# Value

## Conditionals in Closed Set Logic

Over the last couple of days on Twitter, I was involved in a thread, kicked off by Dan Piponi, discussing closed set logic—the natural dual of intuitionistic logic in which the law of the excluded middle holds but the law of non-contradiction fails, and which has models in the closed sets of any topological space, as opposed to the open sets, which model intuitionistic logic. ¶ $$\def\ydash{\succ}$$This logic also has a nice sequent calculus in which sequents have one premise (or zero) and multiple conclusions. In the thread I made the claim that this is a natural and beautiful sequent calculus (it is!) but that the structure of the sequents means that the logic doesn’t have a natural conditional. The dual to the conditional (subtraction) can be defined, for which $$A\ydash B\lor C$$ if and only if $$A-B\ydash C$$. But the traditional conditional rules don’t work so well. ¶ I realised, when I thought about it a bit more, that this fact is something I’ve just believed for the last 20 years or so, but I’ve never seen written down, so now is as good as a time, and here is as good as a place as any to explain what I mean. ¶ ¶ Consider the conditional rules in the classical sequent calculus. They look something like this (give or take variations in the presentation, all equivalent given the classical structural rules): Classical sequent rules for the conditional. ¶ If we restrict these rules to multiple conclusion single... -

### Permissibility of the natural

The usual way to argue that an action is permissible is to argue that the arguments against the action’s permissibility fail. But it would be really nice to be able to give a more positive argument for an action’s permissibility. Sometimes one can do so by showing that the action is obligatory, but (a) that doesn’t help with the permissibility of non-obligatory actions, and (b) often an argument for the obligatoriness of a positive action presupposes the action’s permissibility (e.g., the obligation to kill a dog that is attacking one’s child when no other means of defense is available presupposes the general permissibility of killing dogs with good reason). ¶ Here is a place where Natural Law NL) can provide something quite useful, namely... -

##### Sean Carroll: Extracting the Universe from the Wave Function

¶ Video length: 38:04 ¶ -

Read More @ 3 Quarks Daily
##### george romero (1940 - 2017)

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## All Posts in Value

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Conditionals in Closed Set Logic Over the last couple of days on Twitter, I was involved in a thread, kicked off by Dan Piponi, discussing closed set logic—the natural dual of intuitionistic logic in which the law of the excluded middle holds but the law of non-contradiction fails, and which has models in the closed sets of any topological space, as opposed to the open sets, which model intuitionistic logic. $$\def\ydash{\succ}$$This logic also has a nice sequent calculus in which... Consequently.org -

Siri Hustvedt -The Idea of the Between Synthetic Zero -

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Understanding in Epistemology Understanding in Epistemology Epistemology is often defined as the theory of knowledge, and talk of propositional knowledge (that is, “S knows that p”) has dominated the bulk of modern literature in epistemology. However, epistemologists have recently started to turn more attention to the epistemic state or states of understanding, asking questions about its nature, relationship … Continue reading Understanding in Epistemology → Internet Encyclopedia of Philosophy -

100 PHILOSOPHERS 100 ARTWORKS 100 WORDS #66 Philosopher: Aaron Meskin, University of Leeds Artwork: Oishinbo (1983-2014). Japanese manga series written by Tetsu Kariya and drawn by Akira Hanasaki. Seven thematically-organized anthologies published in English by Viz Media as Oishinbo: A la Carte. Words: What does the aesthetic appreciation of food consist in? How do various values interact in the domain of food? How can food sustain cultural identity? Some of the most interesting explorations of these issues I know of are found... Aesthetics for Birds -

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Theoretical Terms in Science [Revised entry by Holger Andreas on July 20, 2017. Changes to: Main text, Bibliography] A simple explanation of theoreticity says that a term is theoretical if and only if it refers to nonobservational entities. Paradigmatic examples of such entities are electrons, neutrinos, gravitational forces, genes etc. There is yet another explanation of theoreticity: a theoretical term is one whose meaning becomes determined through the axioms of a scientific theory. The meaning of the term 'force',... Stanford Encyclopedia of Philosophy -

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Metagame vs Structure Over on ihobo today, discussion of game structures, metagames, and the monetisation metagame. Here’s an extract: The structure of a game is the framework of the design that compels players to keep playing over the long term. There are numerous different game structures, both chronological, geographical, and in terms of character advancement. Conversely, the metagame is the social consequence of releasing a game into a community of players, an ever-changing set of tactical and strategic... Only a Game -

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Fuzzy Logic [Revised entry by Petr Cintula, Christian G. Fermüller, and Carles Noguera on July 18, 2017. Changes to: Bibliography, readings-by-topic.html] [Editor's Note: The following new entry by Petr Cintula, Christian G. Fermuller, and Carles Noguera replaces the former entry on this topic by the previous author.]... Stanford Encyclopedia of Philosophy -