Combining Texts

All the ideas for 'Improvement of Understanding', 'Gdel's Proof' and 'Identity'

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12 ideas

2. Reason / D. Definition / 2. Aims of Definition
All the intrinsic properties of a thing should be deducible from its definition [Spinoza]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
I could have died at five, but the summation of my adult stages could not [Noonan]
9. Objects / E. Objects over Time / 5. Temporal Parts
Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan]
9. Objects / F. Identity among Objects / 2. Defining Identity
Problems about identity can't even be formulated without the concept of identity [Noonan]
Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan]
Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan]
Identity can only be characterised in a second-order language [Noonan]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
Indiscernibility is basic to our understanding of identity and distinctness [Noonan]
Leibniz's Law must be kept separate from the substitutivity principle [Noonan]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
To understand the properties we must know the essence, as with a circle [Spinoza]
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
The human intellect has not been, and cannot be, fully formalized [Nagel/Newman]