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7807
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The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra]
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Full Idea:
Bolzano said the 'laws of thought' (identity, contradiction, excluded middle) are true, but nothing of interest follows from them. Logic obeys them, but they are not logic's first principles or axioms.
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From:
report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], §3) by George / Van Evra - The Rise of Modern Logic
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A reaction:
An interesting and crucial distinction. For samples of proposed axioms of logic, see Ideas 6408, 7798 and 7797.
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9618
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Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR]
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Full Idea:
Bolzano if the father of 'arithmetization', which sought to found all of analysis on the concepts of arithmetic and to eliminate geometrical notions entirely (with logicism taking it a step further, by reducing arithmetic to logic).
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From:
report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by James Robert Brown - Philosophy of Mathematics Ch. 3
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A reaction:
Brown's book is a defence of geometrical diagrams against Bolzano's approach. Bolzano sounds like the modern heir of Pythagoras, if he thinks that space is essentially numerical.
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9830
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Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett]
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Full Idea:
Bolzano began the process of eliminating intuition from analysis, by proving something apparently obvious (that as continuous function must be zero at some point). Proof reveals on what a theorem rests, and that it is not intuition.
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From:
report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - Frege philosophy of mathematics Ch.6
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A reaction:
Kant was the target of Bolzano's attack. Two responses might be to say that many other basic ideas are intuited but impossible to prove, or to say that proof itself depends on intuition, if you dig deep enough.
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17265
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Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder]
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Full Idea:
Mathematical proofs are philosophical in method if they do not only demonstrate that a certain mathematical truth holds but if they also disclose why it holds, that is, if they uncover its grounds.
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From:
report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Correia,F/Schnieder,B - Grounding: an opinionated introduction 2.3
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A reaction:
I aim to defend the role of explanation in mathematics, but this says that this is only if the proofs are 'philosophical', which may be of no interest to mathematicians. Oh well, that's their loss.
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9185
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Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
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Full Idea:
Bolzano was determined to expel Kantian intuition from analysis, and to prove from first principles anything that could be proved, no matter how obvious it might seem when thought of in geometrical terms.
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From:
report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - The Philosophy of Mathematics 2.3
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A reaction:
This is characteristic of the Enlightenment Project, well after the Enlightenment. It is a step towards Frege's attack on 'psychologism' in mathematics. The problem is that it led us into a spurious platonism. We live in troubled times.
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17264
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Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder]
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Full Idea:
Bolzano conceived of propositions as abstract objects which are structured compounds of concepts and potential contents of judgements and assertions.
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From:
report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Correia,F/Schnieder,B - Grounding: an opinionated introduction 2.3
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A reaction:
Personally I think of propositions as brain events, the constituents of thought about the world, but that needn't contradict the view of them as 'abstract'.
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12232
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A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano]
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Full Idea:
What I mean by 'propositions' is not what the grammarians call a proposition, namely the linguistic expression, but the mere sense of this expression, is what is meant by proposition in itself or object proposition. This sense can be true or false.
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From:
Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], Pref?)
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A reaction:
This seems to be the origin of what we understand by 'proposition'. The disputes are over whether such things exists, and whether they are features of minds or features of the world (resembling facts).
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6248
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Reason is too slow and doubtful to guide all actions, which need external and moral senses [Hutcheson]
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Full Idea:
We boast of our mighty reason above other animals, but its processes are too slow, too full of doubt, to serve us in every exigency, either for our preservation, without external senses, or to influence our actions for good without the moral sense.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §VII.III)
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A reaction:
This idea was taken up by Hume, and it must have influence Hume's general scepticism about the importance of reason. What this idea misses is the enormous influence of prior reasoning on our quick decisions.
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6239
|
We dislike a traitor, even if they give us great benefit [Hutcheson]
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Full Idea:
Let us consider if a traitor, who would sell his own country to us, may not often be as advantageous to us, as an hero who defends us: and yet we can love the treason, and hate the traitor.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §I.VI)
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A reaction:
A nice example, which certainly refutes any claim that morality is entirely and directly self-interested. High-minded idealism, though, is not the only alternative explanation. We admire loyalty, but not loyalty to, say, Hitler.
