Non-deductive Inference Research Articles

The limit of human intelligence

In 1998, Fields medallist Stephen Smale [Smale (1998) [1]] proposed his famous eighteen problems to the mathematicians of this century. The statement of his eighteenth problem is simple but very important. The statement of his problem is, “What are the limits of intelligence, both artificial and human?”. To answer the limit of human intelligence, in this paper, we introduce cognitive-consequence space and cognitive-consequence topology, and mainly prove that deductive and non-deductive parts of a human mind will never be empty. It proves a human being will continue to think and solve problems using both deductive and non-deductive inferences as long as they are alive. Hence, we conclude that human intelligence is limitless. We also introduce cognitive closure, cognitive similarity distance, cognitive limit point, cognitive-continuous function, consequence ideal, consequence filter, Gödel's incompleteness black hole, and study related properties. We also provide suitable justifications to show that cognitive consequence topological space is not similar to that of any existing topological space because it connects cognitive space and consequence operator in one frame to find the limit of human intelligence. Moreover, we also provide justifications to state that artificial intelligence has limitations. Thus, we conclude that human intelligence will always remain superior to artificial intelligence.

Hard to explain? – rozumowania abdukcyjne w prawniczych wnioskowaniach o faktach

The purpose of the article is to apply the concept of abductive reasoning in the description and evaluation of legal inferences about facts. The reflection is conducted in the field of philosophy of law and methodology of science. Based on a critical analysis of the literature I present both Charles Sanders Peirce’s inferential theory of abduction and Peter Lipton’s ‘inference to the best explanation’ (IBE) theory. In colloquial philosophical discourse those terms are sometimes used interchangeably. I argue that, although it is a significant simplification, IBE in principle fits into the broad meaning of abduction which I adopt in the present article. Using the work of Mariusz Urbański and Atocha Aliseda I apply IBE to the explanatory-deductive model of abduction. I utilize abduction understood in this way in the field of law. Based on the review of Polish philosophical and legal literature and the results obtained from the LEX database I show that the concept of abduction is unpopular in the legal doctrine. The main thesis is that abduction in the broad sense offers a significant value added in the description of non-deductive inferences and provides more precise criteria for assessing the quality of reasoning than concepts existing in Polish legal doctrine regarding non-deductive inferences. In the same time it exhibits essential features of those concepts. The analysis allows to examine and determine the relationship between the theories of abduction, IBE and the concepts found in Polish philosophical literature and legal doctrine. Its conclusions allow to introduce these new concepts into the philosophical and legal debate and – also – to describe and evaluate legal non-deductive inferences about facts in a more plausible way. The result gives hope for the methodological strengthening of both the process of making factual findings and the assessment of evidence.

Outline of a Theory of Reasons

AbstractThis paper investigates the logic of reasons. Its aim is to provide an analysis of the sentences of the form ‘p is a reason for q’ that yields a coherent account of their logical properties. The idea that we will develop is that ‘p is a reason for q’ is acceptable just in case a suitably defined relation of incompatibility obtains between p and ¬q. As we will suggest, a theory of reasons based on this idea can solve three challenging puzzles that concern, respectively, contraposing reasons, conflicting reasons, and supererogatory reasons, and opens a new perspective on some classical issues concerning non-deductive inferences.

Causation and Cognition in Early Modern Philosophy ed. by Dominik Perler and Sebastian Bender

