10,658 research outputs found
Do Goedel's incompleteness theorems set absolute limits on the ability of the brain to express and communicate mental concepts verifiably?
Classical interpretations of Goedel's formal reasoning imply that the truth
of some arithmetical propositions of any formal mathematical language, under
any interpretation, is essentially unverifiable. However, a language of
general, scientific, discourse cannot allow its mathematical propositions to be
interpreted ambiguously. Such a language must, therefore, define mathematical
truth verifiably. We consider a constructive interpretation of classical,
Tarskian, truth, and of Goedel's reasoning, under which any formal system of
Peano Arithmetic is verifiably complete. We show how some paradoxical concepts
of Quantum mechanics can be expressed, and interpreted, naturally under a
constructive definition of mathematical truth.Comment: 73 pages; this is an updated version of the NQ essay; an HTML version
is available at http://alixcomsi.com/Do_Goedel_incompleteness_theorems.ht
Legal analogy as an alternative to the deductive model of legal reasoning
This article demonstrates the inadequacy of legal deduction as a method that guarantees the certainty and predictability of law and its outcomes in concrete instances. Inter alia, the Author brings our attention to the far smaller role that the deductive pattern of inference plays in legal thought than one may suppose, since it is rather only a schematic illustration of the decisions that were previously made by recourse to the mental operations of a non-logical nature. In return, he proffers legal analogy as an alternative, by which he understands a mode of thinking which helps the reasoner to take into account a mass of different factors that are traditionally deemed to be relevant for legal thought and decision-making
Logical and Spiritual Reflections
Logical and Spiritual Reflections is a collection of six shorter philosophical works, including: Humeâs Problems with Induction; A Short Critique of Kantâs Unreason; In Defense of Aristotleâs Laws of Thought; More Meditations; Zen Judaism; No to Sodom.
Of these works, the first set of three constitutes the Logical Reflections, and the second set constitutes the Spiritual Reflections.
Humeâs Problems with Induction, which is intended to describe and refute some of the main doubts and objections David Hume raised with regard to inductive reasoning. It replaces the so-called problem of induction with a principle of induction. David Humeâs notorious skepticism was based on errors of observation and reasoning, with regard to induction, causation, necessity, the self and freewill. These are here pointed out and critically analyzed in detail â and more accurate and logical theories are proposed. The present work also includes refutations of Hempelâs and Goodmanâs alleged paradoxes of induction.
A Short Critique of Kantâs Unreason, which is a brief critical analysis of some of the salient epistemological and ontological ideas and theses in Immanuel Kantâs famous Critique of Pure Reason. It shows that Kant was in no position to criticize reason, because he neither sufficiently understood its workings nor had the logical tools needed for the task. Kantâs transcendental reality, his analytic-synthetic dichotomy, his views on experience and concept formation, and on the forms of sensibility (space and time) and understanding (his twelve categories), are here all subjected to rigorous logical evaluation and found deeply flawed â and more coherent theories are proposed in their stead.
In Defense of Aristotleâs Laws of Thought, which addresses, from a phenomenological standpoint, numerous modern and Buddhist objections and misconceptions regarding the basic principles of Aristotelian logic. Many people seem to be attacking Aristotleâs Laws of Thought nowadays, some coming from the West and some from the East. It is important to review and refute such ideas as they arise.
More Meditations, which is a sequel to the authorâs earlier work, Meditations. It proposes additional practical methods and theoretical insights relating to meditation and Buddhism. It also discusses certain often glossed over issues relating to Buddhism â notably, historicity, idolatry, messianism, importation to the West.
Zen Judaism, which is a frank reflection on the tensions between reason and faith in todayâs context of knowledge, and on the need to inject Zen-like meditation into Judaism. This work also treats some issues in ethics and theodicy.
No to Sodom, which is an essay against homosexuality, using biological, psychological, spiritual, ethical and political arguments
Literal Perceptual Inference
In this paper, I argue that theories of perception that appeal to Helmholtzâs idea of unconscious inference (âHelmholtzianâ theories) should be taken literally, i.e. that the inferences appealed to in such theories are inferences in the full sense of the term, as employed elsewhere in philosophy and in ordinary discourse.
In the course of the argument, I consider constraints on inference based on the idea that inference is a deliberate acton, and on the idea that inferences depend on the syntactic structure of representations. I argue that inference is a personal-level but sometimes unconscious process that cannot in general be distinguished from association on the basis of the structures of the representations over which itâs defined. I also critique arguments against representationalist interpretations of Helmholtzian theories, and argue against the view that perceptual inference is encapsulated in a module
Internal representations, external representations and ergonomics: towards a theoretical integration
Epistemic virtues, metavirtues, and computational complexity
I argue that considerations about computational complexity show that all finite agents need characteristics like those that have been called epistemic virtues. The necessity of these virtues follows in part from the nonexistence of shortcuts, or efficient ways of finding shortcuts, to cognitively expensive routines. It follows that agents must possess the capacities â metavirtues âof developing in advance the cognitive virtues they will need when time and memory are at a premium
Truth and Probability
Contains two other essays as well: Further Considerations & Last Papers: Probability and Partial Belief.
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