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All the ideas for 'Frege's Theory of Numbers', 'The Tragedy of Reason' and 'The Question of Ontology'

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26 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
You have to be a Platonist to debate about reality, so every philosopher is a Platonist [Roochnik]
     Full Idea: Everyone who enters into a debate about reality automatically becomes a Platonist. Since such debates are the essence of philosophy, every philosopher is a Platonist.
     From: David Roochnik (The Tragedy of Reason [1990], p.199)
     A reaction: This is correct
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
Philosophy aims to satisfy the chief human desire - the articulation of beauty itself [Roochnik]
     Full Idea: Philosophy, the attempt to articulate the vision of beauty itself, is the attempt to satisfy the highest human desire.
     From: David Roochnik (The Tragedy of Reason [1990], p.120)
     A reaction: A million miles away from modern philosophy, but still an ideal to be taken seriously.
2. Reason / A. Nature of Reason / 2. Logos
Logos is not unconditionally good, but good if there is another person willing to engage with it [Roochnik]
     Full Idea: Logos is not unconditionally good, but good contingent on there being some other person (out there) who is willing to talk with logos, to approach it even as an opponent.
     From: David Roochnik (The Tragedy of Reason [1990], p.175)
'Logos' ranges from thought/reasoning, to words, to rational structures outside thought [Roochnik]
     Full Idea: Logos can mean i) a thought or reasoning, ii) the word which expresses a thought, iii) a rational structure outside human thought. These meanings give 'logos' an extraordinary range.
     From: David Roochnik (The Tragedy of Reason [1990], Intro. 12)
In the seventeenth century the only acceptable form of logos was technical knowledge [Roochnik]
     Full Idea: In the seventeenth century only a certain type of logos was deemed legitimate, namely that identified with technical knowledge (or 'techné').
     From: David Roochnik (The Tragedy of Reason [1990], Intro. 15)
The hallmark of a person with logos is that they give reasons why one opinion is superior to another [Roochnik]
     Full Idea: What is supposed to identify the person of logos from the one without is the commitment to giving reasons explaining why one opinion is superior to another.
     From: David Roochnik (The Tragedy of Reason [1990], Intro. 17)
Human desire has an ordered structure, with logos at the pinnacle [Roochnik]
     Full Idea: Human desire has an ordered structure, with logos at the pinnacle.
     From: David Roochnik (The Tragedy of Reason [1990], p.109)
Logos cannot refute the relativist, and so must admit that it too is a matter of desire (for truth and agreement) [Roochnik]
     Full Idea: Logos cannot refute the radical, consistent and self-conscious relativist. Therefore it must admit that, like the relativist, it itself is essentially a matter of desire. It wants to say what is right and wrong, true and false, and for others to agree.
     From: David Roochnik (The Tragedy of Reason [1990], p.108)
2. Reason / A. Nature of Reason / 4. Aims of Reason
We prefer reason or poetry according to whether basics are intelligible or not [Roochnik]
     Full Idea: Is the arché (basis) intelligible, or is it chaos? Upon this question hinges all, for answering it determines whether poetry or logos is the form of human speech that best does justice to the world.
     From: David Roochnik (The Tragedy of Reason [1990], p.139)
2. Reason / A. Nature of Reason / 8. Naturalising Reason
Modern science, by aiming for clarity about the external world, has abandoned rationality in the human world [Roochnik]
     Full Idea: The modern scientific world view, with all its hope for clarity and precision, has a flipside, …which is its abandonment of rationality in the world of human significance.
     From: David Roochnik (The Tragedy of Reason [1990], p.74)
2. Reason / A. Nature of Reason / 9. Limits of Reason
Attempts to suspend all presuppositions are hopeless, because a common ground must be agreed for the process [Roochnik]
     Full Idea: To debate about suspending all our presuppositions requires a common ground which, upon being established, immediately renders the debate superfluous.
     From: David Roochnik (The Tragedy of Reason [1990], p.144)
Unfortunately for reason, argument can't be used to establish the value of argument [Roochnik]
     Full Idea: Unfortunately for the logos there is no argument that can, without begging the question, establish the goodness of argumentation.
     From: David Roochnik (The Tragedy of Reason [1990], p.106)
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K]
     Full Idea: On saying that a particular number exists, we are not saying that there is something identical to it, but saying something about its status as a genuine constituent of the world.
     From: Kit Fine (The Question of Ontology [2009], p.168)
     A reaction: This is aimed at Frege's criterion of identity, which is to be an element in an identity relation, such as x = y. Fine suggests that this only gives a 'trivial' notion of existence, when he is interested in a 'thick' sense of 'exists'.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K]
     Full Idea: It is not implausible that before the 'introduction' of complex numbers, it would have been incorrect for mathematicians to claim that there was a solution to the equation 'x^2 = -1' under a completely unrestricted understanding of 'there are'.
     From: Kit Fine (The Question of Ontology [2009])
     A reaction: I have adopted this as the crucial test question for anyone's attitude to platonism in mathematics. I take it as obvious that complex numbers were simply invented so that such equations could be dealt with. They weren't 'discovered'!
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K]
     Full Idea: Arguments such as the dispensability argument are attempting to show something about the essentially non-numerical character of physical reality, rather than something about the nature or non-existence of the numbers themselves.
