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Single Idea 14984
[filed under theme 4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
]
Full Idea
Should our fundamental theory of part and whole take 'part' or 'overlap' as primitive?
Gist of Idea
Which should be primitive in mereology - part, or overlap?
Source
Theodore Sider (Writing the Book of the World [2011], 02.3)
Book Ref
Sider,Theodore: 'Writing the Book of the World' [OUP 2011], p.13
Related Idea
Idea 12826
Sum: the sum of individuals is what is overlapped if either of them are, written 'x + y' [Simons]
The
124 ideas
from Theodore Sider
14752
|
Artists 'create' statues because they are essentially statues, and so lack identity with the lump of clay
[Sider]
|
14721
|
Metaphysical enquiry can survive if its conclusions are tentative
[Sider]
|
14722
|
Between presentism and eternalism is the 'growing block' view - the past is real, the future is not
[Sider]
|
14723
|
Talk using tenses can be eliminated, by reducing it to indexical connections for an utterance
[Sider]
|
14724
|
Presentists must deny truths about multiple times
[Sider]
|
14725
|
Maybe motion is a dynamical quantity intrinsic to a thing at a particular time
[Sider]
|
14194
|
Proper ontology should only use categorical (actual) properties, not hypothetical ones
[Sider]
|
14726
|
Four-dimensionalists assert 'temporal parts', 'perduring', and being spread out over time
[Sider]
|
14727
|
Three-dimensionalists assert 'enduring', being wholly present at each moment, and deny 'temporal parts'
[Sider]
|
14729
|
4D says each spatiotemporal object must have a temporal part at every moment at which it exists
[Sider]
|
14728
|
4D says intrinsic change is difference between successive parts
[Sider]
|
14731
|
Temporal parts are instantaneous
[Sider]
|
14730
|
Temporal parts exist, but are not prior building blocks for objects
[Sider]
|
14734
|
The B-series involves eternalism, and the reduction of tense
[Sider]
|
14735
|
Space is 3D and lacks a direction; time seems connected to causation
[Sider]
|
14736
|
The B-theory is adequate, except that it omits to say which time is present
[Sider]
|
14741
|
The ship undergoes 'asymmetric' fission, where one candidate is seen as stronger
[Sider]
|
14743
|
The stage view of objects is best for dealing with coincident entities
[Sider]
|
14740
|
If Tib is all of Tibbles bar her tail, when Tibbles loses her tail, two different things become one
[Sider]
|
14747
|
'Composition as identity' says that an object just is the objects which compose it
[Sider]
|
14745
|
If sortal terms fix the kind and the persistence conditions, we need to know what kinds there are
[Sider]
|
14754
|
If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity
[Sider]
|
14756
|
For Presentists there must always be a temporal vantage point for any description
[Sider]
|
14757
|
Mereological essentialism says an object's parts are necessary for its existence
[Sider]
|
14758
|
How can an instantaneous stage believe anything, if beliefs take time?
