Combining Texts

All the ideas for 'Walking the Tightrope of Reason', 'Philosophy of Arithmetic' and 'Towards a Universal Characteristic'

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32 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
Philosophy may never find foundations, and may undermine our lives in the process [Fogelin]
     Full Idea: Not only is traditional philosophy incapable of discovering the foundations it seeks, but the philosophical enterprise may itself dislodge the contingent, de facto supports that our daily life depends upon.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.2)
     A reaction: In the end Fogelin is not so pessimistic, but he is worried by the concern of philosophers with paradox and contradiction. I don't remotely consider this a reason to reject philosophy, but it might be a reason to keep it sealed off from daily life.
2. Reason / A. Nature of Reason / 1. On Reason
Rationality is threatened by fear of inconsistency, illusions of absolutes or relativism, and doubt [Fogelin]
     Full Idea: The three main threats to our rational lives are fear of inconsistency, illusions (of absolutism and relativism) and doubt.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.4)
     A reaction: This is a very nice analysis of the forces that can destroy the philosopher's aspiration to the rational life. Personally I still suffer from a few illusions about the possibility of absolutes, but I may grow out of it. The other three don't bother me.
2. Reason / A. Nature of Reason / 9. Limits of Reason
Humans may never be able to attain a world view which is both rich and consistent [Fogelin]
     Full Idea: It might be wholly unreasonable to suppose that human beings will ever be able to attain a view of the world that is both suitably rich and completely consistent.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Intro)
     A reaction: Fogelin's lectures develop this view very persuasively. I think all philosophers must believe that the gods could attain a 'rich and consistent' view. Our problem is that we are a badly organised team, whose members keep dying.
A game can be played, despite having inconsistent rules [Fogelin]
     Full Idea: The presence of an inconsistency in the rules that govern a game need not destroy the game.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.2)
     A reaction: He only defends this thesis if the inconsistency is away from the main centre of the action. You can't have an inconsistent definition of scoring a goal or a touchdown.
2. Reason / B. Laws of Thought / 1. Laws of Thought
The law of noncontradiction is traditionally the most basic principle of rationality [Fogelin]
     Full Idea: Traditionally many philosophers (Aristotle among them) have considered the law of noncontradiction to be the deepest, most fundamental principle of rationality.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.1)
     A reaction: For Aristotle, see Idea 1601 (and 'Metaphysics' 1005b28). The only denier of the basic character of the law that I know of is Nietzsche (Idea 4531). Fogelin, despite many qualifications, endorses the law, and so do I.
2. Reason / B. Laws of Thought / 3. Non-Contradiction
The law of noncontradiction makes the distinction between asserting something and denying it [Fogelin]
     Full Idea: People who reject the law of noncontradiction obliterate any significant difference between asserting something and denying it; …this will not move anyone who genuinely opts either for silence or for madness.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.1)
     A reaction: This seems a sufficiently firm and clear assertion of the basic nature of this law. The only rival view seems to be that of Nietzsche (Idea 4531), but then you wonder how Nietzsche is in a position to assert the relativity of the law.
2. Reason / E. Argument / 3. Analogy
Legal reasoning is analogical, not deductive [Fogelin]
     Full Idea: There is almost universal agreement that legal reasoning is fundamentally analogical, not deductive, in character.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.2)
     A reaction: This raises the question of whether analogy can be considered as 'reasoning' in itself. How do you compare the examples? Could you compare two examples if you lacked language, or rules, or a scale of values?
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
'Blind thought' is reasoning without recognition of the ingredients of the reasoning [Leibniz, by Arthur,R]
     Full Idea: Leibniz invented the concept of 'blind thought' - reasoning by a manipulation of characters without being able to recognise what each character stands for.
     From: report of Gottfried Leibniz (Towards a Universal Characteristic [1677]) by Richard T.W. Arthur - Leibniz
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We can assign a characteristic number to every single object [Leibniz]
     Full Idea: The true principle is that we can assign to every object its determined characteristic number.
