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10690
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Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
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Full Idea:
Logic is purely formal either when it is invariant under permutation of object (Tarski), or when it has totally abstracted away from all contents, or it is the constitutive norms for thought.
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From:
JC Beall / G Restall (Logical Consequence [2005], 2)
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A reaction:
[compressed] The third account sounds rather woolly, and the second one sounds like a tricky operation, but the first one sounds clear and decisive, so I vote for Tarski.
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17896
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We need to know the meaning of 'and', prior to its role in reasoning [Prior,AN, by Belnap]
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Full Idea:
For Prior, so the moral goes, we must first have a notion of what 'and' means, independently of the role it plays as premise and as conclusion.
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From:
report of Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink p.132
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A reaction:
The meaning would be given by the truth tables (the truth-conditions), whereas the role would be given by the natural deduction introduction and elimination rules. This seems to be the basic debate about logical connectives.
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17898
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Prior's 'tonk' is inconsistent, since it allows the non-conservative inference A |- B [Belnap on Prior,AN]
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Full Idea:
Prior's definition of 'tonk' is inconsistent. It gives us an extension of our original characterisation of deducibility which is not conservative, since in the extension (but not the original) we have, for arbitrary A and B, A |- B.
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From:
comment on Arthur N. Prior (The Runabout Inference Ticket [1960]) by Nuel D. Belnap - Tonk, Plonk and Plink p.135
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A reaction:
Belnap's idea is that connectives don't just rest on their rules, but also on the going concern of normal deduction.
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6616
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Least action is not a causal law, but a 'global law', describing a global essence [Ellis]
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Full Idea:
The principle of least action is not a causal law, but is what I call a 'global law', which describes the essence of the global kind, which every object in the universe necessarily instantiates.
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From:
Brian Ellis (Katzav on limitations of dispositions [2005])
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A reaction:
As a fan of essentialism I find this persuasive. If I inherit part of my essence from being a mammal, I inherit other parts of my essence from being an object, and all objects would share that essence, so it would look like a 'law' for all objects.
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6615
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A species requires a genus, and its essence includes the essence of the genus [Ellis]
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Full Idea:
A specific universal can exist only if the generic universal of which it is a species exists, but generic universals don't depend on species; …the essence of any genus is included in its species, but not conversely.
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From:
Brian Ellis (Katzav on limitations of dispositions [2005], 91)
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A reaction:
Thus the species 'electron' would be part of the genus 'lepton', or 'human' part of 'mammal'. The point of all this is to show how individual items connect up with the rest of the universe, giving rise to universal laws, such as Least Action.
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6614
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A hierarchy of natural kinds is elaborate ontology, but needed to explain natural laws [Ellis]
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Full Idea:
The hierarchy of natural kinds proposed by essentialism may be more elaborate than is strictly required for purposes of ontology, but it is necessary to explain the necessity of the laws of nature, and the universal applicability of global principles.
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From:
Brian Ellis (Katzav on limitations of dispositions [2005], 91)
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A reaction:
I am all in favour of elaborating ontology in the name of best explanation. There seem, though, to be some remaining ontological questions at the point where the explanations of essentialism run out.
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6612
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Without general principles, we couldn't predict the behaviour of dispositional properties [Ellis]
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Full Idea:
It is objected to dispositionalism that without the principle of least action, or some general principle of equal power, the specific dispositional properties of things could tell us very little about how these things would be disposed to behave.
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From:
Brian Ellis (Katzav on limitations of dispositions [2005], 90)
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A reaction:
Ellis attempts to meet this criticism, by placing dispositional properties within a hierarchy of broader properties. There remains a nagging doubt about how essentialism can account for space, time, order, and the existence of essences.
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