[Sider]
|
14760
|
Four-dimensionalism sees things and processes as belonging in the same category
[Sider]
|
14762
|
Four-dimensionalism says temporal parts are caused (through laws of motion) by previous temporal parts
[Sider]
|
14763
|
Counterparts rest on similarity, so there are many such relations in different contexts
[Sider]
|
14738
|
Some might say that its inconsistency with time travel is a reason to favour three-dimensionalism
[Sider]
|
13678
|
The most popular account of logical consequence is the semantic or model-theoretic one
[Sider]
|
13679
|
Maybe logical consequence is more a matter of provability than of truth-preservation
[Sider]
|
13680
|
Maybe logical consequence is a primitive notion
[Sider]
|
13682
|
Maybe logical consequence is impossibility of the premises being true and the consequent false
[Sider]
|
13683
|
A relation is a feature of multiple objects taken together
[Sider]
|
13724
|
In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation
[Sider]
|
13684
|
The semantical notion of a logical truth is validity, being true in all interpretations
[Sider]
|
13685
|
Natural deduction helpfully allows reasoning with assumptions
[Sider]
|
13686
|
We can build proofs just from conclusions, rather than from plain formulae
[Sider]
|
13687
|
No assumptions in axiomatic proofs, so no conditional proof or reductio
[Sider]
|
13688
|
Good axioms should be indisputable logical truths
[Sider]
|
13689
|
'Theorems' are formulas provable from no premises at all
[Sider]
|
13690
|
Proof by induction 'on the length of the formula' deconstructs a formula into its accepted atoms
[Sider]
|
13691
|
Induction has a 'base case', then an 'inductive hypothesis', and then the 'inductive step'
[Sider]
|
13693
|
A 'supervaluation' assigns further Ts and Fs, if they have been assigned in every precisification
[Sider]
|
13692
|
A 'precisification' of a trivalent interpretation reduces it to a bivalent interpretation
[Sider]
|
13694
|
We can 'sharpen' vague terms, and then define truth as true-on-all-sharpenings
[Sider]
|
13695
|
Supervaluational logic is classical, except when it adds the 'Definitely' operator
[Sider]
|
13696
|
When a variable is 'free' of the quantifier, the result seems incapable of truth or falsity
[Sider]
|
13697
|
Valuations in PC assign truth values to formulas relative to variable assignments
[Sider]
|
13698
|
In a complete logic you can avoid axiomatic proofs, by using models to show consequences
[Sider]
|
13699
|
Compactness surprisingly says that no contradictions can emerge when the set goes infinite
[Sider]
|
13700
|
A 'total' function must always produce an output for a given domain
[Sider]
|
13701
|
A single second-order sentence validates all of arithmetic - but this can't be proved axiomatically
[Sider]
|
13702
|
The identity of indiscernibles is necessarily true, if being a member of some set counts as a property
[Sider]
|
13703
|
λ can treat 'is cold and hungry' as a single predicate
[Sider]
|
13705
|
Truth tables assume truth functionality, and are just pictures of truth functions
[Sider]
|
13704
|
It is hard to say which are the logical truths in modal logic, especially for iterated modal operators
[Sider]
|
13706
|
Intuitively, deontic accessibility seems not to be reflexive, but to be serial
[Sider]
|
13707
|
Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible
[Sider]
|
13708
|
S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid
[Sider]
|
13709
|
Logical truths must be necessary if anything is
[Sider]
|
13710
|
In D we add that 'what is necessary is possible'; then tautologies are possible, and contradictions not necessary
[Sider]
|
13711
|
System B introduces iterated modalities
[Sider]
|
13712
|
Epistemic accessibility is reflexive, and allows positive and negative introspection (KK and K¬K)
[Sider]
|
13714
|
We can treat modal worlds as different times
[Sider]
|
13715
|
You can employ intuitionist logic without intuitionism about mathematics
[Sider]
|
13716
|
'If B hadn't shot L someone else would have' if false; 'If B didn't shoot L, someone else did' is true
[Sider]
|
13717
|
Transworld identity is not a problem in de dicto sentences, which needn't identify an individual
[Sider]
|
13719
|
Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost
[Sider]
|
13720
|
Converse Barcan Formula: □∀αφ→∀α□φ
[Sider]
|
13718
|
The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic
[Sider]
|
13721
|
'Strong' necessity in all possible worlds; 'weak' necessity in the worlds where the relevant objects exist
[Sider]
|
13723
|
System B is needed to prove the Barcan Formula
[Sider]
|
13722
|
A 'theorem' is an axiom, or the last line of a legitimate proof
[Sider]
|
9218
|
Maybe what distinguishes philosophy from science is its pursuit of necessary truths
[Sider]
|
14977
|
Metaphysics is not about what exists or is true or essential; it is about the structure of reality
[Sider]
|
14978
|
A property is intrinsic if an object alone in the world can instantiate it
[Sider]
|
14980
|
There is a real issue over what is the 'correct' logic
[Sider]
|
14981
|
Philosophical concepts are rarely defined, and are not understood by means of definitions
[Sider]
|
14982
|
If I used Ramsey sentences to eliminate fundamentality from my theory, that would be a real loss
[Sider]
|
14983
|
Accept the ontology of your best theory - and also that it carves nature at the joints
[Sider]
|
14984
|
Which should be primitive in mereology - part, or overlap?
