Combining Philosophers

All the ideas for Gorgias, Peter Koellner and Scott Shalkowski

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16 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

17884	Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
	Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory.
	From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro)

17893	'Reflection principles' say the whole truth about sets can't be captured [Koellner]
	Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level.
	From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1)

5. Theory of Logic / K. Features of Logics / 5. Incompleteness

17894	We have no argument to show a statement is absolutely undecidable [Koellner]
	Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable.
	From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3)

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

17890	There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
	Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable).
	From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)
	A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

17887	PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
	Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem].
	From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1)
	A reaction: Each expansion brings a limitation, but then you can expand again.

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

17891	Arithmetical undecidability is always settled at the next stage up [Koellner]
	Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next.
	From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4)

7. Existence / A. Nature of Existence / 3. Being / d. Non-being

18933	Not-Being obviously doesn't exist, and the five modes of Being are all impossible [Gorgias, by Diog. Laertius]
	Full Idea: I. Nothing exists. a) Not-Being does not exist. b) Being does not exist as everlasting, as created, as both, as One, or as Many. II. If anything does exist, it is incomprehensible. III. If existence is comprehensible, it is incommunicable.
	From: report of Gorgias (fragments/reports [c.443 BCE], B03) by Diogenes Laertius - Lives of Eminent Philosophers 09
	A reaction: [Also Sextus Empiricus, Against Logicians I.65-] For Part I he works through all the possible modes of being he can think of, and explains why none of them are possible. It is worth remembering that Gorgias loved rhetoric, not philosophy!

9. Objects / D. Essence of Objects / 1. Essences of Objects

14221	Serious essentialism says everything has essences, they're not things, and they ground necessities [Shalkowski]
	Full Idea: Serious essentialism is the position that a) everything has an essence, b) essences are not themselves things, and c) essences are the ground for metaphysical necessity and possibility.
	From: Scott Shalkowski (Essence and Being [2008], 'Intro')
	A reaction: If a house is being built, it might acquire an identity first, and only get an essence later. Essences can be physical, but if you extract them you destroy thing thing of which they were the essence. Does all of this apply to abstract 'things'.

9. Objects / D. Essence of Objects / 6. Essence as Unifier

14222	Essences are what it is to be that (kind of) thing - in fact, they are the thing's identity [Shalkowski]
	Full Idea: The route into essentialism is, first, a recognition that the essence of a thing is "what it is to be" that (kind of) thing; the essence of a thing is just its identity.
	From: Scott Shalkowski (Essence and Being [2008], 'Essent')
	A reaction: The first half sounds right, and very Aristotelian. The second half is dramatically different, controversial, and far less plausible. Slipping in 'kind of' is also highly dubious. This remark shows, I think, some confusion about essences.

9. Objects / D. Essence of Objects / 13. Nominal Essence

14226	We distinguish objects by their attributes, not by their essences [Shalkowski]
	Full Idea: In ordinary contexts, we distinguish objects not by their essences but by their attributes.
	From: Scott Shalkowski (Essence and Being [2008], 'Ess and Know')
	A reaction: Hence we have a gap between what bestows identity intrinsically, and how we bestow identity conventionally. If you could grasp the essence of something, you might predict a new attribute, as yet unobserved.

9. Objects / D. Essence of Objects / 15. Against Essentialism

14225	Critics say that essences are too mysterious to be known [Shalkowski]
	Full Idea: According to critics, the thorniest problem for essentialism is the question of our knowledge of essence. It is usually at this point that terms of abuse such as 'dark', 'mysterious', and 'occult' are wheeled out.
	From: Scott Shalkowski (Essence and Being [2008], 'Ess and Know')
	A reaction: I'm inclined to think that the existence of essences can be fairly conclusively inferred, but that attributing a precise identity to them is the biggest challenge.

10. Modality / A. Necessity / 4. De re / De dicto modality

14223	De dicto necessity has linguistic entities as their source, so it is a type of de re necessity [Shalkowski]
	Full Idea: De dicto necessity is a species of de re necessity. Anyone prone to countenance de dicto necessity must recognise mental and/or linguistic entities, thus counting each of them as a res to which necessity attaches.
	From: Scott Shalkowski (Essence and Being [2008], 'Essent')
	A reaction: This seems to rest on the Kit Fine thought that analytic necessities seem to derive from the essences of words such as 'bachelor'. I like this idea: all necessity is de re, but some of the 'things' are words.

10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds

9220	Lewis must specify that all possibilities are in his worlds, making the whole thing circular [Shalkowski, by Sider]
	Full Idea: If purple cows are simply absent from Lewis's multiverse, then certain correct propositions turn out to be impossible. Lewis must require a world for every possibility. But then it is circular, as the multiverse needs modal notions to characterize it.
	From: report of Scott Shalkowski (Ontological Ground of Alethic Modality [1994], 3.9) by Theodore Sider - Reductive Theories of Modality 3.9
	A reaction: [Inversely, a world containing a round square would make that possible] This sounds very nice, though Sider rejects it (p.197). I've never seen how you could define possibility using the concept of 'possible' worlds.

19. Language / C. Assigning Meanings / 7. Extensional Semantics

14224	Equilateral and equiangular aren't the same, as we have to prove their connection [Shalkowski]
	Full Idea: That 'all and only equilateral triangles are equiangular' required proof, and not for mere curiosity, is grounds for thinking that being an equilateral triangle is not the same property as being an equiangular triangle.
	From: Scott Shalkowski (Essence and Being [2008], 'Serious')
	A reaction: If you start with equiangularity, does equilateralness then require proof? This famous example is of two concepts which seem to be coextensional, but seem to have a different intension. Does a dependence relation drive a wedge between them?

19. Language / F. Communication / 1. Rhetoric

5864	Destroy seriousness with laughter, and laughter with seriousness [Gorgias]
	Full Idea: Destroy the seriousness of others with laughter, and their laughter with seriousness.
	From: Gorgias (fragments/reports [c.443 BCE]), quoted by Aristotle - The Art of Rhetoric 1419b
	A reaction: This sounds like brilliant tactical advice, which should be on the wall of every barrister's chambers. This is a case of rhetoric having something to teach us which is nothing at all to do with truth. It is more like learning karate.

9866	Gorgias says rhetoric is the best of arts, because it enslaves without using force [Gorgias, by Plato]
	Full Idea: Gorgias insists that the art of persuasion is superior to all others because it enslaves all the rest, with their own consent, not by force, and is therefore by far the best of all the arts.
	From: report of Gorgias (fragments/reports [c.443 BCE]) by Plato - Philebus 58a
	A reaction: A nice point, and it is not unreasonable to rank the arts in order of their power. To enchant, without achieving agreement, and to speak truth without persuading, are both very fine, but there is something about success that cannot be gainsaid.