     From: Kit Fine (The Question of Ontology [2009], p.160)
     A reaction: This is aimed at Hartry Field. If Quine was right, and we only believe in numbers because of our science, and then Field shows our science doesn't need it, then Fine would be wrong. Quine must be wrong, as well as Field.
7. Existence / A. Nature of Existence / 1. Nature of Existence
'Exists' is a predicate, not a quantifier; 'electrons exist' is like 'electrons spin' [Fine,K]
     Full Idea: The most natural reading of 'electrons exist' is that there are electrons while, on our view, the proper reading should be modeled on 'electrons spin', meaning every electron spins. 'Exists' should be treated as a predicate rather than a quantifier.
     From: Kit Fine (The Question of Ontology [2009], p.167)
     A reaction: So existence IS a predicate (message to Kant). Dunno. Electrons have to exist in order to spin, but they don't have to exist in order to exist. But they don't have to exist to be 'dead'.
7. Existence / A. Nature of Existence / 4. Abstract Existence
Just as we introduced complex numbers, so we introduced sums and temporal parts [Fine,K]
     Full Idea: Just as one can extend the domain of discourse to include solutions to the equation 'x^2=-1' so one can extend the domain of discourse to include objects that satisfy the condition 'x is the sum of the G's' or 'x is a temporal part of the object b at t'.
     From: Kit Fine (The Question of Ontology [2009], p.164)
     A reaction: This thought lies behind Fine's 'Proceduralism'. I take it that our collection of abstracta consists entirely of items we have either deliberately or unthinkingly 'introduced' into our discourse when they seemed useful. They then submit to certain laws.
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Real objects are those which figure in the facts that constitute reality [Fine,K]
     Full Idea: The real objects are the objects of reality, those that figure in the facts by which reality is constituted.
     From: Kit Fine (The Question of Ontology [2009], p.172)
     A reaction: And these need to be facts over and above the basic facts. Thus, does the 'equator' constitute reality, over and above the Earth being a rotating sphere? Does 'six' constitute reality, over and above all the possible groups of six objects?
Being real and being fundamental are separate; Thales's water might be real and divisible [Fine,K]
     Full Idea: Being the case in reality and being fundamental are not sufficient for one another. If one agrees with Thales that the world is composed of water, and with Aristotle that water is indefinitely divisible, then water would be real but not fundamental.
     From: Kit Fine (The Question of Ontology [2009], p.174)
     A reaction: Presumably the divisibility would make a reductionist account of water possible. The Atlantic Ocean is real, but water molecules would have a more prominent place in the ontology of any good metaphysician.
7. Existence / D. Theories of Reality / 1. Ontologies
For ontology we need, not internal or external views, but a view from outside reality [Fine,K]
     Full Idea: We need to straddle both of Carnap's internal and external views. It is only by standing outside of reality that we are able to occupy a standpoint from which the constitution of reality can be adequately described.
     From: Kit Fine (The Question of Ontology [2009], p.174)
     A reaction: See Idea 4840! I thoroughly approve of this idea, which almost amounts to a Credo for the modern metaphysician. Since we can think outside our room, or our country, or our era, or our solar system, I think we can do what Fine is demanding.
7. Existence / D. Theories of Reality / 3. Reality
Reality can be viewed neutrally, or as an object of desire [Roochnik]
     Full Idea: There are two extremes: the Aristotelian views reality simply as reality, and the sophist or poet views reality only as an object of desire.
     From: David Roochnik (The Tragedy of Reason [1990], p.199)
     A reaction: Not sure about the second one. Does this express an actual desire, or just a hope? Could there be a mind for which its reality was only an aspiration?
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
Ontological claims are often universal, and not a matter of existential quantification [Fine,K]
     Full Idea: I suggest we give up on the account of ontological claims in terms of existential quantification. The commitment to the integers is not an existential but a universal commitment, to each of the integers, not to some integer or other.
     From: Kit Fine (The Question of Ontology [2009], p.167)
     A reaction: In classical logic it is only the existential quantifier which requires the domain to be populated, so Fine is more or less giving up on classical logic as a tool for doing ontology (apparently?).
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
Relativism is a disease which destroys the possibility of rational debate [Roochnik]
     Full Idea: Relativism is disease, is pollution, for it negates the efficacy of logos. It destroys the possibility of a complete rational debate of fundamental questions.
     From: David Roochnik (The Tragedy of Reason [1990], p.41)
19. Language / F. Communication / 1. Rhetoric
Reasoning aims not at the understanding of objects, but at the desire to give beautiful speeches [Roochnik]
     Full Idea: Logos originates not in a cognitive capacity for the apprehension of objects, but in the desire to give birth to beautiful speeches.
     From: David Roochnik (The Tragedy of Reason [1990], p.124)
     A reaction: It is hard for us to grasp this, but it might be quite life-enhancing if we could return to that old way of thought.
If relativism is the correct account of human values, then rhetoric is more important than reasoning [Roochnik]
     Full Idea: If relativism offers an accurate description of human values, then rhetoric replaces logos as the most fundamental human activity.
     From: David Roochnik (The Tragedy of Reason [1990], p.47)
     A reaction: Or putting it another way, logos (reason) becomes meaningless. I suppose, though, that a relativist can conduct conditional reasoning (but must belief in some rules of reason).