technique, showing that in some cases the very notion of the elements of a claim or a defense breaks down. In Part Im, I will suggest the outlines of a logic for legal argument that operates defeasibly and so is significantly different from the classical logic presented vividly and engagingly in a wonderful new text, Premises and Conclusions, by Robert Rodes and Howard Pospesel.

Why was Alchourrón afraid of snakes?

In the last papers published by Alchourrón, he attacked non-monotonic logics, which he considered philosophically unsound for the representation of defeasible reasoning. Instead of a non-monotonic consequence relation, he proposed a formal representation of defeasibility based on an AGM-like revision of implicit assumptions connected to the premises. Given that this is a procedure to generate non-monotonic logics, it is not clear, from a mathematical standpoint, why he was so suspicious of such logics. In the present paper we try to answer this question based on Alchourrón' s convictions about epistemology, particularly the epistemology of law. We also propose another revision operator on theories called refinement, which provides a faithful representation of the sort of epistemic change considered by Alchourrón as intrinsic to defeasibility.En sus últimos escritos publicados, Alchourrón desarrolló un ataque contra las lógicas no-monotónicas, que consideraba filosóficamente inadecuadas a la representación del razonamiento derrotable. En vez de una relación de consecuencia no-monotónica, él propuso una representación formal de la derrotabilidad basada en un modelo de revisión (tipo-AGM) de las asunciones implícitas ligadas a las premisas. Dado que éste es un procedimiento para generar lógicas no-monotónicas, no está claro -en el nivel matemático- por qué él era tan desconfiado de tales lógicas. En el presente texto intentamos contestar a esta pregunta basados en las convicciones de Alchourrón sobre epistemología, particularmente la epistemología jurídica. También proponemos otro operador de revisión aplicado a las teorías, llamado refinamiento, que proporciona una representación fiel de la especie de cambio epistémico considerado por Alchourrón como intrínseco a la derrotabilidad

Hierarchical Trade and Endogenous Price Distortions

We study the allocation of commodities through a two-stage hierarchy of competitive markets. Groups or countries trade at global prices while individuals within a group trade at local prices. We identify the free trade and the autarky equilibrium as polar cases. We show that no other two-stage market equilibria exist if the commodity space is two-dimensional. An example demonstrates that other, so-called intermediate equilibria exist for three-dimensional commodity spaces. The example also exhibits endogenous price distortions in third countries when some countries follow distortionary trade policies. We give two existence proofs for intermediate equilibria in higher dimensions. Each proof provides an explicit construction of special classes of intermediate equilibria.

Taxes, Status Goods, and Piracy

This paper studies the design of indirect redistributive taxation and of corrective taxation, as well as the formation of equilibrium indirect tax policies via a political process, in the presence of status goods, allowing for the possibility that illegal copies of those goods may be purchased on black markets (the phenomenon of "piracy"). Heavy taxation of status goods, despite the fact these are typically overconsumed, is not particularly favoured in a social welfare maximisation context, because the tax rate is highly distortionary, due to the presence of piracy. Corrective taxation, aimed at remedying the inefficiencies associated with the consumption externalities generated by the status goods, is made ineffective by piracy. In contrast with the normative results, the median voter model predicts an inefficiently large tax rate on status goods when piracy is widespread.social status, indirect taxes, corrective taxes, median voter, piracy

A Unifying Field in Logics: Neutrosophic Logic.

The author makes an introduction to non-standard analysis, then extends the dialectics to “neutrosophy” – which became a new branch of philosophy. This new concept helps in generalizing the intuitionistic, paraconsistent, dialetheism, fuzzy logic to “neutrosophic logic” – which is the first logic that comprises paradoxes and distinguishes between relative and absolute truth. Similarly, the fuzzy set is generalized to “neutrosophic set”. Also, the classical and imprecise probabilities are generalized to “neutrosophic probability”

Defeasibility and Balancing

“Defeasibility” and “balancing” are expressions introduced in recent times to deal with long-standing legal phenomena, which in the context of the constitutional state acquire a special prominence. What is at issue, in fact, is the necessity to recognise exceptions implicit in the norms, in order to provide the legal system with the flexibility needed to maximise the chances of finding a correct—just—answer without abandoning the legal system; and (which to a large extent is another aspect of the same phenomenon) to resolve difficult cases (those for which there is no predefined rule, but only principles) argumentatively, by resorting to a procedure, balancing, the use of which does not necessarily imply an exercise in arbitrariness, although it does involve certain risks that recommend a prudent and limited use of this resource. The last part of the paper summarises the ideas that legal theorists and practitioners should bear in mind in order to understand and make proper use of these two controversial but indispensable notions