Reviewed by: Causation and Cognition in Early Modern Philosophy ed. by Dominik Perler and Sebastian Bender Nick Westberg and Jean-Luc Solère Dominik Perler and Sebastian Bender, editors. Causation and Cognition in Early Modern Philosophy. Routledge Studies in Seventeenth-Century Philosophy. New York: Routledge, 2020. Pp. vi + 361. Cloth, $112.00. This volume is a welcome addition to early modern scholarship, providing a source of reflection on the connection between cognition theory and causation theory. The collection's great merit is exploiting this cognition-causation connection to provide a new avenue for historical research that is at the same time philosophically significant. Several of the essays advance our understanding of key figures by using this connection to settle longstanding interpretive disputes. (Besides those detailed in the present paragraph, the excellent pieces by Julia Jorati on Leibniz, Sebastian Bender on Berkeley, and Martine Pécharman on Hobbes also fall under this heading.) For instance, in "Descartes on the Causal Structure of Cognition," Alison Simmons rejects both the concurrentist and the occasionalist readings and argues that Descartes, in fact, does not endorse any view about the metaphysics of causation. Instead, he is more interested in showing the success of mechanism. Mechanistic physics can account for all the bodily interactions that lead up to perception. Thus, philosophers may dispense with the Aristotelian assimilation thesis and its underlying physics. In "Knowing Mind through Knowing Body," Daniel Garber provides an answer to the "Pancreas Problem" in Spinoza scholarship. Awareness is distinguished from mere perception, which may be not conscious. Moreover, awareness results from the body's interaction with an external body, whereas (unconscious) perception does not require such interaction and can be purely internal. This helps explain Spinoza's criticism of Descartes's cogito argument. By extension from the definition of awareness, self-consciousness—that is, the idea of the idea of one's body—depends upon interaction with external bodies. So, one cannot separate self-consciousness from causal relations with the external world. Peter Kail likewise uses the cognition-causation connection to engage a longstanding debate, defending the view that David Hume is not a radical skeptic. He argues that Hume's criticism of causation only precludes one sense in which the mind is a cause of inferences, that is, the sense in which it deductively infers. Hume instead treats reason as a reliable mechanism that leads us to nondeductive inferences. Other essays use the cognition-causation connection not to wade into perennial scholarly disputes, but rather to open up historical inquiry to lesser-known philosophers. These figures are often taken to be minor on account of their quirky positions. But this collection reveals that an unorthodox position in one domain (causation or cognition) is often the result of a unique thesis defended in the other. For instance, in "Nothing Is Simply One Thing," Julia [End Page 688] Borcherding shows that Anne Conway advances her non-unitary theory of mind because she significantly alters Descartes's account of change. Likewise, in "Cartesian Causation and Cognition," Tad Schmaltz argues that Géraud de Cordemoy embraces occasionalism about the mind's perceptions because he reasons that Cartesian metaphysics renders causation between finite substances impossible. Again, Dominik Perler, in "Suárez on Cognition and Causation," illuminates Suárez's unorthodox view of the intellect as a coordinated efficient cause of ideas. He shows that Suárez's view is a last-ditch attempt within Aristotelianism to replace a failed assimilation thesis. The pieces by Sarah Hutton on Cudworth, David Cunning on Cavendish, and Han Thomas Adriaenssen on John Sergeant and Antoine Le Grand fall in the same group of essays that explore lesser-known figures. The excellent contributions of Martin Lin on Spinoza's causal axiom, Stephan Schmid on Malebranche, and James Van Cleve on Reid form a third group. Not only are they analytically thorough, but they also bring illuminating contemporary analysis to bear on this collection's theme. The collection is not without its issues. For one thing, the pieces do not fit together as a cohesive whole. This is due to the broad scope of figures (eighteen philosophers, spanning divergent perspectives from about 1600 to about 1750) and the differing interpretive methods. The...

Logical abductivism and non-deductive inference

Logic, in one of the many sense of that term, is a theory about what follows from what and why. Arguably, the correct theory has to be determined by abduction. Over recent years, so called logical anti-exceptionalists have investigated this matter. Current discussions have been restricted to deductive logic. However, there are also, of course, various forms of non-deductive reasoning. Indeed, abduction itself is one of these. What is to be said about the way of choosing the best theory of non-deductive inferences? It would seem clear that an anti-exceptionalist should hold that essentially the same method of choice should apply to non-deductive logic. A number of issues need to be faced in the process, not the least of which is the circularity involved in an abductive justification for a theory of abduction. This paper discusses matters.

Uwagi o doniosłości koncepcji domniemań relewantnych prawnokarnie

This paper deals with the question of presumptions relevant in criminal law, including the so-called substantive law presumption of guilt. Any normative connotations of this presumption are definitively excluded. The considerations are based on one of the theoretical concepts of factual presumptions (preasumptiones hominis), the so-called mixed concept, whereby presumptions are perceived as evidentiary simplifications, a particular form of non-deductive inferences which neither restrict the principle of free appraisal of evidence nor shift the burden of proof against the law. A critical analysis is made of selected doctrinal conceptions, especially those that favour distinguishing presumptions that are relevant in criminal law. Attention is also devoted to the notion of findings of fact, especially in the context of their relation to the category of legal assessments of criminal agencies during the trial. A hypothesis is formulated that findings of fact can relate to assertions about facts referring to objective reality, as well as about conventional facts in law, for which facts the constitutive rules determine the elements of the structure of an offence viewed from the dogmatic perspective.

