1 A Simple Partition

2

3

4 A partition can be more or less refined

5

6

7 Partition A partition is the drawing of a (typically complex) fiat boundary over a certain domain

8 Artist’s Grid

9 Label/Address System A partition typically comes with labels and/or an address system

10 Montana

11 Cerebral Cortex

12 Mouse Chromosome Five

13 Partitions can sometimes create objects fiat objects = objects determined by partitions

14 Kansas

15 = objects which exist independently of our partitions (objects with bona fide boundaries) bona fide objects

16 Vagueness in the Fiat Realm

17 Crispness in the Fiat Realm – some types of partitions determine their own fiat objects

18 Montana

19 Baarle

20 Baarle

21

22 California Land Cover

23 a partition is transparent (veridical) = its fiat boundaries correspond at least to fiat boundaries on the side of the objects in its domain if we are lucky they correspond to bona fide boundaries (JOINTS OF REALITY)

24 The case of holes hollows tunnels cavities

25 Are all holes fiat objects hollows tunnels cavities

26 Are all holes fiat objects?

27 Did hollows and tunnels exist before human cognitive agents came along? Rabbit holes, worm holes Geospatial forms as precursors of evolution

28 Controlled Airspace

29 What is a lake ?

30 A filled hole ?

31 What is a lake ? 1. a three-dimensional body of water ? 2. a two-dimensional sheet of water ? 3. a depression (hole) in the Earth’s surface (possibly) filled with water ? are dry lakes lakes? or merely places where lakes used to be?

32 Each of these has problems: If we take : 1. a lake is three-dimensional body of water then a lake can never be half full

33 What is a valley ?

34 A hole in the ground with bona fide boundaries at the floor and walls and a fiat lid

35 Grand Canyon

36 mountain is the most prominent kind of geographic object in the common-sense ontology. But it is absent from the scientific ontology as a kind of thing... the latter includes slope steepness and direction at every point, but represented as fields What is a mountain ?

37 Mountain bona fide upper boundaries at and around the summit but with (graded, clinal, vague) fiat base:

38 where does the mountain start ?

39 Everest Mount Everest

40 How to produce a theory of the common-sense geographic realm ? 1.mereology (theory of wholes and parts, including negative parts) 2.theory of partitions, granularity and vagueness 3.the theory of fiat boundaries 4.qualitative geometry and qualitative topology Why not set theory?

41 Partitions are artefacts of our cognition = of our referring, perceiving, classifying, mapping activity

42 and they always have a certain granularity when I see an apple my partition does not recognize the molecules in the apple

43 Goodman: Many worlds Me: Many partitions

44 The theory of partitions is a theory of foregrounding, of setting into relief

45 You use the name ‘Mont Blanc’ to refer to a certain mountain You see Mont Blanc from a distance In either case your attentions serve to foreground a certain portion of reality Setting into Relief

46 You use the name ‘Mont Blanc’ to refer to a certain mountain You see Mont Blanc from a distance In either case your attentions serve to foreground a certain portion of reality Setting into Relief

47 You use the name ‘Mont Blanc’ to refer to a certain mountain You see Mont Blanc from a distance In either case your attentions serve to foreground a certain portion of reality Setting into Relief

48 You use the name ‘Mont Blanc’ to refer to a certain mountain You see Mont Blanc from a distance In either case your attentions serve to foreground a certain portion of reality Setting into Relief

49 Foreground/Background

50 The Problem of the Many There is no single answer to the question as to what it is to which the term ‘Mont Blanc’ refers. Many parcels of reality are equally deserving of the name ‘Mont Blanc’ – Think of its foothills and glaciers, and the fragments of moistened rock gradually peeling away from its exterior; think of all the rabbits crawling over its surface

51 Mont Blanc from Lake Annecy

52 The world itself is not vague Rather, many of the terms we use to refer to objects in reality are such that, when we use these terms, we stand to the corresponding parcels of reality in a relation that is one-to-many rather than one-to-one. Something similar applies also when we perceive objects in reality.

53 Many but almost one David Lewis: There are always outlying particles, questionable parts of things, not definitely included and not definitely not included.

54 John

55 Tracing Over Granularity: if x is recognized by a partition A, and y is part of x, it does not follow that y is recognized by A. When you think of John on the baseball field, then the cells in John’s arm and the fly next to his ear belong to the portion of the world that does not fall under the beam of your referential searchlight. They are traced over.

56 Recall Husserl’s theory of Abschattungen Ship of Theseus: different partitions of the same underlying factual material

57 John

58 Granularity Cognitive acts of Setting into Relief: the Source of Partitions

59 Granularity Cognitive acts of Setting into Relief: the Source of Partitions Partititions: the Source of Granularity

60 Granularity Cognitive acts of Setting into Relief: the Source of Partitions Partititions: the Source of Granularity Granularity: the Source of Vagueness

61 John

62 Tracing Over Granularity: if x is recognized by a partition A, and y is part of x, it does not follow that y is recognized by A. When you think of John on the baseball field, then the cells in John’s arm and the fly next to his ear belong to the portion of the world that does not fall under the beam of your referential searchlight. They are traced over.

63 John

64 Granularity the source of vagueness... your partition does not recognize parts beneath a certain size. This is why your partition is compatible with a range of possible views as to the ultimate constituents of the objects included in its foreground domain

65 Granularity the source of vagueness It is the coarse-grainedness of our partitions which allows us to ignore questions as to the lower-level constituents of the objects foregrounded by our uses of singular terms. This in its turn is what allows such objects to be specified vaguely Our attentions are focused on those matters which lie above whatever is the pertinent granularity threshold.

