Indeterminacy and Legal Reasoning

We have now mapped the set of analogies Ai,j to conceptual and mechanical meanings. This allows us to recognize how the Group Algebraic System G decomposes into five smaller subsystems, each of which relate to well-known symbolic systems. Furthermore, by recognizing the algorithmic transformations between these subsystems, we can apply each representing a single component of the Group Algebraic System G, or model how algorithms are used in mathematics, by mapping its meaning onto the corresponding transformation steps between the subsystems. (...) Thus, we have transformed a Group Algebraic System G into five simpler subsystems (namely, symbolic analogic, lateral algebraic, calculus of infinity tensors, perturbations in waves, and algorithmic formation of symbols), each of which may also be represented algorithmically. This mapping process serves as a the basis for studying the algebraic machinery used in mathematics and logic to manipulate symbols, such as the classical logical systems or algebraic systems, using algorithms. (shrink)

The topic of exemplarity has attracted considerable interest in philosophy, legal theory, literary studies and art recently. There is broad consensus that exemplary cases mediate between singular instances and general concepts or norms. The aim of this article is to provide an additional perspective on the logic of exemplarity. First, inspired by Jacques Derrida’s discussion of exemplarity, I shall argue that there is a kind of différance between (singular) examples and (general) exemplars. What an example exemplifies, the exemplarity of the (...) example, eludes any fixed identity and follows a logic of supplement. Second, I shall present the so-called logic of exemplarity. The received paraconsistent view has it that the exemplar of X is an X and, at the same time, is not an X. Inspired by Ludwig Wittgenstein’s discussion of the standard metre, I would like to present an alternative paracomplete view whereby we can say of an exemplar of X neither that it is an X nor that it is not an X. (shrink)

The rise of populism and its consequences – such as democratic backsliding, the erosion of constitutional principles, and the weakening of the rule of law – are among the most pressing issues facing comparative constitutional scholars today. To address these emerging challenges, the Unconstitutional Constitutional Amendment Doctrine (UCAD) has emerged as the most promising remedy for the “third counterwave of democracy”. However, a fundamental problem with UCAD is how to apply it effectively without undermining constitutional democracy, as it is often (...) criticised and deemed illegitimate from the perspective of democratic principles. (shrink)

This work is a attempt to describe various braches of mathematics and the analogies betwee them. Namely: 1) Symbolic Analogic 2) Lateral Algebraic Expressions 3) Calculus of Infin- ity Tensors Energy Number Synthesis 4) Perturbations in Waves of Calculus Structures (Group Theory of Calculus) 5) Algorithmic Formation of Symbols (Encoding Algorithms) The analogies between each of the branches (and most certainly other branches) of mathematics form, ”logic vectors.” Forming vector statements of logical analogies and semantic connections between the di↵erentiated branches (...) of math- ematics is useful. It’s useful, because it gives us a linguistic notation from which we can derive other insights. These combined insights from the logical vector space connections yield a combination of Numeric Energy and the logic space. Thus, I have derived and notated many of the most useful tangent ideas from which even more correlations and connections ca be drawn. Using AI, these branches can be used to form even more connections through training of lan- guage engines on the derived models. Through the vector logic space and the discovery of new sheaf (Limbertwig), vast combinations of novel, mathematical statements are derived. This paves the way for an AGI that is not rigid, but flex- ible, like a Limbertwig. The Limbertwig sheaf is open, meaning it can receive other mathematical logic vectors with di↵erent designated meanings (of infi- nite or finite indicated elements). Furthermore, the articulation of these syntax forms evolves language away from imperative statements into a mathematically emotive space. Indeed, shown within, we see how the supramanifold of logic is shared with the supramanifold of space-time mathematically. Developing clean mathematical spaces can help meditation, thought pro- cess, acknowledgment of ideas spoken into that cognitive-spacetime and in turn, methods by which paradoxes can be resolved linguistically. This toolkit should be useful to all in the sciences as well as those bridging the humantities to mathematics. Using our memories as a toolkit to aggregate these ideas breaks down bound- aries between them in a new, exciting way. Merging philosophy and Quantum Mechanics together through the lens of symbolic analogies gives the tools to unravel this mystery of all mysteries. Mathematics thus exists as a bridge al- beit a complex one between the two disciplines, giving life to a composite art of problem-solving. Furthermore, mathematics yields to millions of other applications that are potentially limited only by our imagination. From massive data sets used for predictive analytics to emerging fields in medicine, mathematics is an energy and force at the center of possibilities. The power of mathematics to help manage life exists in its ability to shape and model the world in which we live and interact with one another. In conclusion, mathematics is a powerful tool that creates bridges and con- nections between many disciplines and serves as a powerful form of analytical data consumption. It provides language-rich bridges from which to assemble vast fields of theoretical investigations and create groundbreaking innovations. As we approach new horizons in the technology timeline, mathematics will con- tinue to be a powerful driver of creativity and progress. (shrink)