     From: Gottfried Leibniz (Towards a Universal Characteristic [1677], p.18)
     A reaction: I add this as a predecessor of Gödel numbering. It is part of Leibniz's huge plan for a Universal Characteristic, to map reality numerically, and then calculate the truths about it. Gödel seems to allow metaphysics to be done mathematically.
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.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
Everything is subsumed under number, which is a metaphysical statics of the universe, revealing powers [Leibniz]
     Full Idea: There is nothing which is not subsumable under number; number is therefore a fundamental metaphysical form, and arithmetic a sort of statics of the universe, in which the powers of things are revealed.
     From: Gottfried Leibniz (Towards a Universal Characteristic [1677], p.17)
     A reaction: I take numbers to be a highly generalised and idealised description of an aspect of reality (seen as mainly constituted by countable substances). Seeing reality as processes doesn't lead us to number. So I like this idea.
10. Modality / C. Sources of Modality / 3. Necessity by Convention
Conventions can only work if they are based on something non-conventional [Fogelin]
     Full Idea: Convention, to exist at all, must have a basis in something that is not conventional; conventions, to work, need something nonconventional to build upon and shape.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.3)
     A reaction: Fogelin attributes his point to Hume. I agree entirely. No convention could ever possibly catch on in a society unless there were some point to it. If you can't see a point to a convention (like wearing ties) then start looking, because it's there.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
My view is 'circumspect rationalism' - that only our intellect can comprehend the world [Fogelin]
     Full Idea: My own view might be called 'circumspect rationalism' - the view that our intellectual faculties provide our only means for comprehending the world in which we find oruselves.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.3)
     A reaction: He needs to say more than that to offer a theory, but I like the label, and it fits the modern revival of rationalism, with which I sympathise, and which rests, I think, on Russell's point that self-evidence comes in degrees, not as all-or-nothing truth.
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
Knowledge is legitimate only if all relevant defeaters have been eliminated [Fogelin]
     Full Idea: In general a knowledge claim is legitimate only if all relevant defeaters have been eliminated.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.4)
     A reaction: The problem here is what is 'relevant'. Fogelin's example is 'Are you sure the suspect doesn't have a twin brother?' If virtual reality is relevant, most knowledge is defeated. Certainly, imaginative people feel that they know less than others.
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
For coherentists, circularity is acceptable if the circle is large, rich and coherent [Fogelin]
     Full Idea: Coherentists argue that if the circle of justifications is big enough, rich enough, coherent enough, and so on, then there is nothing wrong circularity.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.4)
     A reaction: There must always be something wrong with circularity, and no god would put up with it, but we might have to. Of course, two pieces of evidence might be unconnected, such as an equation and an observation.
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
A rule of justification might be: don't raise the level of scrutiny without a good reason [Fogelin]
     Full Idea: One rule for the justification of knowledge might be: Do not raise the level of scrutiny in the absence of a particular reason that triggers it.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.4)
     A reaction: That won't decide the appropriate level of scrutiny from which to start. One of my maxims is 'don't set the bar too high', but it seems tough that one should have to justify moving it. The early scientists tried raising it, and were amazed by the results.
13. Knowledge Criteria / D. Scepticism / 2. Types of Scepticism
Scepticism is cartesian (sceptical scenarios), or Humean (future), or Pyrrhonian (suspend belief) [Fogelin]
     Full Idea: The three forms of scepticism are cartesian, Humean and Pyrrhonian. The first challenges belief by inventing sceptical scenarios; the second doubts the future; the third aims to suspend belief.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.4)
     A reaction: A standard distinction is made between methodological and global scepticism. The former seems to be Cartesian, and the latter Pyrrhonian. The interest here is see Hume placed in a distinctive category, because of his views on induction.
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Scepticism deals in remote possibilities that are ineliminable and set the standard very high [Fogelin]
     Full Idea: Sceptical scenarios deal in wildly remote defeating possibilities, so that the level of scrutiny becomes unrestrictedly high, and they also usually deal with defeators that are in principle ineliminable.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.4)
     A reaction: The question of how high we 'set the bar' seems to me central to epistemology. There is clearly an element of social negotiation involved, centring on what is appropriate. If, though, scepticism is 'ineliminable', we must face up to that.
