26 ideas
| 22138 | Science rests on scholastic metaphysics, not on Hume, Kant or Carnap [Boulter] |
| Full Idea: The metaphysical principles that allow the scientist to learn from experience are scholastic, not Humean or Kantian or those of twentieth-century positivism. | |
| From: Stephen Boulter (Why Medieval Philosophy Matters [2019], 2) | |
| A reaction: Love this. Most modern philosophers of science would be deeply outraged by this, but I reckon that careful and open-minded interviews with scientists would prove it to be correct. We want to know the essential nature of electrons. |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| Full Idea: One can distinguish at least two quite different senses of logic: as an instrument of demonstration, and perhaps as an instrument for the characterization of structures. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: This is trying to capture the proof-theory and semantic aspects, but merely 'characterizing' something sounds like a rather feeble aspiration for the semantic side of things. Isn't it to do with truth, rather than just rule-following? |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| Full Idea: Elementary logic cannot characterize the usual mathematical structures, but seems to be distinguished by its completeness. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| Full Idea: The expressive power of second-order logic is too great to admit a proof procedure, but is adequate to express set-theoretical statements, and open questions such as the continuum hypothesis or the existence of big cardinals are easily stated. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| Full Idea: In sentential logic there is a simple proof that all truth functions, of any number of arguments, are definable from (say) 'not' and 'and'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §0) | |
| A reaction: The point of 'say' is that it can be got down to two connectives, and these are just the usual preferred pair. |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| Full Idea: The symbols ∀ and ∃ may, to start with, be regarded as extrapolations of the truth functional connectives ∧ ('and') and ∨ ('or') to infinite domains. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §5) |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| Full Idea: One might add to one's logic an 'uncountable quantifier', or a 'Chang quantifier', or a 'two-argument quantifier', or 'Shelah's quantifier', or 'branching quantifiers'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) | |
| A reaction: [compressed - just listed for reference, if you collect quantifiers, like collecting butterflies] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| Full Idea: Skolem deduced from the Löwenheim-Skolem theorem that 'the absolutist conceptions of Cantor's theory' are 'illusory'. I think it is clear that this conclusion would not follow even if elementary logic were in some sense the true logic, as Skolem assumed. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §7) | |
| A reaction: [Tharp cites Skolem 1962 p.47] Kit Fine refers to accepters of this scepticism about the arithmetic of infinities as 'Skolemites'. |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| Full Idea: The Löwenheim-Skolem property seems to be undesirable, in that it states a limitation concerning the distinctions the logic is capable of making, such as saying there are uncountably many reals ('Skolem's Paradox'). | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| Full Idea: Soundness would seem to be an essential requirement of a proof procedure, since there is little point in proving formulas which may turn out to be false under some interpretation. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| Full Idea: Putting completeness and compactness together, one has axiomatizability. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §1) |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| Full Idea: In general, if completeness fails there is no algorithm to list the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: I.e. the theory is not effectively enumerable. |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| Full Idea: It is strange that compactness is often ignored in discussions of philosophy of logic, since the most important theories have infinitely many axioms. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: An example of infinite axioms is the induction schema in first-order Peano Arithmetic. |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| Full Idea: The compactness condition seems to state some weakness of the logic (as if it were futile to add infinitely many hypotheses). To look at it another way, formalizations of (say) arithmetic will admit of non-standard models. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| Full Idea: A complete logic has an effective enumeration of the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| Full Idea: Despite completeness, the mere existence of an effective enumeration of the valid formulas will not, by itself, provide knowledge. For example, one might be able to prove that there is an effective enumeration, without being able to specify one. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: The point is that completeness is supposed to ensure knowledge (of what is valid but unprovable), and completeness entails effective enumerability, but more than the latter is needed to do the key job. |
