Combining Texts

All the ideas for 'works', 'Philosophy of Arithmetic' and 'The Sophist'

unexpand these ideas     |    start again     |     specify just one area for these texts


25 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
We must fight fiercely for knowledge, understanding and intelligence [Plato]
     Full Idea: We need to use every argument we can to fight against anyone who does away with knowledge, understanding, and intelligence, but at the same time asserts anything at all about anything.
     From: Plato (The Sophist [c.359 BCE], 249c)
     A reaction: Thus showing that reason is only central if you want to put a high value on it?
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
The desire to split everything into its parts is unpleasant and unphilosophical [Plato]
     Full Idea: To try to set apart everything from everything is not only especially jangling, but it is the mark of someone altogether unmusical and unphilosophic.
     From: Plato (The Sophist [c.359 BCE], 259e)
2. Reason / C. Styles of Reason / 1. Dialectic
Good analysis involves dividing things into appropriate forms without confusion [Plato]
     Full Idea: It takes expertise in dialectic to divide things by kinds and not to think that the same form is a different one or that a different form is the same.
     From: Plato (The Sophist [c.359 BCE], 253d)
Dialectic should only be taught to those who already philosophise well [Plato]
     Full Idea: The dialectical capacity - you won't give it to anyone else, I suspect, except to whoever philosophises purely and justly.
     From: Plato (The Sophist [c.359 BCE], 253e)
2. Reason / C. Styles of Reason / 2. Elenchus
In discussion a person's opinions are shown to be in conflict, leading to calm self-criticism [Plato]
     Full Idea: They collect someone's opinions together during the discussion, put them side by side, and show that they conflict with each other at the same time on the same subjects.... The person sees this, gets angry at themselves, and calmer towards others.
     From: Plato (The Sophist [c.359 BCE], 230b)
     A reaction: He goes on to say that the process is like a doctor purging a patient of internal harms. If anyone talks for long enough (even a good philosopher), their opinions will probably be seen to be in conflict. But which opinions do you abandon?
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett]
     Full Idea: Husserl contends that 0 is not a number, on the grounds that 'nought' is a negative answer to the question 'how many?'.
     From: report of Edmund Husserl (Philosophy of Arithmetic [1894], p.144) by Michael Dummett - Frege philosophy of mathematics Ch.8
     A reaction: I seem to be in a tiny minority in thinking that Husserl may have a good point. One apple is different from one orange, but no apples are the same as no oranges. That makes 0 a very peculiar number. See Idea 9838.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Multiplicity in general is just one and one and one, etc. [Husserl]
     Full Idea: Multiplicity in general is no more than something and something and something, etc.; ..or more briefly, one and one and one, etc.
     From: Edmund Husserl (Philosophy of Arithmetic [1894], p.85), quoted by Gottlob Frege - Review of Husserl's 'Phil of Arithmetic'
     A reaction: Frege goes on to attack this idea fairly convincingly. It seems obvious that it is hard to say that you have seventeen items, if the only numberical concept in your possession is 'one'. How would you distinguish 17 from 16? What makes the ones 'multiple'?
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]
     Full Idea: Husserl famously argued that one should not explain number in terms of equinumerosity (or one-one correspondence), but should explain equinumerosity in terms of sameness of number, which should be characterised in terms of counting.
     From: report of Edmund Husserl (Philosophy of Arithmetic [1894]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: [Heck admits he hasn't read the Husserl] I'm very sympathetic to Husserl, though nearly all modern thinking favours Frege. Counting connects numbers to their roots in the world. Mathematicians seem oblivious of such things.
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
What does 'that which is not' refer to? [Plato]
     Full Idea: What should the name 'that which is not' be applied to?
     From: Plato (The Sophist [c.359 BCE], 237c)
     A reaction: This leads into a discussion of the problem, in The Sophist. It became a large issue when modern logic was being developed by Frege and Russell.
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
If statements about non-existence are logically puzzling, so are statements about existence [Plato]
     Full Idea: When the question was put to us as to the name of 'that which is not', to whatever one must apply it, we got stuck in every kind of perplexity. Are we now in any less perplexity about 'that which is'?
     From: Plato (The Sophist [c.359 BCE], 250d)
     A reaction: Nice. This precapitulates the whole story of modern philosophy of language. What started as a nagging doubt about reference to non-existents ends as bewilderment about everything we say.
7. Existence / A. Nature of Existence / 6. Criterion for Existence
To be is to have a capacity, to act on other things, or to receive actions [Plato]
     Full Idea: A thing really is if it has any capacity, either by nature to do something to something else or to have even the smallest thing done to it by the most trivial thing, even if it only happens once. I'll define those which are as nothing other than capacity.
     From: Plato (The Sophist [c.359 BCE], 247e)
     A reaction: If philosophy is footnotes to Plato, this should be the foundational remark in all discussions of existence (though Parmenides might claim priority). It seems to say 'to be is to have a causal role (active or passive)'. It also seems essentialist.
7. Existence / D. Theories of Reality / 6. Physicalism
Some alarming thinkers think that only things which you can touch exist [Plato]
     Full Idea: One group drags everything down to earth, insisting that only what offers tangible contact is, since they define being as the same as body, despising anyone who says that something without a body is. These are frightening men.
     From: Plato (The Sophist [c.359 BCE], 246b)
