Combining Texts

All the ideas for 'Principle of Life and Plastic Natures', 'Cardinality, Counting and Equinumerosity' and 'Philosophy of Science: Very Short Intro (2nd ed)'

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28 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
The meaning of a number isn't just the numerals leading up to it [Heck]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
Is counting basically mindless, and independent of the cardinality involved? [Heck]
Counting is the assignment of successively larger cardinal numbers to collections [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
We can know 'just as many' without the concepts of equinumerosity or numbers [Heck]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Children can use numbers, without a concept of them as countable objects [Heck]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Equinumerosity is not the same concept as one-one correspondence [Heck]
We can understand cardinality without the idea of one-one correspondence [Heck]
7. Existence / C. Structure of Existence / 2. Reduction
Multiple realisability is said to make reduction impossible [Okasha]
12. Knowledge Sources / B. Perception / 1. Perception
Not all of perception is accompanied by consciousness [Leibniz]
14. Science / A. Basis of Science / 3. Experiment
Not all sciences are experimental; astronomy relies on careful observation [Okasha]
Randomised Control Trials have a treatment and a control group, chosen at random [Okasha]
14. Science / A. Basis of Science / 6. Falsification
The discoverers of Neptune didn't change their theory because of an anomaly [Okasha]
Science mostly aims at confirming theories, rather than falsifying them [Okasha]
14. Science / B. Scientific Theories / 1. Scientific Theory
Theories with unobservables are underdetermined by the evidence [Okasha]
14. Science / B. Scientific Theories / 5. Commensurability
Two things can't be incompatible if they are incommensurable [Okasha]
14. Science / C. Induction / 1. Induction
Induction is inferences from examined to unexamined instances of a given kind [Okasha]
14. Science / C. Induction / 6. Bayes's Theorem
If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
Souls act as if there were no bodies, and bodies act as if there were no souls [Leibniz]
22. Metaethics / B. Value / 2. Values / e. Death
Death and generation are just transformations of an animal, augmented or diminished [Leibniz]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
Not all of matter is animated, any more than a pond full of living fish is animated [Leibniz]
Every particle of matter contains organic bodies [Leibniz]
27. Natural Reality / A. Classical Physics / 1. Mechanics / b. Laws of motion
Galileo refuted the Aristotelian theory that heavier objects fall faster [Okasha]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
Mechanics shows that all motion originates in other motion, so there is a Prime Mover [Leibniz]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
All substances are in harmony, even though separate, so they must have one divine cause [Leibniz]