66 Mont Blanc from Chatel

67 Mont Blanc (Tricot)

68 Bill Clinton is one person – these are both supertrue Mont Blanc is one mountain

69 they are true no matter which of the many aggregates of matter you assign as precisified referent

70 Bill Clinton is one person – both are true on the appropriate level of granularity (our normal, common-sense ontology is in perfect order as it stands) Mont Blanc is one mountain

71 Standard Supervaluationism A sentence is supertrue if and only if it is true under all precisifications. A sentence is superfalse if and only if it is false under all precisifications. A sentence which is true under some ways of precisifying and false under others is said to fall down a supervaluational truth-value gap. Its truth-value is indeterminate.

72 Are those rabbits part of Mont Blanc?

73 Example of Gaps On Standard Supervaluationism Rabbits are part of Mont Blanc falls down a supertruth-value gap

74 Different Contexts In a perceptual context it is supertrue that these rabbits are part of Mont Blanc In a normal context of explicit assertion it is superfalse that these rabbits are part of Mont Blanc In a real estate context in a hunting community it is supertrue that these rabbits are part of that mountain

75 So, even with Rabbits are part of Mont Blanc, there are no gaps. Are there any naturally occurring contexts with gaps?

76 Supervaluationism Contextualized We pay attention in different ways and to different things in different contexts So: the range of available precisified referents and the degree and the type of vagueness by which referring terms are affected will be dependent on context.

77 Supervaluationism Contextualized The range of admissible precisifications depends on context The evaluations of supervaluationism should be applied not to sentences taken in the abstract but to judgments taken in their concrete real-world contexts

78 No gaps The everyday judgments made in everyday contexts do not fall down supervaluational truth- value gaps because the sentences which might serve as vehicles for such judgments are in normal contexts not judgeable

79 Gaps and Gluts Consider: Rabbits are part of Mont Blanc is in a normal context unjudgeable Compare: Sakhalin Island is both Japanese and not Japanese

80 Problem cases An artist is commissioned to paint a picture of Jesus Christ and uses himself as a model. Consider the judgment: ‘This is an image of Jesus Christ’

81 No gaps Just as sentences with truth-value gaps are unjudgeable, so also are sentences with truth-value gluts. (Solution, here, to the liar paradox. Pragmatic approach to problematic cases (e.g. liar paradox) ontologically clarified by contextualized supervaluationism

82 Normal contexts including normal institutional contexts have immune systems which protect them against problematic utterances such utterances are not taken seriously as expressing judgments

83 Judgments exist only as occurring episodes within natural contexts... thus they are partly determined by the immune systems which natural contexts standardly possess

84 Judgments and Evolution Most naturally occurring contexts possess immune systems because those which did not would have been eliminated in the struggle for survival. But the semantics hereby implied has nothing to do with pragmatic eliminations of objective truth normally favored by proponents of evoluationary epistemology

85 Contextualized Supervaluationism A judgment p is supertrue if and only if: (T1) it successfully imposes in its context C a partition of reality assigning to its constituent singular terms corresponding families of precisified aggregates, and (T2) the corresponding families of aggregates are such that p is true however we select individuals from the many candidate precisifications.

86 Supertruth and superfalsehood are not symmetrical: A judgment p is superfalse if and only if either: (F0) it fails to impose in its context C a partition of reality in which families of aggregates corresponding to its constituent singular referring terms are recognized,

87 Falsehood or both: (F1) the judgment successfully imposes in its context C a partition of reality assigning to its constituent singular terms corresponding families of precisified aggregates, and (F2) the corresponding families of aggregates are such that p is false however we select individuals from the many candidate precisifications.

88 Pragmatic presupposition failure: In case (F0), p fails to reach the starting gate for purposes of supervaluation Consider: „Karol Wojtyła is more intelligent than the present Pope“

89 Lake Constance an ontological black hole in the middle of Europe

90 Lake Constance No international treaty establishes where the borders of Switzerland, Germany, and Austria in or around Lake Constance lie. Switzerland takes the view that the border runs through the middle of the Lake. Austria and Germany take the view that all three countries have shared sovereignty over the whole Lake.

91 Lake Constance If you buy a ticket to cross the lake by ferry in a Swiss railway station your ticket will take you only as far as the Swiss border (= only as far as the middle of the lake)

92 but for all normal contexts concerning fishing rights, taxation, shipping, death at sea, etc., there are treaties regulating how decisions are to be made (with built in immune-systems guarding against problematic utterances)

93 Lake Constance (D, CH, A) Switzerland Austria Germany

94 That Water is in Switzerland You point to a certain kilometer-wide volume of water in the center of the Lake, and you assert: [Q] That water is in Switzerland. Does [Q] assert a truth on some precisifications and a falsehood on others?

95 No By criterion (F0) above, [Q] is simply (super)false. Whoever uses [Q] to make a judgment in the context of currently operative international law is making the same sort of radical mistake as is someone who judges that Karol Wojtyła is more intelligent than the present Pope.

96 Reaching the Starting Gate In both cases reality is not such as to sustain a partition of the needed sort. The relevant judgment does not even reach the starting gate as concerns our ability to evaluate its truth and falsehood via assignments of specific portions of reality to its constituent singular terms.

97 Partitions do not care Our ordinary judgments, including our ordinary scientific judgments, have determinate truth-values because the partitions they impose upon reality do not care about the small (molecule-sized) differences between different precisified referents.

98 Again: Enduring types of (social, legal, administrative, planning) contexts have immune systems to prevent the appearance of the sort of problematic vagueness that is marked by gaps and gluts

99 No Gaps ‘Bald’, ‘cat’, ‘dead’, ‘mountain’ are all vague But corresponding (normal) judgments nonetheless have determinate truth- values. There are (on one way of precisifying ‘normal’ in the above) no truth-value gaps

100 p hilosophical contexts are not normal

101 DOWN WITH PHILOSOPHY !

102 THE END