The use of AI algorithms in criminal trials has been the subject of very lively ethical and legal debates recently. While there are concerns over the lack of accuracy and the harmful biases that certain algorithms display, new algorithms seem more promising and might lead to more accurate legal decisions. Algorithms seem especially relevant for bail decisions, because such decisions involve statistical data to which human reasoners struggle to give adequate weight. While getting the right legal outcome is a strong (...) desideratum of criminal trials, advocates of the relational theory of procedural justice give us good reason to think that fairness and perceived fairness of legal procedures have a value that is independent from the outcome. According to this literature, one key aspect of fairness is trustworthiness. In this paper, I argue that using certain algorithms to assist bail decisions could increase three diferent aspects of judges’ trustworthiness: (1) actual trustworthiness, (2) rich trustworthiness, and (3) perceived trustworthiness. (shrink)

This paper advocates for a general policy of penal leniency: judges should often sentence offenders to a punishment less severe than initially preferred. The argument’s keystone is the relatively uncontroversial Minimal Invasion Principle (MIP). MIP says that when more than one course of action satisfies a state’s legitimate aim, only the least invasive is permissibly pursued. I contend that MIP applies in two common sentencing situations. In the first, all sentences within a statutorily specified range are equally proportionate. Here MIP (...) applies directly. In the second, judges reasonably believe that one of the sentences within the range is the most proportionate, but can’t identify it with any certainty. In these cases of sentencing uncertainty, judges must be indifferent between their preferred sentence and a softer one, and this indifference triggers MIP. MIP thus frequently mandates some degree of leniency. I conclude with some comments on statistical uncertainty. (shrink)

Reasoning by default is a relevant aspect of everyday life that has traditionally attracted the attention of many fields of research, from psychology to the philosophy of logic, from economics to artificial intelligence. Also in the field of law, default reasoning is widely used by lawyers, judges and other legal decision-makers. In this paper, a philosopher of language (Carlo Penco) and a philosopher of law (Damiano Canale) attempt to explore some uses of default reasoning that are scarcely considered by legal (...) theory. In particular, the dialogue dwells on the notion of literal meaning, witness testimony, and the problem of disagreement among experts in legal proceedings. The paper is intended as a sort of brain storming useful to identify new lines of research straddling philosophy of law, cognitive psychology and philosophy of language. (shrink)

An annotated bibliography of legal epistemology.

This article juxtaposes a jurisprudential thesis and a practical problem in an attempt to gain critical insight into both. The jurisprudential thesis is Dworkin’s rights thesis. The practical problem revolves around judicial resort to the floodgates argument in civil adjudication (or, more specifically, a version of this argument focused on adjudicative resources, which is dubbed here the FA). The analysis yields three principal observations: (1) Judicial resort to the FA is discordant with the rights thesis. (2) The rights thesis is (...) instructive in one way but mistaken in another. While Dworkin has highlighted some valid and sound reasons against judicial policymaking, his conclusive exclusion of judicial policymaking from civil law adjudication is erroneous. Civil law adjudication, it is argued, is an arena of ineliminable tension between principle and policy. (3) The FA is a type of policy argument particularly vulnerable to objections against judicial policymaking. There should, therefore, be a (rebuttable) presumption against judicial resort to it. (shrink)

Recension de la traduction française de l'ouvrage de F. Schauer, Penser en Juriste, Dalloz, 2018.

It causes many difficulties for jurisprudence to define the notion of judicial activism. At the very beginning it had rather a journalistic character, but but over time it has become a serious charge against these judges who act on the basis of their vision of what the law ought to be like rather than what it actually is like. On the ground of the polish legal theory the echoes of the dispute about judicial activism are reflected in the discussions about (...) the nature of legal interpretation. Transposing the problem of activism into the problem of interpretation allows the use of analysis tools that were previously unavailable. One of these tools are concepts emerged on the neopragmatist philosophy of Stanley Fish. Fish tries to describe the nature of the interpretation in the context of reader-response criticism and the concept of interpretive communities. Application of Fish's philosophy in the field of legal theory provides constructive conclusions about the concepts of judicial activism and judicial law-making. (shrink)

