green numbers give full details.
|
back to list of philosophers
|
expand these ideas
Ideas of Michal Walicki, by Text
[Norwegian, fl. 2012, At the University of Bergen, Norway.]
|
2012
|
Introduction to Mathematical Logic
|
|
History B.4
|
p.13
|
17742
|
Scotus based modality on semantic consistency, instead of on what the future could allow
|
|
History E.1.3
|
p.33
|
17747
|
A 'model' of a theory specifies interpreting a language in a domain to make all theorems true
|
|
History E.2
|
p.34
|
17748
|
The L-S Theorem says no theory (even of reals) says more than a natural number theory
|
|
History E.2.1
|
p.35
|
17749
|
Post proved the consistency of propositional logic in 1921
|
|
History Intro
|
p.2
|
17741
|
To determine the patterns in logic, one must identify its 'building blocks'
|
|
1.1
|
p.45
|
17752
|
The empty set is useful for defining sets by properties, when the members are not yet known
|
|
1.1
|
p.45
|
17753
|
The empty set avoids having to take special precautions in case members vanish
|
|
2.1.1
|
p.69
|
17754
|
Inductive proof depends on the choice of the ordering
|
|
2.3
|
p.88
|
17755
|
Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals
|
|
2.3
|
p.88
|
17756
|
The union of finite ordinals is the first 'limit ordinal'; 2ω is the second...
|
|
2.3
|
p.89
|
17760
|
Two infinite ordinals can represent a single infinite cardinal
|
|
2.3
|
p.89
|
17758
|
Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion
|
|
2.3
|
p.89
|
17757
|
Members of ordinals are ordinals, and also subsets of ordinals
|
|
2.3
|
p.89
|
17759
|
Ordinals play the central role in set theory, providing the model of well-ordering
|
|
4.1
|
p.118
|
17761
|
A compact axiomatisation makes it possible to understand a field as a whole
|
|
4.1
|
p.122
|
17763
|
Axiomatic systems are purely syntactic, and do not presuppose any interpretation
|
|
4.1
|
p.122
|
17762
|
In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate
|
|
5.1
|
p.143
|
17764
|
Boolean connectives are interpreted as functions on the set {1,0}
|
|
7 Intro
|
p.183
|
17765
|
Propositional language can only relate statements as the same or as different
|