15 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. |
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| Full Idea: In present-day mathematics, it is set theory that serves as the background theory in which other branches of mathematics are developed. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: [He cites Bourbaki as an authority for this] See Benacerraf for a famous difficulty here, when you actually try to derive an ontology from the mathematicians' working practices. |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| Full Idea: On the structuralist interpretation, theorems of analysis concerning the real numbers R are about all complete ordered fields. So R, which appears to be the name of a specific structure, is taken to be a variable ranging over structures. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: Since I am beginning to think that nearly all linguistic expressions should be understood as variables, I find this very appealing, even if Burgess hates it. Terms slide and drift, and are vague, between variable and determinate reference. |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
| Full Idea: One might meet the 'Van Inwagen Problem' by saying that the intrinsic properties of the object playing the role of 2 will differ from one model to another, so that no statement about the intrinsic properties of 'the' real numbers will make sense. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §5) | |
| A reaction: There seems to be a potential confusion among opponents of structuralism between relations at the level of actual mathematical operations, and generalisations about relations, which are captured in the word 'patterns'. Call them 'meta-relations'? |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| Full Idea: It is to set theory that one turns for the very definition of 'structure', ...and this creates a problem of circularity if we try to impose a structuralist interpretation on set theory. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: This seems like a nice difficulty, especially if, like Shapiro, you wade in and try to give a formal account of structures and patterns. Resnik is more circumspect and vague. |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| Full Idea: Abstract algebra, such as group theory, is not concerned with the features common to all models of the axioms, but rather with the relationships among different models of those axioms (especially homomorphic relation functions). | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: It doesn't seem to follow that structuralism can't be about the relations (or patterns) found when abstracting away and overviewing all the models. One can study family relations, or one can study kinship in general. |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| Full Idea: The 'Van Inwagen Problem' for structuralism is of explaining how a mathematical relation (such as set membership, or the ratios of an ellipse) can fit into one of the three scholastics types of relations: are they internal, external, or intrinsic? | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §5) | |
| A reaction: The difficulty is that mathematical objects seem to need intrinsic properties to get any of these three versions off the ground (which was Russell's complaint against structures). |
| 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. |
| 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. |
| 16764 | The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus] |
| Full Idea: Every accident of a living thing, as well as all its organs and temperaments and its dispositions are conserved by the soul. We see this from experience, since when that soul recedes, all these dissolve and become corrupted. | |
| From: Franciscus Toletus (Commentary on 'De Anima' [1572], II.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.5 | |
| A reaction: A nice example of observing a phenemonon, but not being able to observe the dependence relation the right way round. Compare Descartes in Idea 16763. |