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All the ideas for 'Defending the Axioms', 'Truth' and 'Notebooks'

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38 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.
1. Philosophy / F. Analytic Philosophy / 3. Analysis of Preconditions
In "if and only if" (iff), "if" expresses the sufficient condition, and "only if" the necessary condition [Engel]
     Full Idea: Necessary and sufficient conditions are usually expressed by "if and only if" (abbr. "iff"), where "if" is the sufficient condition, and "only if" is the necessary condition.
     From: Pascal Engel (Truth [2002], §1.1)
     A reaction: 'I take my umbrella if and only if it is raining' (oh, and if I'm still alive). There may be other necessary conditions than the one specified. Oh, and I take it if my wife slips it into my car…
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.
3. Truth / A. Truth Problems / 5. Truth Bearers
Are truth-bearers propositions, or ideas/beliefs, or sentences/utterances? [Engel]
     Full Idea: The tradition of the Stoics and Frege says that truth-bearers are propositions, Descartes and the classical empiricist say they are ideas or beliefs, and Ockham and Quine say they are sentences or utterances.
     From: Pascal Engel (Truth [2002], §1.1)
     A reaction: I'm with propositions, which are unambiguous, can be expressed in a variety of ways, embody the 'logical form' of sentences, and could be physically embodied in brains (the language of thought?).
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
The redundancy theory gets rid of facts, for 'it is a fact that p' just means 'p' [Engel]
     Full Idea: The redundancy theory gets rid of facts, for 'it is a fact that p' just means 'p'.
     From: Pascal Engel (Truth [2002], §2.2)
     A reaction: But then when you ask what p means, you have to give the truth-conditions for its assertion, and you find you have to mention the facts after all.
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
We can't explain the corresponding structure of the world except by referring to our thoughts [Engel]
     Full Idea: The correspondence theory implies displaying an identity or similarity of structure between the contents of thoughts and the way the world is structured, but we seem only to be able to say that the world's structure corresponds to our thoughts.
     From: Pascal Engel (Truth [2002], §1.2)
     A reaction: I don't accept this. The structure of the world gives rise to our thoughts. There is an epistemological problem here (big time!), but that doesn't alter the metaphysical situation of what truth is supposed to be, which is correspondence.
3. Truth / D. Coherence Truth / 1. Coherence Truth
The coherence theory says truth is an internal relationship between groups of truth-bearers [Engel]
     Full Idea: The coherence theory of truth says that it is a relationship between truth-bearers themselves, that is between propositions or beliefs or sentences.
     From: Pascal Engel (Truth [2002], §1.1)
     A reaction: We immediately begin to wonder how many truth-bearers are required. Two lies can be coherent. It is hard to make thousands of lies coherent, but not impossible. What fixes the critical number. 'All possible propositions' is not much help.
3. Truth / D. Coherence Truth / 2. Coherence Truth Critique
Any coherent set of beliefs can be made more coherent by adding some false beliefs [Engel]
     Full Idea: Any coherent set of beliefs can be made more coherent by adding to it one or more false beliefs.
     From: Pascal Engel (Truth [2002], §1.3)
     A reaction: A simple but rather devastating point. It is the policeman manufacturing a bogus piece of evidence to clinch the conviction, the scientist faking a single observation to fill in the last corner of a promising theory.
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationism seems to block philosophers' main occupation, asking metatheoretical questions [Engel]
     Full Idea: Deflationism about truth seems to deprive us of any hope of asking genuinely metatheoretical questions, which are the questions that occupy philosophers most of the time.
     From: Pascal Engel (Truth [2002], §2.5)
     A reaction: This seems like the best reason for moving from deflationism to at least minimalism. Clearly one can talk meaningfully about the success of assertions and theories. You can say a sentence is true, but not assert it.
Deflationism cannot explain why we hold beliefs for reasons [Engel]
     Full Idea: The deflationist view is silent about the fact that our assertions and beliefs are generally made or held for certain reasons.
     From: Pascal Engel (Truth [2002], §2.5)
     A reaction: The point here must be that I attribute strength to my beliefs, depending on how much support I have for them - how much support for their real truth. I scream "That's really TRUE!" when I have very good reasons.
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Maybe there is no more to be said about 'true' than there is about the function of 'and' in logic [Engel]
     Full Idea: We could compare the status of 'true' with the status of the logical operator 'and' in logic. Once we have explained how it functions to conjoin two propositions, there is not much more to be said about it.
     From: Pascal Engel (Truth [2002], §2.4)
     A reaction: A good statement of the minimalist view. I don't believe it, because I don't believe that truth is confined to language. An uneasy feeling I can't put into words can turn out to be true. Truth is a relational feature of mental states.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
     Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original.