The Pursuit of Knowledge and the Problem of the Unconceived Alternatives

In the process of scientific discovery, knowledge ampliation is pursued by means of non-deductive inferences. When ampliative reasoning is performed, probabilities cannot be assigned objectively. One of the reasons is that we face the problem of the unconceived alternatives: we are unable to explore the space of all the possible alternatives to a given hypothesis, because we do not know how this space is shaped. So, if we want to adequately account for the process of knowledge ampliation, we need to develop an account of the process of scientific discovery which is not exclusively based on probability calculus. We argue that the analytic view of the method of science advocated by Cellucci is interestingly suited to this goal, since it rests on the concept of plausibility. In this perspective, in order to account for how probabilities are in fact assigned in uncertain contexts and knowledge ampliation is really pursued, we have to take into account plausibility-based considerations.

Abductively robust inference

Inference to the Best Explanation (IBE) is widely criticized for being an unreliable form of ampliative inference – partly because the explanatory hypotheses we have considered at a given time may all be false, and partly because there is an asymmetry between the comparative judgment on which an IBE is based and the absolute verdict that IBE is meant to license. In this paper, I present a further reason to doubt the epistemic merits of IBE and argue that it motivates moving to an inferential pattern in which IBE emerges as a degenerate limiting case. Since this inferential pattern is structurally similar to an argumentative strategy known as Inferential Robustness Analysis (IRA), it effectively combines the most attractive features of IBE and IRA into a unified approach to non-deductive inference.

Bootstrapping and dogmatism

Dogmatists claim that having a perceptual experience as of p can provide one with immediate and defeasible warrant to believe that p. A persistent complaint against this position is that it sanctions an intuitively illicit form of reasoning: bootstrapping. I argue that dogmatism has no such commitments. Dogmatism is compatible with a principle that disallows the final non-deductive inference in the bootstrapping procedure. However, some authors have maintained that such strategy is doomed to failure because earlier stages of in the bootstrapping inference are already problematic. I argue that insofar as these inferences appear problematic, the dogmatist is not committed to sanctioning them. I conclude that the bootstrapping argument presents no significant objection to the claim that perceptual experiences can provide immediate and defeasible warrant to believe their contents.

Analysis of the Talmudic Argumentum a Fortiori Inference Rule (Kal Vachomer) Using Matrix Abduction

We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Ana-logy and the rule of Argumentum A Fortiori. Given a matrix A with entries in {0, 1}, we allow for one or more blank squares in the matrix, say ai,j =?. The method allows us to decide whether to declare ai,j = 0 or ai,j = 1 or ai,j =? undecided. This algorithmic method is then applied to modelling several legal and practical reasoning situations including the Talmudic rule of Kal-Vachomer. We add an Appendix showing that this new rule of Matrix Abduction, arising from the Talmud, can also be applied to the analysis of paradoxes in voting and judgement aggregation. In fact we have here a general method for executing non-deductive inferences.

Analysis of the Talmudic Argumentum A Fortiori Inference Rule (Kal Vachomer) using Matrix Abduction

We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix \({\mathbb {A}}\) with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a i,j =?. The method allows us to decide whether to declare a i,j = 0 or a i,j = 1 or a i,j =? undecided. This algorithmic method is then applied to modelling several legal and practical reasoning situations including the Talmudic rule of Kal-Vachomer. We add an Appendix showing that this new rule of Matrix Abduction, arising from the Talmud, can also be applied to the analysis of paradoxes in voting and judgement aggregation. In fact we have here a general method for executing non-deductive inferences.

A Mathematical Model of Deductive and Non-Deductive Inferences

Induction and abduction are well known non-deductive inferences. We shall propose a view that design is also another form of non-deductive inference, and give a mathematical model of deductive and non-deductive inferences based on Barwise and Seligman's mathematical theory of information flow. In our model, inferences are classified into three categories, and we can show that deduction and abduction are in the same category, although induction is different. Furthermore, we shall show also that non-deductive inferences are interpretable mutually, and investigate also mathematical properties of the model. In particular, we shall prove a generalized version of the Abstract Completeness Theorem by Barwise and Seligman.

