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All the ideas for 'Mahaprajnaparamitashastra', 'Notebooks' and 'Mathematics without Foundations'

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22 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Seek wisdom rather than truth; it is easier [Joubert]
     Full Idea: To seek wisdom rather than truth. It is more within our grasp.
     From: Joseph Joubert (Notebooks [1800], 1797)
     A reaction: A nice challenge to the traditional goal of philosophy. The idea that we should 'seek truth' only seems to have emerged during the Reformation. The Greeks may well never have dreamed of such a thing.
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
We must think with our entire body and soul [Joubert]
     Full Idea: Everything we think must be thought with our entire being, body and soul.
     From: Joseph Joubert (Notebooks [1800], 1798)
     A reaction: Not just that thinking must be a whole-hearted activity, but that the very contents of our thinking will be better if it arises out of being a physical creature, and not just a disembodied reasoner. Maybe the bowels are not needed to analyse set theory.
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
The love of certainty holds us back in metaphysics [Joubert]
     Full Idea: What stops or holds us back in metaphysics is a love of certainty.
     From: Joseph Joubert (Notebooks [1800], 1814)
     A reaction: This is a prominent truth from the age of Descartes, but may have diminished in the twenty-first century. The very best metaphysicians (e.g. Aristotle and Lewis) always end in a trail of dots when things become unsure.
2. Reason / A. Nature of Reason / 9. Limits of Reason
The truths of reason instruct, but they do not illuminate [Joubert]
     Full Idea: There are truths that instruct, perhaps, but they do not illuminate. In this class are all the truths of reasoning.
     From: Joseph Joubert (Notebooks [1800], 1800)
     A reaction: A rather romantic view, which strikes me as false. An inspiring truth can suddenly collapse when you see why it must be false. Equally a line of reasoning can lead to a truth which need becomes an illumination.
3. Truth / A. Truth Problems / 1. Truth
Truth consists of having the same idea about something that God has [Joubert]
     Full Idea: Truth consists of having the same idea about something that God has.
     From: Joseph Joubert (Notebooks [1800], 1800)
     A reaction: Presumably sceptics about the existence of objective truth must also be sceptical about the possibility of such a God. I think Joubert is close to the nature of truth here. It is a remote and barely imaginable ideal.
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
We understand some statements about all sets [Putnam]
     Full Idea: We seem to understand some statements about all sets (e.g. 'for every set x and every set y, there is a set z which is the union of x and y').
     From: Hilary Putnam (Mathematics without Foundations [1967], p.308)
     A reaction: His example is the Axiom of Choice. Presumably this is why the collection of all sets must be referred to as a 'class', since we can talk about it, but cannot define it.
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
I do not believe mathematics either has or needs 'foundations' [Putnam]
     Full Idea: I do not believe mathematics either has or needs 'foundations'.
     From: Hilary Putnam (Mathematics without Foundations [1967])
     A reaction: Agreed that mathematics can function well without foundations (given that the enterprise got started with no thought for such things), the ontology of the subject still strikes me as a major question, though maybe not for mathematicians.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
     Full Idea: I believe that under certain circumstances revisions in the axioms of arithmetic, or even of the propositional calculus (e.g. the adoption of a modular logic as a way out of the difficulties in quantum mechanics), is fully conceivable.
     From: Hilary Putnam (Mathematics without Foundations [1967], p.303)
     A reaction: One can change the axioms of a system without necessarily changing the system (by swapping an axiom and a theorem). Especially if platonism is true, since the eternal objects reside calmly above our attempts to axiomatise them!
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Maybe mathematics is empirical in that we could try to change it [Putnam]
     Full Idea: Mathematics might be 'empirical' in the sense that one is allowed to try to put alternatives into the field.
     From: Hilary Putnam (Mathematics without Foundations [1967], p.303)
     A reaction: He admits that change is highly unlikely. It take hardcore Millian arithmetic to be only changeable if pebbles start behaving very differently with regard to their quantities, which appears to be almost inconceivable.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Science requires more than consistency of mathematics [Putnam]
     Full Idea: Science demands much more of a mathematical theory than that it should merely be consistent, as the example of the various alternative systems of geometry dramatizes.
     From: Hilary Putnam (Mathematics without Foundations [1967])
     A reaction: Well said. I don't agree with Putnam's Indispensability claims, but if an apparent system of numbers or lines has no application to the world then I don't consider it to be mathematics. It is a new game, like chess.
