10009
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Substitutional quantification is just a variant of Tarski's account [Wallace, by Baldwin]
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Full Idea:
In a famous paper, Wallace argued that all interpretations of quantifiers (including the substitutional interpretation) are, in the end, variants of that proposed by Tarski (in 1936).
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From:
report of Wallace, J (On the Frame of Reference [1970]) by Thomas Baldwin - Interpretations of Quantifiers
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A reaction:
A significant-looking pointer. We must look elsewhere for Tarski's account, which will presumably subsume the objectual interpretation as well. The ontology of Tarski's account of truth is an enduring controversy.
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7485
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For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson]
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Full Idea:
For Pythagoreans, one, 1, is not a true number but the 'essence' of number, out of which the number system emerges.
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From:
report of Pythagoras (reports [c.530 BCE], Ch.8) by Peter Watson - Ideas Ch.8
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A reaction:
I think this is right! Counting and numbers only arise once the concept of individuality and identity have arisen. Counting to one is no more than observing the law of identity. 'Two' is the big adventure.
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14528
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Maybe modal thought is unavoidable, as a priori recognition of necessary truth-preservation in reasoning [Hale/Hoffmann,A]
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Full Idea:
There are 'transcendental' arguments saying that modal thought is unavoidable - recognition, a priori, of the necessarily truth-preserving character of some forms of inference is a precondition for rational thought in general, and scientific theorizing.
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From:
Bob Hale/ Aviv Hoffmann (Introduction to 'Modality' [2010], 1)
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A reaction:
So the debate about the status of logical truths and valid inference, are partly debates about whether out thought has to involve modality, or whether it could just be about the actual world. I take possibilities and necssities to be features of nature.
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3053
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Pythagoras taught that virtue is harmony, and health, and universal good, and God [Pythagoras, by Diog. Laertius]
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Full Idea:
Pythagoras taught that virtue is harmony, and health, and universal good, and God.
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From:
report of Pythagoras (reports [c.530 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 08.1.19
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A reaction:
I like the link with health, because I consider that a bridge over the supposed fact-value gap. Very Pythagorean to think that virtue is harmony. Plato liked that thought.
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5244
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For Pythagoreans, justice is simply treating all people the same [Pythagoras, by Aristotle]
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Full Idea:
Some even think that what is just is simple reciprocity, as the Pythagoreans maintained, because they defined justice simply as having done to one what one has done to another.
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From:
report of Pythagoras (reports [c.530 BCE], 28) by Aristotle - Nicomachean Ethics 1132b22
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A reaction:
One wonders what Pythagoreans made of slavery. Aristotle argues that officials, for example, have superior rights. The Pythagorean idea makes fairness the central aspect of justice, and that must at least be partly right.
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