[Sider]
|
14985
|
The notion of law doesn't seem to enhance physical theories
[Sider]
|
14986
|
Conceptual analysts trust particular intuitions much more than general ones
[Sider]
|
14987
|
Many of the key theories of modern physics do not appear to be 'laws'
[Sider]
|
14988
|
A theory which doesn't fit nature is unexplanatory, even if it is true
[Sider]
|
14989
|
Problem predicates in induction don't reflect the structure of nature
[Sider]
|
14990
|
Bayes produces weird results if the prior probabilities are bizarre
[Sider]
|
14991
|
Space has real betweenness and congruence structure (though it is not the Euclidean concepts)
[Sider]
|
14992
|
We don't care about plain truth, but truth in joint-carving terms
[Sider]
|
14994
|
Extreme doubts about metaphysics also threaten to undermine the science of unobservables
[Sider]
|
14995
|
Predicates can be 'sparse' if there is a universal, or if there is a natural property or relation
[Sider]
|
14997
|
Two applications of 'grue' do not guarantee a similarity between two things
[Sider]
|
14999
|
Prior to conventions, not all green things were green?
[Sider]
|
14998
|
Conventions are contingent and analytic truths are necessary, so that isn't their explanation
[Sider]
|
15001
|
'Tonk' is supposed to follow the elimination and introduction rules, but it can't be so interpreted
[Sider]
|
15000
|
'It is raining' and 'it is not raining' can't be legislated, so we can't legislate 'p or ¬p'
[Sider]
|
15004
|
'Gunk' is an object in which proper parts all endlessly have further proper parts
[Sider]
|
15005
|
Explanations must cite generalisations
[Sider]
|
15003
|
It seems unlikely that the way we speak will give insights into the universe
[Sider]
|
15008
|
Is fundamentality in whole propositions (and holistic), or in concepts (and atomic)?
[Sider]
|
15009
|
We must distinguish 'concrete' from 'abstract' and necessary states of affairs.
[Sider]
|
15010
|
Your metaphysics is 'cheating' if your ontology won't support the beliefs you accept
[Sider]
|
15011
|
If the ultimate explanation is a list of entities, no laws, patterns or mechanisms can be cited
[Sider]
|
15012
|
Orthodox truthmaker theories make entities fundamental, but that is poor for explanation
[Sider]
|
15013
|
Tables and chairs have fundamental existence, but not fundamental natures
[Sider]
|
15017
|
Supervenience is a modal connection
[Sider]
|
15014
|
Unlike things, stuff obeys unrestricted composition and mereological essentialism
[Sider]
|
15016
|
Analyticity has lost its traditional role, which relied on truth by convention
[Sider]
|
15015
|
It seems possible for a correct definition to be factually incorrect, as in defining 'contact'
[Sider]
|
15019
|
Define logical constants by role in proofs, or as fixed in meaning, or as topic-neutral
[Sider]
|
15020
|
Classical logic is good for mathematics and science, but less good for natural language
[Sider]
|
15021
|
The central question in the philosophy of time is: How alike are time and space?
[Sider]
|
15024
|
The spotlight theorists accepts eternal time, but with a spotlight of the present moving across it
[Sider]
|
15023
|
The Barcan schema implies if X might have fathered something, there is something X might have fathered
[Sider]
|
15025
|
The world does not contain necessity and possibility - merely how things are
[Sider]
|
15027
|
If truths are necessary 'by convention', that seems to make them contingent
[Sider]
|
15028
|
Conventionalism doesn't seem to apply to examples of the necessary a posteriori
[Sider]
|
15026
|
Essence (even if nonmodal) is not fundamental in metaphysics
[Sider]
|
15033
|
Humeans says mathematics and logic are necessary because that is how our concept of necessity works
[Sider]
|
15030
|
Humeans say that we decide what is necessary
[Sider]
|
15029
|
Modal accounts of logical consequence are simple necessity, or essential use of logical words
[Sider]
|
15031
|
Modal terms in English are entirely contextual, with no modality outside the language
[Sider]
|
15018
|
Intentionality is too superficial to appear in the catalogue of ultimate physics
[Sider]
|