The Fine Structure of Inference to the Best Explanation

Traditionally, philosophers have focused mostly on the logical template of inference. The paradigm-case has been deductive inference, which is topic-neutral and context-insensitive. The study of deductive rules has engendered the search for the Holy Grail: syntactic and topic-neutral accounts of all prima facie reasonable inferential rules. The search has hoped to find rules that are transparent and algorithmic, and whose following will just be a matter of grasping their logical form. Part of the search for the Holy Grail has been to show that the so-called scientific method can be formalised in a topic-neutral way. We are all familiar with Carnap's inductive logic, or Popper's deductivism or the Bayesian account of scientific method. There is no Holy Grail to be found. There are many reasons for this pessimistic conclusion. First, it is questionable that deductive rules are rules of inference. Second, deductive logic is about updating one's belief corpus in a consistent manner and not about what one has reasons to believe simpliciter. Third, as Duhem was the first to note, the so-called scientific method is far from algorithmic and logically transparent. Fourth, all attempts to advance coherent and counterexample-free abstract accounts of scientific method have failed. All competing accounts seem to capture some facets of scientific method, but none can tell the full story. Fifth, though the new Dogma, Bayesianism, aims to offer a logical template (Bayes's theorem plus conditionalisation on the evidence) that captures the essential features of non-deductive inference, it is betrayed by its topic-neutrality. It supplements deductive coherence with the logical demand for probabilistic coherence among one's degrees of belief. But this extended sense of coherence is (almost) silent on what an agent must infer or believe. The root of the problem with the search for the Holy Grail is that there is a type of inference broadly called 'defeasible', or 'ampliative'

Can Non-Deductive Inferences Be Subjectively Justified?

Can Non-Deductive Inferences Be Subjectively Justified?

Present doldrums, pleasant prospects

Robert Brandom’s effort to examine the prospects of inferentialism (inspired by Wilfrid Sellars’ work) is examined in terms of the uncertainties of contemporary philosophy and Brandom’s reading of selected prominent figures in the history of philosophy. The very idea of there being anything like a set of rules governing non-deductive inference (inferentialism) is problematic; so is Brandom’s reading of the figures he has selected in order to illuminate his own proposal along historical lines. We never quite learn how inferentialism bears on the trajectory of Eurocentric philosophy and what the corrective is that Brandom advocates.

Spatial inference with geometric proportional analogies

We describe an instance-based reasoning solution to a variety of spatial reasoning problems. The solution centers on identifying an isomorphic mapping between labelled graphs that represent some problem data and a known solution instance. We describe a number of spatial reasoning problems that are solved by generating non-deductive inferences, integrating topology with area (and other) features. We report the accuracy of our algorithm on different categories of spatial reasoning tasks from the domain of Geographical Information Science. The generality of our approach is illustrated by also solving geometric proportional (IQ-test type) analogy problems.

The ‘requirement of total evidence’ and its role in phylogenetic systematics

The question of whether or not to partition data for the purposes of inferring phylogenetic hypotheses remains controversial. Opinions have been especially divided since Kluge's (1989, Systematic Zoology 38, 7–25) claim that data partitioning violates the requirement of total evidence (RTE). Unfortunately, advocacy for or against the RTE has not been based on accurate portrayals of the requirement. The RTE is a basic maxim for non-deductive inference, stipulating that evidence must be considered if it has relevance to an inference. Evidence is relevant if it has a positive or negative effect on a given conclusion. In the case of ℈partitioned’ phylogenetic inferences, the RTE is violated, and the basis for rational belief in any conclusion is compromised, unless it is shown that the partitions are evidentially irrelevant to one another. The goal of phylogenetic systematics is to hypothesize past causal conditions to account for observed shared similarities among two or more species. Such inferences are non-deductive, necessitating consideration of the RTE. Some phylogeneticists claim the parsimony criterion as justification for the RTE. There is no relation between the two – parsimony is a relation between a hypothesis and causal question(s). Parsimony does not dictate the content of premises prior to an inference. ℈Taxonomic congruence,’ ℈supertrees,’ and ℈conditional combination’ methods violate the RTE. Taxonomic congruence and supertree methods also fail to achieve the intended goal of phylogenetic inference, such that ℈consensus trees’ and ℈supertrees’ lack an empirical basis. ℈Conditional combination’ is problematic because hypotheses derived from partitioned data cannot be compared – a causal hypothesis inferred to account for a set of effects only has relevance to those effects, not any comparative relevance to other causal hypotheses. A similar problem arises in the comparisons of hypotheses derived from different causal theories.