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
Whenever there's speech it has to be about something [Plato]
     Full Idea: Whenever there's speech it has to be about something. It's impossible for it not to be about something.
     From: Plato (The Sophist [c.359 BCE], 262e)
     A reaction: [Quoted by Marcus about ontological commitment] The interesting test case would be speech about the existence of circular squares.
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Good thinkers spot forms spread through things, or included within some larger form [Plato]
     Full Idea: It takes dialectic to divide things by kinds...such a person can discriminate a single form spread through a lot of separate things…and forms included in a single outside form…or a form connected as a unit through many wholes.
     From: Plato (The Sophist [c.359 BCE], 253d)
     A reaction: [compressed] This is very helpful in indicating the complex structure of the Forms that Plato envisages. If you talk of the meanings of words (other than names), though, it comes to the same thing. Wise people fully understand their language.
The not-beautiful is part of the beautiful, though opposed to it, and is just as real [Plato]
     Full Idea: So 'the not beautiful' turns out to be ..both marked off within one kind of those that are, and also set over against one of those that are, ..and the beautiful is no more a being than the not beautiful.
     From: Plato (The Sophist [c.359 BCE], 257d)
     A reaction: [dialogue eliminated] This is a highly significant passage, for two reasons. It suggests that the Form of the beautiful can have parts, and also that the negations of Forms are Forms themselves (both of which come as a surprise).
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
If we see everything as separate, we can then give no account of it [Plato]
     Full Idea: To dissociate each thing from everything else is to destroy totally everything there is to say. The weaving together of forms is what makes speech [logos] possible for us.
     From: Plato (The Sophist [c.359 BCE], 259e)
     A reaction: This I take to be the lynchpin of metaphysics. We are forced to see the world in a way which enables us to give some sort of account of it. Our metaphysics is 'inference to the best logos'.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
A soul without understanding is ugly [Plato]
     Full Idea: The soul that lacks understanding must be set down as ugly.
     From: Plato (The Sophist [c.359 BCE], 228d)
     A reaction: The teleological view of things understands their nature in things of their perfection. and the essence of beauty is perfection. It is the mind's nature to know. Failing to know is as ugly as allowing your crops to die.
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege]
     Full Idea: Husserl identifies a 'unitary mental act' where several contents are connected or related to one another, and also a difference-relation where two contents are related to one another by a negative judgement.
     From: report of Edmund Husserl (Philosophy of Arithmetic [1894], p.73-74) by Gottlob Frege - Review of Husserl's 'Phil of Arithmetic' p.322
     A reaction: Frege is setting this up ready for a fairly vicious attack. Where Hume has a faculty for spotting resemblances, it is not implausible that we should also be hard-wired to spot differences. 'You look different; have you changed your hair style?'
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol]
     Full Idea: Husserl said that the clarification of any concept is made by determining its psychological origin. He is concerned with the psychological origins of the operation of calculating cardinal numbers.
     From: report of Edmund Husserl (Philosophy of Arithmetic [1894]) by Victor Velarde-Mayol - On Husserl 2.2
     A reaction: This may not be the same as the 'psychologism' that Frege so despised, because Husserl is offering a clarification, rather than the intrinsic nature of number concepts. It is not a theory of the origin of numbers.
18. Thought / E. Abstraction / 8. Abstractionism Critique
Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl]
     Full Idea: Husserl substitutes his account of the process of concept-formation for a delineation of the concept. It is above all in making this substitution that psychologism is objectionable (and Frege opposed it so vehemently).
     From: comment on Edmund Husserl (Philosophy of Arithmetic [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.2
     A reaction: While this is a powerful point which is a modern orthodoxy, it hardly excludes a study of concept-formation from being of great interest for other reasons. It may not appeal to logicians, but it is crucial part of the metaphysics of nature.
Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl]
     Full Idea: Husserl saw that abstracted units, though featureless, must in some way retain their distinctness, some shadowy remnant of their objects. So he wanted to correlate like-numbered sets, not just register their identity, but then abstractionism fails.
     From: comment on Edmund Husserl (Philosophy of Arithmetic [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.12
     A reaction: Abstractionism is held to be between the devil and the deep blue sea, of depending on units which are identifiable, when they are defined as devoid of all individuality. We seem forced to say that the only distinction between them is countability.
23. Ethics / A. Egoism / 1. Ethical Egoism
Wickedness is an illness of the soul [Plato]
     Full Idea: Wickedness is a sedition and illness of the soul.
     From: Plato (The Sophist [c.359 BCE], 228b)
25. Social Practice / E. Policies / 5. Education / c. Teaching
Didactic education is hard work and achieves little [Plato]
     Full Idea: With a lot of effort the admonitory species of education accomplishes little.
     From: Plato (The Sophist [c.359 BCE], 230a)
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
Philosophers are the forefathers of heretics [Tertullian]
     Full Idea: Philosophers are the forefathers of heretics.
     From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
I believe because it is absurd [Tertullian]
     Full Idea: I believe because it is absurd ('Credo quia absurdum est').
     From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2
     A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though.