13. Knowledge Criteria / E. Relativism / 1. Relativism
Radical perspectivism replaces Kant's necessary scheme with many different schemes [Fogelin]
     Full Idea: We reach radical perspectivism by replacing Kant's single, necessary categorial scheme with a plurality of competing categorial schemes.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.3)
     A reaction: It certainly looks as if Kant sent us down a slippery slope into the dafter aspects of twentieth century relativism. The best antidote I know of is Davidson's (e.g. Idea 6398). But then it seems unimaginative to say that only one scheme is possible.
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 / A. Modes of Thought / 5. Rationality / b. Human rationality
We are also irrational, with a unique ability to believe in bizarre self-created fictions [Fogelin]
     Full Idea: We as human beings are also irrational animals, unique among animals in our capacity to place faith in bizarre fictions of our own construction.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Intro)
     A reaction: This is glaringly true, and a very nice corrective to the talk of Greeks and others about man as the 'rational animal'. From a distance we might be described by Martians as the 'mad animal'. Is the irrational current too strong to swim against?
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.
21. Aesthetics / A. Aesthetic Experience / 3. Taste
Critics must be causally entangled with their subject matter [Fogelin]
     Full Idea: Critics must become causally entangled with their subject matter.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.6)
     A reaction: This remark is built on Hume's views. You may have a strong view about a singer, but it may be hard to maintain when someone plays you six rival versions of the same piece. I agree entirely with the remark. It means there are aesthetic experts.
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
The word 'beautiful', when deprived of context, is nearly contentless [Fogelin]
     Full Idea: Like the word 'good', the word 'beautiful', when deprived of contextual support, is nearly contentless.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.6)
     A reaction: If I say with, for example, Oscar Wilde that beauty is the highest ideal in life, this doesn't strike me as contentless, but I still sympathise with Fogelin's notion that beauty is rooted in particulars.
21. Aesthetics / C. Artistic Issues / 5. Objectivism in Art
Saying 'It's all a matter to taste' ignores the properties of the object discussed [Fogelin]
     Full Idea: "It is all a matter of taste" may be an all-purpose stopper of discussions of aesthetic values, but it also completely severs the connection with the actual properties of the object under consideration.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.6)
     A reaction: This remark grows out of his discussion of Hume. I like this remark, which ties in with Particularism in morality, and with the central role of experiments in science. The world forces beliefs on us.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Cynics are committed to morality, but disappointed or disgusted by human failings [Fogelin]
     Full Idea: Cynics are usually unswerving in their commitment to a moral ideal, but disappointed or disgusted by humanity's failure to meet it.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.3)
     A reaction: I felt quite suicidal the other day when I saw someone park diagonally across two parking spaces. They can't seem to grasp the elementary Kantian slogan 'What if everybody did that?' It's all hopeless. I wonder if I am becoming a bit of a Cynic?
25. Social Practice / D. Justice / 3. Punishment / a. Right to punish
Deterrence, prevention, rehabilitation and retribution can come into conflict in punishments [Fogelin]
     Full Idea: The purposes of punishment include deterrence, prevention, rehabilitation, and retribution, but they don't always sit well together. Deterrence is best served by making prisons miserable places, but this may run counter to rehabilitation.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.2)
     A reaction: It seems to most educated people that retribution should be pushed far down the list if we are to be civilised (see Idea 1659), and yet personal revenge for a small act of aggression seems basic, normal and acceptable. We dream of rehabilitation.
Retributivists say a crime can be 'paid for'; deterrentists still worry about potential victims [Fogelin]
     Full Idea: A strict retributivist is likely to say that once a crime is paid for, that's that; a deterrence theorist is likely to say that the protection of potential victims overrides the released convict's right to a free and fresh start.
     From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.2)
     A reaction: Interesting since the retributivist here has the more liberal attitude. Reformists will also have a dilemma when years in prison have failed to reform the convict. Virtue theorists like balance, and sensitively consider our relations with the criminals.