The abduction of phylogenetic hypotheses

The formal structure of the inference of a phylogenetic hypothesis is analyzed in the context of the different classes of reasoning applied in all fields of science. Rather than making the traditional distinction between deductive and inductive reasoning, it is shown that phylogenetic hypotheses are derived from a form of non-deductive inference commonly known as abduction. In making distinctions between abductive, deductive, and inductive inferences, the relationships between the origins of hypotheses and their testing become apparent. Abduction serves to provide explanatory hypotheses as tentative answers to specifiable causal questions. It is by way of deduction that specific potential test consequences are determined, whereas induction sensu stricto characterizes the act of carrying out a particular test. The formal structure of phylogenetic inference as a form of abduction is presented. Significant implications arise in recognizing that phylogenetic hypotheses are the products of abductive inference. The most apparent of these are that the distinctions between parsimony and likelihood as methodological criteria are unfounded. Parsimony refers to the relation between a causal question(s) and the hypothesis that serves as an answer for that question(s), whereas likelihood refers to the relation between the evidence as premises and the hypothesis allowed by those premises. The consequence is that parsimony has logical priority over likelihood in abduction, such that the likelihood of any hypothesis is maximized in the event that a causal theory of descent with modification is applied as fully as possible to observed shared similarities. In contrast, the application of rate-dependent theories, under the guise of maximum likelihood, are at odds with observations of shared similarities among two or more species and the causal questions regarding such observations; any rate-dependent theory only pertains to effects that are only tokogenetic in scope, not phylogenetic (sensu Hennig 1966). In recognizing phylogenetic hypotheses as answers to causal questions, the popular conception of testing such hypotheses by the introduction of new characters is incorrect. New character distributions cannot be deduced from a cladogram since such a structure only has causal relevance to the characters for which the hypothesis was inferred. The proper testing of a phylogenetic hypothesis requires the deduction of specific consequences as closely related as possible to the specified causal events of character origins and fixation, and subsequent speciation events. Such consequences must be effects that are independent of the class of effects the hypothesis was intended to explain, i.e., character data. As a result, effects that stand as legitimate potential test evidence are those effects that best support the different sets of causal events presented in the hypothesis. Problems with the popular applications of support indices, as offered by the bootstrap, jackknife, and permutation tests, are discussed. The main problem with these techniques is that they are only useful for testing statistical hypotheses, not explanatory hypotheses. Similarly, Bremer support analysis cannot provide indications of clade support because it is empirically meaningless to compare cladograms of different length, as each hypothesis only has relevance to the respective observations it explains.

Directed Convergence in Stable Percept Acquisition

We view a perceptual capacity as a nondeductive inference, represented as a function from a set of premises to a set of conclusions. The application of the function to a single premise to produce a single conclusion is called a “percept” or “instantaneous percept.” We define a stable percept as a convergent sequence of instantaneous percepts. Assuming that the sets of premises and conclusions are metric spaces, we introduce a strategy for acquiring stable percepts, called directed convergence. We consider probabilistic inferences, where the premise and conclusion sets are spaces of probability measures, and in this context we study Bayesian probabilistic/recursive inference. In this type of Bayesian inference the premises are probability measures, and the prior as well as the posterior is updated nontrivially at each iteration. This type of Bayesian inference is distinguished from classical Bayesian statistical inference where the prior remains fixed, and the posterior evolves by conditioning on successively more punctual premises. We indicate how the directed convergence procedure may be implemented in the context of Bayesian probabilistic/recursive inference. We discuss how the L∞ metric can be used to give numerical control of this type of Bayesian directed convergence.

Haack's Evidence and Inquiry

The foundherentism of Professor Haack's Evidence and Inquiry is presented as an alternative to epistemic foundationalism and coherentism. Although I regard her criticism of these alternatives as penetrating and conclusive, I am not convinced by her foundherentism. The principal cause of my skepticism is that she fails to supply some of the detail I regard as crucial for a plausible theory of epistemic justification, but I also think that she does not come fully to terms with a basic problem faced squarely (though not successfully) by the alternative views that she rejects. These limitations in the presentation of her foundherentism may perhaps be overcome by an elaboration or further development of her views. I am convinced that an elaboration capable of overcoming these shortcomings will move her in a different direction, but I will not defend that conviction here. I begin with the basic problem with which she does not, in my view, fully come to terms. This is the problem of how epistemically justified empirical propositions can reasonably be supposed to be true, approximately true, or probable. Foundationalists argued that any propositions to which we can justifiably accord this status must either (a) report facts that can be ascertained by direct inspection or (b) be ultimately inferable by truth-preserving rules from premisses that do report such facts. Although the evident need for nondeductive inference in empirical matters has always raised formidable problems for foundationalists, they have usually expressed the belief that permissible rules of nondeductive inference have the property of taking one from true premisses to true conclusions more often than not. If such rules can reasonably be said to have this property, then the propositions that happen to be justified by foundationalist criteria (however few, relatively speaking, they may be) can reasonably be said to be true more often than not. Such criteria are, in Haack's terms, truth-indicative.