„O pełnej znajomości prawa można mówić tylko wówczas, gdy zna się prawo i wytworzone przez praktykę reguły posługiwania się nim” – pisał swego czasu Marek Zirk-Sadowski. Pogląd ten wiąże się z niezwykle istotnym sporem o kryterium poprawności dokonywanej przez sędziów wykładni prawa. Zlokalizowanie takiego kryterium wydaje się być szczególnie ważne choćby ze względu na zawartą w naszym systemie prawnym konieczność realizowania zasady trójpodziału władzy, zgodnie z którą w procesie stosowania prawa nie może dochodzić do tzw. kryptoprawotwórstwa. Celem niniejszego tekstu jest (...) zaprezentowanie wybranych koncepcji poprawności wykładni prawa oraz ich krytyka w świetle neopragmatyzmu Stanley'a Fisha, filozofa prawa oraz profesora literaturoznawstwa, którego głównym przedmiotem refleksji był problem interpretacji. Filozofia amerykańskiego neopragmatysty opiera się na dwóch koncepcjach: reader-response criticism i wspólnotach interpretacyjnych. Reader-response criticism polega na skupieniu się na afektywnym aspekcie procesu interpretacji, uznając czytelnika za kluczową instancję tego procesu; koncepcja wspólnot interpretacyjnych z kolei ma wytłumaczyć, dlaczego podmiot interpretuje w taki a nie inny sposób. Zaproponowana przez Fisha metoda pozwala uznać, że de facto jedynym możliwym kryterium poprawności wykładni są inne decyzje sędziowskie. W świetle powyższych uwag wydaje się zasadnym stwierdzenie, że podejście Fisha umożliwia pogłębienie refleksji na temat jednej z kluczowych kwestii zarówno dla praktyki jak i teorii prawniczej, tj. poprawności wykładni prawa. (shrink)

This paper argues that several sorts of metaphysical and semantic indeterminacy afflict the causal relation. If, as it is plausible to hold, there is a relationship between causation and moral responsibility, then indeterminacy in the causal relation results in indeterminacy of moral responsibility more generally.

This paper challenges the Critical Legal Studies (CLS) claims of legal indeterminacy. It shall use a legal formalist logic and language as its main assertion, further maintaining that the CLS claims is only grounded in ambiguity and confusion. CLS is a legal theory that challenges and overturns accepted norms and standards in legal theory and practice. They maintained that law in the historical and contemporary society has an alleged impartiality, and it is used as a tool of privilege and power (...) – law is politics. Consequently, CLS maintained that these results to indeterminacy of law. Legal indeterminacy can be summed up as contrary to the common understanding that legal materials, statutes and case law, do not really answer legal disputes. Legal principles and doctrines, as CLS scholars claim, are said to be indeterminate, for it is riddle with gaps, conflicts, and anomalies that are widely present even in simple cases. Legal indeterminacy also rises because of the underlying political power – law is politics – that implicates law as merely a tool for oppression. This thesis shows that CLS assertions with legal indeterminacy is only grounded on ambiguity. On one hand, using the main concept of legal formalist logic and language grounded with sub-arguments: inherent generality of legal language, reasoned elaboration, and neutral principles, it refutes the CLS claims of legal indeterminacy. On the other, the paper maintains that their main reason of legal indeterminacy, ‘law is politics’, is merely a statement of fact that currently happens in society is sentimental and weak through counterexamples. (shrink)

Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so (...) that ignorance of their nature is profound. (shrink)

When the United States Supreme Court used the expression “with all deliberate speed” in the case Brown v. Board of Education, it did so presumably because of its vagueness. Many jurists, economists, linguists, and philosophers accordingly assume that vagueness can be strategically used to one’s advantage. Roy Sorensen has cast doubt on this assumption by strictly differentiating between vagueness and generality. Indeed, most arguments for the value of vagueness go through only when vagueness is confused with generality. Sorensen claims that (...) vagueness – correctly understood – has no function in law inter alia because judges lie systematically when confronted with borderline cases. I argue that both claims are wrong. First, judges do not need to resort to lying when adjudicating borderline cases, and even if they had to, this would not render vagueness useless. Secondly, vagueness has several important functions in law such as the reduction of decision costs and the delegation of power. Although many functions commonly attributed to the vagueness of legal expressions are in fact due to their generality or other semantic properties, vagueness has at least these two functions in law. (shrink)

Fifty years of effort in artificial intelligence (AI) and the formalization of legal reasoning have produced both successes and failures. Considerable success in organizing and displaying evidence and its interrelationships has been accompanied by failure to achieve the original ambition of AI as applied to law: fully automated legal decision-making. The obstacles to formalizing legal reasoning have proved to be the same ones that make the formalization of commonsense reasoning so difficult, and are most evident where legal reasoning has to (...) meld with the vast web of ordinary human knowledge of the world. Underlying many of the problems is the mismatch between the discreteness of symbol manipulation and the continuous nature of imprecise natural language, of degrees of similarity and analogy, and of probabilities. (shrink)

To move beyond vague platitudes about the importance of context in legal reasoning or natural language understanding, one must take account of ideas from artificial intelligence on how to represent context formally. Work on topics like prior probabilities, the theory-ladenness of observation, encyclopedic knowledge for disambiguation in language translation and pathology test diagnosis has produced a body of knowledge on how to represent context in artificial intelligence applications.