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Single Idea 22609
[filed under theme 5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
]
Full Idea
First-order predicate logic was accepted so easily by the philosophical community …because philosophy was already geared toward a neo-Humean view of both science and philosophy as primarily descriptive rather than explanatory.
Gist of Idea
Philosophers accepted first-order logic, because they took science to be descriptive, not explanatory
Source
R.D. Ingthorsson (A Powerful Particulars View of Causation [2021], 1.8)
Book Ref
'Oxford Handbook of Philosophy of Time', ed/tr. Callender,Craig [OUP 2013], p.15
A Reaction
The point, I think, is that explanatory thinking needs second-order logic, where the properties (or powers) are players in the game, and not just adjuncts of the catalogue of objects. I find this idea mind-expanding. (That's a good thing).
Related Idea
Idea 22610
It is difficult to handle presentism in first-order logic [Ingthorsson]
The
23 ideas
with the same theme
[logic where variables only refer to objects]:
22873
|
Liberalism should improve the system, and not just ameliorate it
[Dewey]
|
21495
|
Theoretical and practical politics are both concerned with the best lives for individuals
[Russell]
|
18956
|
Asserting first-order validity implicitly involves second-order reference to classes
[Putnam]
|
10767
|
Elementary logic is complete, but cannot capture mathematics
[Tharp]
|
13840
|
First-order logic is the strongest complete compact theory with Löwenheim-Skolem
[Hacking]
|
13844
|
A limitation of first-order logic is that it cannot handle branching quantifiers
[Hacking]
|
18108
|
First-order logic is not decidable: there is no test of whether any formula is valid
[Bostock]
|
18109
|
The completeness of first-order logic implies its compactness
[Bostock]
|
10478
|
Since first-order languages are complete, |= and |- have the same meaning
[Hodges,W]
|
19315
|
In quantified language the components of complex sentences may not be sentences
[Kirkham]
|
17788
|
First-order logic only has its main theorems because it is so weak
[Mayberry]
|
13624
|
The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed
[Shapiro]
|
13660
|
Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable
[Shapiro]
|
13662
|
First-order logic was an afterthought in the development of modern logic
[Shapiro]
|
13673
|
The notion of finitude is actually built into first-order languages
[Shapiro]
|
10588
|
First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems
[Shapiro]
|
10897
|
A first-order 'sentence' is a formula with no free variables
[Zalabardo]
|
10986
|
Not all validity is captured in first-order logic
[Read]
|
13534
|
In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide
[Wolf,RS]
|
13535
|
First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation
[Wolf,RS]
|
20100
|
Classical liberalism seeks freedom of opinion, of private life, of expression, and of property
[Micklethwait/Wooldridge]
|
21122
|
Liberal Nationalism says welfare states and democracy needed a shared sense of nationality
[Shorten]
|
22609
|
Philosophers accepted first-order logic, because they took science to be descriptive, not explanatory
[Ingthorsson]
|