     From: Penelope Maddy (Defending the Axioms [2011], 1.3)
     A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure.
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
     Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation.
     From: Penelope Maddy (Defending the Axioms [2011], 3.3)
     A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics.
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
Deflationism must reduce bivalence ('p is true or false') to excluded middle ('p or not-p') [Engel]
     Full Idea: It is said that deflationism cannot even formulate the principle of bivalence, for 'either p is true or p is false' will amount to the principle of excluded middle, 'either p or not-p'.
     From: Pascal Engel (Truth [2002], §2.4)
     A reaction: Presumably deflationists don't lost any sleep over this - in fact, it looks like a good concise way to state the deflationist thesis. However, excluded middle refers to a proposition (not-p) that was never mentioned by bivalence. Cf Idea 6163.
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
     Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers.
     From: Penelope Maddy (Defending the Axioms [2011], 1.3)
If two mathematical themes coincide, that suggest a single deep truth [Maddy]
     Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth.
     From: Penelope Maddy (Defending the Axioms [2011], 5.3ii)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
     Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals.
     From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
     Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness.
     From: Penelope Maddy (Defending the Axioms [2011], 3.4)
     A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
     Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics.
     From: Penelope Maddy (Defending the Axioms [2011], 2.3)
     A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor.
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
The Humean theory of motivation is that beliefs may be motivators as well as desires [Engel]
     Full Idea: A problem for the Humean theory of motivation is that it is disputed that beliefs are only representational states, which cannot, unlike desires, move us to act.
     From: Pascal Engel (Truth [2002], §4.2)
     A reaction: This is a crucial issue for Humeans and empiricists. Rationalists claim that people act for reasons, so that reasons are intrinsically motivational (like the Form of the Good), and reasons may even be considered direct causes of actions.
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
Our beliefs are meant to fit the world (i.e. be true), where we want the world to fit our desires [Engel]
     Full Idea: Belief is said to 'aim at truth', in the sense that beliefs are the kind of mental states that have to be true for the mind to 'fit' the world (where our desires have the opposite 'direction of fit'; the world is supposed to fit our desires).
     From: Pascal Engel (Truth [2002], §2.5)
     A reaction: I don't think it is possible to give a plausible definition of belief without mentioning truth. Hume's account of them as thoughts with a funny feeling attached is ridiculous. Thinking is an activity, not a passive state.
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
'Evidentialists' say, and 'voluntarists' deny, that we only believe on the basis of evidence [Engel]
     Full Idea: The 'evidentialists' (such as Locke and Hume) deny, and the 'voluntarists' (such as William James) affirm, that we ought to, or at least may, believe for other reasons than evidential epistemic reasons (e.g. for pragmatic reasons).
     From: Pascal Engel (Truth [2002], §5.2)
     A reaction: No need to be black-or-white here. Blatant evidence compels belief, but we may also come to believe by spotting a coherence, without additional evidence. We can also be in a state of trying to believe something. But see 4764.
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
Pragmatism is better understood as a theory of belief than as a theory of truth [Engel]
     Full Idea: Pragmatism in general is better construed as a certain conception of belief, rather than as a distinctive conception of truth.
     From: Pascal Engel (Truth [2002], §1.5)
     A reaction: Which is why aspiring relativists drift towards the pragmatic theory - because they want to dispense with truth (and hence knowledge), and put mere belief in its place.
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.
13. Knowledge Criteria / C. External Justification / 5. Controlling Beliefs
We cannot directly control our beliefs, but we can control the causes of our involuntary beliefs [Engel]
     Full Idea: Direct psychological voluntarism about beliefs seems to be false, but we can have an indirect voluntary control on many of our beliefs, by manipulating the states in us that are involuntary and which lead to certain beliefs.
     From: Pascal Engel (Truth [2002], §5.2)
     A reaction: Very nice! This points two ways - to scientific experiments, which can have compelling outcomes (see Fodor), and to brain-washing, and especially auto-brainwashing (only reading articles which support your favourites theories). What magazines do you take?
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.
17. Mind and Body / C. Functionalism / 1. Functionalism
Mental states as functions are second-order properties, realised by first-order physical properties [Engel]
     Full Idea: For functionalism mental states as roles are second-order properties that have to be realised in various ways in first-order physical properties.
     From: Pascal Engel (Truth [2002], §3.3)
     A reaction: I take that to be properties-of-properties, as in 'bright red' or 'poignantly beautiful'. I am inclined to think (with Edelman) that mind is a process, not a property.
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.
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.