2,816 research outputs found
Reasoning about Knowledge in Linear Logic: Modalities and Complexity
In a recent paper, Jean-Yves Girard commented that âit has been a long time since philosophy has stopped intereacting with logicâ[17]. Actually, it has no
Dynamic Epistemic Logic and Logical Omniscience
Epistemic logics based on the possible worlds semantics suffer from the problem of logical omniscience, whereby agents are described as knowing all logical consequences of what they know, including all tautologies. This problem is doubly challenging: on the one hand, agents should be treated as logically non-omniscient, and on the other hand, as moderately logically competent. Many responses to logical omniscience fail to meet this double challenge because the concepts of knowledge and reasoning are not properly separated. In this paper, I present a dynamic logic of knowledge that models an agentâs epistemic state as it evolves over the course of reasoning. I show that the logic does not sacrifice logical competence on the altar of logical non- omniscience
Thinking Impossible Things
âThere is no use in trying,â said Alice; âone canât believe impossible things.â âI dare say you havenât had much practice,â said the Queen. âWhen I was your age, I always did it for half an hour a day. Why, sometimes Iâve believed as many as six impossible things before breakfastâ.
Lewis Carroll, Through the Looking Glass.
It is a rather common view among philosophers that one cannot, properly speaking, be said to believe, conceive, imagine, hope for, or seek what is impossible.
Some philosophers, for instance George Berkeley and the early Wittgenstein, thought that logically contradictory propositions lack cognitive meaning (informational content) and cannot, therefore, be thought or believed. Philosophers who do not go as far as Berkeley and Wittgenstein in denying that impossible propositions or states of affairs are thinkable, may still claim that it is impossible to rationally believe an impossible proposition. On a classical âCartesianâ view of belief, belief is a purely mental state of the agent holding true a proposition p that she âgraspsâ and is directly acquainted with. But if the agent is directly acquainted with an impossible proposition, then, presumably, she must know that it is impossible. But surely no rational agent can hold true a proposition that she knows is impossible. Hence, no rational agent can believe an impossible proposition. Thus it seems that on the Cartesian view of propositional attitudes as inner mental states in which proposition are immediately apprehended by the mind, it is impossible for a rational agent to believe, imagine or conceive an impossible proposition.
Ruth Barcan Marcus (1983) has suggested that a belief attribution is defeated once it is discovered that the proposition, or state of affairs that is believed is impossible. According to her intuition, just as knowledge implies truth, belief implies possibility.
It is commonplace that people claim to believe propositions that later turn out to be impossible. According to Barcan Marcus, the correct thing to say in such a situation is not: I once believed that A but I donât believe it any longer since I have come to realize that it is impossible that A. What one should say is instead: It once appeared to me that I believed that A, but I did not, since it is impossible that A. Thus, Barcan Marcus defends what we might call Aliceâs thesis: Necessarily, for any proposition p and any subject x, if x believes p, then p is possible.
Aliceâs thesis that it is impossible to hold impossible beliefs, seems to come into conflict with our ordinary practices of attributing beliefs. Consider a mathematical example. Some mathematicians believe that CH (the continuum hypothesis) is true and others believe that it is false. But if CH is true, then it is necessarily true; and if it is false, then it is necessarily false. Regardless of whether CH is true or false, the conclusion seems to be that there are mathematicians who believe impossible propositions.
