Why There Can\u27t be a Logic of Induction

Carap\u27s attempt to develop an inductive logic has been criticized on a variety of grounds, and while there may be some philosophers who believe that difficulties with Carnap\u27s approach can be overcome by further elaborations and modifications of his system, I think it is fair to say that the consensus is that the approach as a whole cannot succeed. In writing a paper on problems with inductive logic (and with Carnap\u27s approach in particular), I might therefore be accused of beating a dead horse. However, there are still some (e.g., Spirtes, Glymour and Scheines 1993) who seem to believe that purely formal methods for scientific inference can be developed. It may still then be useful to perform an autopsy on a dead horse when establishing the cause of death can shed light on issues of current concern. My intention in this paper is to point out a problem in Carnap\u27s inductive logic which has not been clearly articulated, and which applies generally to any inductive logic. My conclusion will be that scientific inference is inevitably and ineliminably guided by background beliefs and that different background beliefs lead to the application of different inductive rules and different standards of evidentiary relevance. At the end of this paper I will discuss the relationship between this conclusion and the problem of justifying induction

The Problem of Analogical Inference in Inductive Logic

We consider one problem that was largely left open by Rudolf Carnap in his work on inductive logic, the problem of analogical inference. After discussing some previous attempts to solve this problem, we propose a new solution that is based on the ideas of Bruno de Finetti on probabilistic symmetries. We explain how our new inductive logic can be developed within the Carnapian paradigm of inductive logic-deriving an inductive rule from a set of simple postulates about the observational process-and discuss some of its properties.Comment: In Proceedings TARK 2015, arXiv:1606.0729

Apperceptive patterning: Artefaction, extensional beliefs and cognitive scaffolding

In “Psychopower and Ordinary Madness” my ambition, as it relates to Bernard Stiegler’s recent literature, was twofold: 1) critiquing Stiegler’s work on exosomatization and artefactual posthumanism—or, more specifically, nonhumanism—to problematize approaches to media archaeology that rely upon technical exteriorization; 2) challenging how Stiegler engages with Giuseppe Longo and Francis Bailly’s conception of negative entropy. These efforts were directed by a prevalent techno-cultural qualifier: the rise of Synthetic Intelligence (including neural nets, deep learning, predictive processing and Bayesian models of cognition). This paper continues this project but first directs a critical analytic lens at the Derridean practice of the ontologization of grammatization from which Stiegler emerges while also distinguishing how metalanguages operate in relation to object-oriented environmental interaction by way of inferentialism. Stalking continental (Kapp, Simondon, Leroi-Gourhan, etc.) and analytic traditions (e.g., Carnap, Chalmers, Clark, Sutton, Novaes, etc.), we move from artefacts to AI and Predictive Processing so as to link theories related to technicity with philosophy of mind. Simultaneously drawing forth Robert Brandom’s conceptualization of the roles that commitments play in retrospectively reconstructing the social experiences that lead to our endorsement(s) of norms, we compliment this account with Reza Negarestani’s deprivatized account of intelligence while analyzing the equipollent role between language and media (both digital and analog)

The Improbability of Inductive Logic

In some arguments, premises and conclusions are so related that if the former are true, so, necessarily, are the latter. Arguments having this property are said to be valid; those which lack it are said to be invalid. Some invalid arguments are worthless, but others are not. Among the latter are many arguments used by scientists, such as the arguments by which laws are inferred from their instances. These arguments, one wants to say, do not guarantee the truth of their conclusions, but they nevertheless make them more probable. Though not valid, they are inductively strong. Thus there arises the idea of an inductive logic, a logic which would provide a method for determining inductive strength, just as deductive logic provides a method for determining validity. An inductive logic, if one could be developed, would give insight into both the nature and the grounds of scientific inference. The principles of such a logic would be the principles in accordance with which scientific reasoning proceeds, and showing such principles to be logical would leave little doubt as to their justifiability. The motives for developing an inductive logic are thus clear. What is less clear is that such a logic is actually possible. In recent years there has been heated controversy on this point, with philosophers such as Carnap and Hempel defending inductive logic, and other philosophers, such as Popper, claiming that there can be no such thing. The purpose of this paper is to consider whether anything worthy of the name inductive logic could ever be developed

Frequentist statistics as a theory of inductive inference

After some general remarks about the interrelation between philosophical and statistical thinking, the discussion centres largely on significance tests. These are defined as the calculation of $p$-values rather than as formal procedures for ``acceptance'' and ``rejection.'' A number of types of null hypothesis are described and a principle for evidential interpretation set out governing the implications of $p$-values in the specific circumstances of each application, as contrasted with a long-run interpretation. A variety of more complicated situations are discussed in which modification of the simple $p$-value may be essential.Comment: Published at http://dx.doi.org/10.1214/074921706000000400 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

The Counterpart Principle of Analogical Support by Structural Similarity

We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures

The limits and basis of logical tolerance: Carnap’s combination of Russell and Wittgenstein

<p><i>Notes</i>: All data series were filtered by 40-yr Butterworth low-pass filter prior to statistical analysis. Differencing:</p>△<p>no difference,</p>α<p>1^stdifference. Significance (2-tailed):</p>∧<p>p<0.1,</p><p>*p<0.05,</p><p>**p<0.01,</p><p>***p<0.001.</p