| 22134 | Thoughts are general, but the world isn't, so how can we think accurately? [Boulter] |
| Full Idea: Our thoughts are full of generalities, but the world contains no generalities. So how can our thoughts accurately represent the world? This is the problem of universals. | |
| From: Stephen Boulter (Why Medieval Philosophy Matters [2019], 1) | |
| A reaction: I so love it when someone comes up with a really clear explanation of a problem, and this is a beauty from Stephen Boulter. Only a really clear explanation can motivate philosophical issues for non-philosophers. |
| 22150 | Logical possibility needs the concepts of the proposition to be adequate [Boulter] |
| Full Idea: One can only be sure that a proposition expresses a genuine logical possibility if one can be sure that one's concepts are adequate to things referred to in the proposition. | |
| From: Stephen Boulter (Why Medieval Philosophy Matters [2019], 4) | |
| A reaction: Boulter says this is a logical constraint place on logical possibility by the scholastics which tends to be neglected by modern thinkers, who only worry about whether the proposition implies a contradiction. So we now use thought experiments. |
| 22139 | Experiments don't just observe; they look to see what interventions change the natural order [Boulter] |
| Full Idea: Experiments differ from observational studies in that experiments usually involve intervening in some way in the natural order to see if altering something about that order causes a change in the response of that order. | |
| From: Stephen Boulter (Why Medieval Philosophy Matters [2019], 2) | |
| A reaction: Not convinced by this. Lots of experiments isolate a natural process, rather than 'intervening'. Chemists constantly purify substances. Particle accelerators pick out things to accelerate. Does 'intervening' in nature even make sense? |
| 22136 | Science begins with sufficient reason, de-animation, and the importance of nature [Boulter] |
| Full Idea: Three assumptions needed for the emergence of science are central to medieval thought: that the natural order is subject to the principle of sufficient reason, that nature is de-animated, and that it is worthy of study. | |
| From: Stephen Boulter (Why Medieval Philosophy Matters [2019], 2) | |
| A reaction: A very illuminating and convincing observation. Why did Europe produce major science? The answer is likely to be found in Christianity. |
| 14644 | If my conception of pain derives from me, it is a contradiction to speak of another's pain [Malcolm] |
| Full Idea: If I obtain my conception of pain from pain that I experience, then it will be a part of my conception of pain that I am the only being that can experience it. For me it will be contradiction to speak of another's pain. | |
| From: Norman Malcolm (Wittgenstein's 'Philosophical Investigations' [1954]), quoted by Alvin Plantinga - De Re and De Dicto p.44 | |
| A reaction: This obviously has the private language argument in the background. It seems to point towards a behaviourist view, that I derive pain from external behaviour in the first instance. So how do I connect the behaviour to the feeling? |
| 22135 | Our concepts can never fully capture reality, but simplification does not falsify [Boulter] |
| Full Idea: While the natural order is richer than our conceptual representations of it, nonetheless our concepts can be adequate to real singulars because simplification is not falsification. | |
| From: Stephen Boulter (Why Medieval Philosophy Matters [2019], 1) | |
| A reaction: I don't know if 'simplification' is one of the faculties I am trying to identify. I suspect it is a common factor among most of our intellectual faculties. I love 'simplification is not falsification'. Vagueness isn't falsification either. |
| 22152 | Aristotelians accept the analytic-synthetic distinction [Boulter] |
| Full Idea: Aristotle and the scholastics accept the analytic/synthetic distinction, but do not take it to be particularly significant. | |
| From: Stephen Boulter (Why Medieval Philosophy Matters [2019], 5) | |
| A reaction: I record this because I'm an Aristotelian, and need to know what I'm supposed to think. Luckily, I accept the distinction. |
| 22156 | The facts about human health are the measure of the values in our lives [Boulter] |
| Full Idea: The objective facts relating to human health broadly construed are the facts that measure the moral value of our actions, policies and institutions. | |
| From: Stephen Boulter (Why Medieval Philosophy Matters [2019], 6) | |
| A reaction: This is the Aristotelian approach to facts and values, which I thoroughly endorse. To say there is nothing instrinsically wrong with being unhealthy is an absurd attitude. |
| 1422 | God's existence is either necessary or impossible, and no one has shown that the concept of God is contradictory [Malcolm] |
| Full Idea: God's existence is either impossible or necessary. It can be the former only if the concept of such a being is self-contradictory or in some way logically absurd. Assuming that this is not so, it follows that He necessarily exists. | |
| From: Norman Malcolm (Anselm's Argument [1959], §2) | |
| A reaction: The concept of God suggests paradoxes of omniscience, omnipotence and free will, so self-contradiction seems possible. How should we respond if the argument suggests God is necessary, but evidence suggests God is highly unlikely? |