7. Existence / D. Theories of Reality / 4. Anti-realism
You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
     Full Idea: Surely the mere fact that we may never know whether the continuum hypothesis is true or false is by itself just no reason to think that it doesn't have a truth value!
     From: Hilary Putnam (Mathematics without Foundations [1967])
     A reaction: This is Putnam in 1967. Things changed later. Personally I am with the younger man all they way, but I reserve the right to totally change my mind.
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
To know is to see inside oneself [Joubert]
     Full Idea: To know: it is to see inside oneself.
     From: Joseph Joubert (Notebooks [1800], 1800)
     A reaction: Extreme internalism about justification! Personally I am becoming convinced that 'know' (unlike 'believe' and 'true') is an entirely social concept. Fools spend a lot of time instrospecting; wise people ask around, and check in books.
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
The imagination has made more discoveries than the eye [Joubert]
     Full Idea: The imagination has made more discoveries than the eye.
     From: Joseph Joubert (Notebooks [1800], 1797)
     A reaction: As a fan of the imagination, I love this one. I suspect that imagination, which was marginalised by Descartes, is actually the single most important aspect of thought (in slugs as well as humans). Abstraction requires imagination.
18. Thought / A. Modes of Thought / 1. Thought
A thought is as real as a cannon ball [Joubert]
     Full Idea: A thought is a thing as real as a cannon ball.
     From: Joseph Joubert (Notebooks [1800], 1801)
     A reaction: Nice. The realisation of a thought can strike someone as if they have been assaulted, and hearing some remarks can be as bad as being stabbed. That is quite apart from political consequences. Joubert is good on the physicality of thinking.
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
Where does the bird's idea of a nest come from? [Joubert]
     Full Idea: The idea of the nest in the bird's mind, where does it come from?
     From: Joseph Joubert (Notebooks [1800], 1800)
     A reaction: I think this is a very striking example in support of innate ideas. Most animal behaviour can be explained as responses to stimuli, but the bird seems to hold a model in its mind while it collects its materials.
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
He gives his body up to pleasure, but not his soul [Joubert]
     Full Idea: He gives his body up to pleasure, but not his soul.
     From: Joseph Joubert (Notebooks [1800], 1799)
     A reaction: A rather crucial distinction in the world of hedonism. There seems something sincere about someone who pursues pleasure body and soul, and something fractured about the pursuit of pleasure without real commitment. The split seems possible.
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
What will you think of pleasures when you no longer enjoy them? [Joubert]
     Full Idea: What will you think of pleasures when you no longer enjoy them?
     From: Joseph Joubert (Notebooks [1800], 1802)
     A reaction: A lovely test question for aspiring young hedonists! It doesn't follow at all that we will despise past pleasures. The judgement may be utilitarian - that we regret the pleasures that harmed others, but love the harmless ones. Shame is social.
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
Virtue is hard if we are scorned; we need support [Joubert]
     Full Idea: It would be difficult to be scorned and to live virtuously. We have need of support.
     From: Joseph Joubert (Notebooks [1800], 1800)
     A reaction: He seems to have hit on what I take to be one of the keys to Aristotle: that virtue is a social matter, requiring both upbringing and a healthy culture. But we can help to create that culture, as well as benefiting from it.
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
25. Social Practice / E. Policies / 5. Education / a. Aims of education
In raising a child we must think of his old age [Joubert]
     Full Idea: In raising a child we must think of his old age.
     From: Joseph Joubert (Notebooks [1800], 1809)
     A reaction: Very nice, and Aristotle would approve. If educators think much about the future, it rarely extends before the child's first job. We should be preparing good grand-parents, as well as parents and employees. Educate for retirement!
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
We can't exactly conceive virtue without the idea of God [Joubert]
     Full Idea: If we exclude the idea of God, it is impossible to have an exact idea of virtue.
     From: Joseph Joubert (Notebooks [1800], 1808)
     A reaction: I suspect that an 'exact' idea is impossible even with an idea of God. This is an interesting defence of the importance of God in moral thinking, but it only requires the concept of a supreme being, and not belief.
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
We cannot speak against Christianity without anger, or speak for it without love [Joubert]
     Full Idea: We cannot speak against Christianity without anger, or speak for it without love.
     From: Joseph Joubert (Notebooks [1800], 1801)
     A reaction: This seems to be rather true at the present time, when a wave of anti-religious books is sweeping through our culture. Presumably this remark used to be true of ancient paganism, but it died away. Christianity, though, is very personal.