Examples of apparent beliefs in impossible propositions outside of mathematics are also easy to come by. Consider, for example, Kripkeâs (1999) story of the Frenchman Pierre who without realizing it has two different names âLondonâ and âLondresâ for the same city, London. After having arrived in London, Pierre may assent to âLondres is beautiful and London is not beautifulâ without being in any way irrational. It seems reasonably to infer from this that Pierre believes that Londres is beautiful and London is not beautiful. But since âLondresâ and âLondonâ are rigid designators for the same city, it seems to follow from this that Pierre believes the inconsistent proposition that we may express as âLondon is both beautiful and not beautifulâ
Some Metaphysical Implications of Hegelâs Theodicy
This paper examines Hegelâs claim that philosophy âhas no other object than Godâ as a claim about the essentiality of the idea of God to philosophy. On this idealist interpretation, even atheistic philosophies would presuppose rationally evaluable ideas of God, despite denials of the existence of anything corresponding to those ideas. This interpretation is then applied to Hegelâs version of idealism in relation to those of two predecessors, Leibniz and Kant. Hegel criticizes the idea of the Christian God present within his predecessors in terms of his own heterodox reading of the Trinity in order to resolve a paradox affecting them -- the âparadox of perspectivismâ
Interactive Unawareness Revisited
We analyze a model of interactive unawareness introduced by Heifetz, Meier
and Schipper (HMS). We consider two axiomatizations for their model, which
capture different notions of validity. These axiomatizations allow us to
compare the HMS approach to both the standard (S5) epistemic logic and two
other approaches to unawareness: that of Fagin and Halpern and that of Modica
and Rustichini. We show that the differences between the HMS approach and the
others are mainly due to the notion of validity used and the fact that the HMS
is based on a 3-valued propositional logic.Comment: 26 page
Stepping theories of active logic with two kinds of negation
This paper formulates a stepping theory formalism with two kinds of negation dealing with one of the areas of Active Logic, a new kind of logic aimed at performing practical tasks in real time knowledge-based AI systems. In addition to the standard logical negation, the proposed formalism uses the so-called subjective negation interpreted as inability to arrive at some conclusion through reasoning by a current time. The semantics of the proposed formalism is defined as an~argumentation structure
Soul Substance (jÄ«va dravya) â As Expounded In Dravyasamgraha
Soul substance (jÄ«va dravya) is ubiquitous but unseen. Driving force within each one of us, it has been, since time immemorial, a subject matter of research by philosophers, religious leaders and laity. Still, ambiguity and misconceptions prevail as regard its real nature. Some negate the existence of soul and attribute consciousness to the union of four basic substances â earth (prthvÄ«), water (jala), fire (agni), and air (vÄyu); death leads to its annihilation. Some believe it to be momentary, devoid of self-existence. Still others consider it a product of illusion (mÄyÄ) or ignorance (avidyÄ) as all objects are manifestations of Brahma; only the one eternally undivided Brahma exists. All such conceptions are based on absolutism like: existence (bhÄvaikÄnta) and non-existence (abhÄvaikÄnta), non-dualism (advaita-ekÄnta) and separateness (prthaktva-ekÄnta), and permanence (nityatva-ekÄnta) and momentariness (ksanika-ekÄnta). Jaina epistemology goes beyond the superficial and examines objects of knowledge from all possible points of view. It asserts that the entity (dharmÄ«) and its attributes (dharma) are neither absolutely dependent (Äpeksika) nor absolutely independent (anÄpeksika). Only an entity which has general (sÄmÄnya â concerning the substance, dravya) and particular (viĆesa â concerning the mode, paryÄya) attributes can be the subject of knowledge. Substance without its modification and modification without its substance cannot be the subject of valid knowledge; only their combination can be the subject of knowledge
Knowability Relative to Information
We present a formal semantics for epistemic logic, capturing the notion of knowability relative to information (KRI). Like Dretske, we move from the platitude that what an agent can know depends on her (empirical) information. We treat operators of the form K_AB (âB is knowable on the basis of information Aâ) as variably strict quantifiers over worlds with a topic- or aboutness- preservation constraint. Variable strictness models the non-monotonicity of knowledge acquisition while allowing knowledge to be intrinsically stable. Aboutness-preservation models the topic-sensitivity of information, allowing us to invalidate controversial forms of epistemic closure while validating less controversial ones. Thus, unlike the standard modal framework for epistemic logic, KRI accommodates plausible approaches to the Kripke-Harman dogmatism paradox, which bear on non-monotonicity, or on topic-sensitivity. KRI also strikes a better balance between agent idealization and a non-trivial logic of knowledge ascriptions
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