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6240
|
The moral sense is not an innate idea, but an ability to approve or disapprove in a disinterested way [Hutcheson]
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Full Idea:
The moral sense is not an innate idea or knowledge, but a determination of our minds to receive the simple ideas of approbation or condemnation, from actions observed, antecedent to any opinions of advantage or loss to redound to ourselves.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §I.VIII)
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A reaction:
This may claim a pure moral intuition, but it is also close to Kantian universalising of the rules for behaviour. It is also a variation on Descartes' 'natural light' of reason. Of course, if we say the ideas are 'received', where are they received from?
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6242
|
We cannot choose our moral feelings, otherwise bribery could affect them [Hutcheson]
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Full Idea:
Neither benevolence nor any other affection or desire can be directly raised by volition; if they could, then we could be bribed into any affection whatsoever toward any object.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §II.IV)
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A reaction:
Of course, notoriously, the vast mass of people have often been bribed to love a politician, by low taxes, or bread and circuses. Still, you cannot choose to love or admire someone, you just do. Not much free will there.
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6244
|
Human nature seems incapable of universal malice, except what results from self-love [Hutcheson]
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Full Idea:
Human nature seems scarce capable of malicious disinterested hatred, or an ultimate desire of the misery of others, when we imagine them not pernicious to us, or opposite to our interests; ..that is only the effect of self-love, not disinterested malice.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §II.VII)
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A reaction:
I suppose it is true that even the worst criminals brooding in prison don't wish the entire population of some foreign country to die in pain. Only a very freakish person would wish the human race were extinct. A very nice observation.
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6243
|
As death approaches, why do we still care about family, friends or country? [Hutcheson]
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Full Idea:
How comes it that we do not lose, at the approach of death, all concern for our families, friends, or country?
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §II.V)
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A reaction:
A nice question. No doubt some people do cease to care, but on the whole it raises the 'last round' problem in social contract theory, which is why fulfil your part of a bargain if it is too late to receive the repayment afterwards?
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7903
|
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
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Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
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From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
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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').
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6241
|
Contempt of danger is just madness if it is not in some worthy cause [Hutcheson]
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Full Idea:
Mere courage, or contempt of danger, if we conceive it to have no regard to the defence of the innocent, or repairing of wrongs or self-interest, would only entitle its possessor to bedlam.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §II.I)
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A reaction:
If many criminals would love to rob a bank, but only a few have the nerve to attempt it, we can hardly deny that the latter exhibit a sort of courage. The Greeks say that good sense must be involved, but few of them were so moral about courage.
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6245
|
That action is best, which procures the greatest happiness for the greatest number [Hutcheson]
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Full Idea:
That action is best, which procures the greatest happiness for the greatest number; and that worst, which, in like manner, occasions misery.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §III.VIII)
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A reaction:
The first use of a phrase taken up by Bentham. This is not just an anticipation of utilitarianism, it is utilitarianism, with all its commitment to consequentialism (but see Idea 6246), and to the maximising of happiness. It is a brilliant idea.
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6251
|
The loss of perfect rights causes misery, but the loss of imperfect rights reduces social good [Hutcheson]
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Full Idea:
Perfect rights are necessary to the public good, and it makes those miserable whose rights are thus violated; …imperfect rights tend to the improvement and increase of good in a society, but are not necessary to prevent universal misery.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §VII.VI)
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A reaction:
This is a very utilitarian streak in Hutcheson, converting natural law into its tangible outcome in actual happiness or misery. The distinction here is interesting (taken up by Mill), but there is a very blurred borderline.
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6249
|
If goodness is constituted by God's will, it is a tautology to say God's will is good [Hutcheson]
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Full Idea:
To call the laws of the supreme Deity good or holy or just, if these be constituted by laws, or the will of a superior, must be an insignificant tautology, amounting to no more than 'God wills what he wills' or 'His will is conformable to his will'.
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From:
Francis Hutcheson (Treatise 2: Virtue or Moral Good [1725], §VII.V)
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A reaction:
This argues not only against God as the source of morality, but also against any rules, such as those of the Categorical Imperative. Why should I follow the Categorical Imperative? What has value must dictate the rules. Is obedience the highest value?
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