Combining Texts
Ideas for
'works', 'Higher-Order Logic' and 'Human Knowledge: its scope and limits'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
11 ideas
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588
|
First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
|
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298
|
Some say that second-order logic is mathematics, not logic [Shapiro]
|
10299
|
If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
|
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300
|
Logical consequence can be defined in terms of the logical terminology [Shapiro]
|
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
4730
|
For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
|
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
16489
|
Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell]
|
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290
|
Second-order variables also range over properties, sets, relations or functions [Shapiro]
|
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10590
|
Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
|
10292
|
Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
|
10296
|
The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
|
10297
|
The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
|