Combining Texts

All the ideas for 'The Principles of Chemistry', 'Dialogues Concerning Natural Religion' and 'Model Theory'

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37 ideas

2. Reason / D. Definition / 7. Contextual Definition
The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
2. Reason / E. Argument / 3. Analogy
An analogy begins to break down as soon as the two cases differ [Hume]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
|= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
|= should be read as 'is a model for' or 'satisfies' [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
Models in model theory are structures, not sets of descriptions [Hodges,W]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
Events are baffling before experience, and obvious after experience [Hume]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
Mendeleev saw three principles in nature: matter, force and spirit (where the latter seems to be essence) [Mendeleev, by Scerri]
27. Natural Reality / F. Chemistry / 2. Modern Elements
Elements don't survive in compounds, but the 'substance' of the element does [Mendeleev]
27. Natural Reality / F. Chemistry / 3. Periodic Table
Mendeleev focused on abstract elements, not simple substances, so he got to their essence [Mendeleev, by Scerri]
Mendeleev had a view of elements which allowed him to overlook some conflicting observations [Mendeleev]
28. God / A. Divine Nature / 3. Divine Perfections
We can't assume God's perfections are like our ideas or like human attributes [Hume]
28. God / B. Proving God / 1. Proof of God
The objects of theological reasoning are too big for our minds [Hume]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
No being's non-existence can imply a contradiction, so its existence cannot be proved a priori [Hume]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
A chain of events requires a cause for the whole as well as the parts, yet the chain is just a sum of parts [Hume]
If something must be necessary so that something exists rather than nothing, why can't the universe be necessary? [Hume]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
The thing which contains order must be God, so see God where you see order [Hume]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
Analogy suggests that God has a very great human mind [Hume]
How can we pronounce on a whole after a brief look at a very small part? [Hume]
If the divine cause is proportional to its effects, the effects are finite, so the Deity cannot be infinite [Hume]
Design cannot prove a unified Deity. Many men make a city, so why not many gods for a world? [Hume]
From a ship you would judge its creator a genius, not a mere humble workman [Hume]
Creation is more like vegetation than human art, so it won't come from reason [Hume]
This excellent world may be the result of a huge sequence of trial-and-error [Hume]
Humans renew their species sexually. If there are many gods, would they not do the same? [Hume]
This Creator god might be an infant or incompetent or senile [Hume]
Order may come from an irrational source as well as a rational one [Hume]
Motion often begins in matter, with no sign of a controlling agent [Hume]
The universe could settle into superficial order, without a designer [Hume]
Ideas arise from objects, not vice versa; ideas only influence matter if they are linked [Hume]
A surprise feature of all products of 9 looks like design, but is actually a necessity [Hume]
The universe may be the result of trial-and-error [Hume]
From our limited view, we cannot tell if the universe is faulty [Hume]
Why would we infer an infinite creator from a finite creation? [Hume]