Corpus evidence — top 10 passages

Most-relevant passages from the entire indexed corpus (67,286 paragraph chunks across YouTube transcripts, PubMed, arXiv, archive.org, Stanford Encyclopedia of Philosophy, OpenAlex, and more) ranked by semantic similarity (bge-small-en-v1.5).

1. 01 · blog0.760

   A number of philosophers have argued that our cognitive representations have, or can have, a map-like rather than a linguistic structure (Lewis 1994; Braddon-Mitchell and Jackson 1996; Camp 2007, 2018; Rescorla 2009; though see Blumson 2012 and Johnson 2015 for concerns about whether map-like and language-like structures are importantly distinct). Map-like representational systems are both productive and systematic: By recombination and repetition of its elements, a map can represent indefinitely many potential states of affairs; and a map-like system that has the capacity, for example, to rep…

   blog/plato-stanford-edu/belief.md

2. 02 · blog0.741

   One can think, following van Benthem (1996: 206–208), that since sets (histories) are generally considered in a particular situation and with specific purposes in mind, there is no reason to take all possible sets (histories) into account; it is preferable to circumscribe the range of the quantification over sets that is relevant to the purposes at stake. An example of this way of proceeding can be found in Stirling (1992), where interesting (first-order and second-order) closure properties are identified for the set of branches (or paths, or runs, or histories) in temporal logic for computer …

   blog/plato-stanford-edu/branching-time.md

3. 03 · blog0.730

   Arguably, this conceptual tension between boundaries understood as lower-dimensional entities and boundaries understood as thin layers, or zones, reflects an irreducible ambiguity in ordinary speech (Stroll 1977, 1979). And, arguably, it is only the first conception that gives rise to the puzzles outlined in the foregoing sections; bulky boundaries and border zones can be treated as ordinary, extended proper parts of the bodies and regions they bound. Yet a general theory of boundaries should have something to say about the second conception as well — and more generally about the interaction b…

   blog/plato-stanford-edu/boundary.md

4. 04 · blog0.728

   The surface of a (continuous) sphere, for example, is two-dimensional (it has no “substance” or “divisible bulk”), the Mason-Dixon Line is one-dimensional (it has “length” but no “breadth”), and a boundary point such as the vertex of a cone is zero-dimensional (it extends in no direction). This intuition has become common currency in contemporary philosophy through Johnson (1922: 168; 1924: 163–164) and is germane to much of what we ordinarily say about boundaries. Yet it is problematic insofar as it contrasts with several independent intuitions that are of a piece with both common sense and p…

   blog/plato-stanford-edu/boundary.md

5. 05 · pubmed0.723

   Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable. However, many are statistically "selfsimilar," meaning that each portion can be considered a reduced-scale image of the whole. In that case, the degree of complication can be described by a quantity D that has many properties of a "dimension," though it is fractional; that is, it exceeds the value unity associated with the ordinary, rectifiable, curves.

   pubmed/PMID-17837158-how-long-is-the-coast-of-britain-statistical-self-similarity/info.md

6. 06 · blog0.722

   On the basis of Manders’ analysis he formulates three conditions necessary for a diagrammatic proof practice to be rigorous: a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object; b) the information thus displayed is not metrical; and c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. De Toffoli conceptualizes the diagrams of a diagrammatic proof method as a kind of notation in 2022 . She terms them mathematical diagrams and advances the following as a ‘Carnapian expl…

   blog/plato-stanford-edu/diagrams-and-diagrammatical-reasoning.md

7. 07 · blog0.720

   Mullā Ṣadrā, argued that change of substantial nature can never be instantaneous and must therefore be gradual: insofar as it is impossible for there to be “formless” matter, there can never be an instant when something has lost the previous form and not yet gained the new one ( Asfār , IV, 274). (2) The boundary belongs either to A or to B , though it may be indeterminate to which of A and B it belongs. This view builds on Bolzano’s classic analysis of the continuum (1851: §66), which in turn is mirrored by the standard account of point-set topology (see e.g. Kelley 1955). It implies that con…

   blog/plato-stanford-edu/boundary.md

8. 08 · blog0.720

   On the other hand, perhaps just because the linguistic view requires inference for what appears to happen automatically on the maps view, the linguistic view can more easily account for failures of rationality, in which not all the necessary changes are made and the subject ends up with an inconsistent view. Indeed generally speaking it’s unclear how the map view can accommodate inconsistent beliefs unless one allows a proliferation of maps, with the complications that ensue (like redundancy and mechanisms for relating the maps; Yalcin 2021). Certain sorts of indeterminacy may also be more dif…

   blog/plato-stanford-edu/belief.md

9. 09 · blog0.719

   See the above-mentioned entry on Newton’s view of space, time, and motion as well as the entries on Leibniz’s philosophy of physics , classical theories of absolute and relational space and motion , post-Newtonian theories of absolute and relational space and motion , and the hole argument. 3. The Topology of Time It’s natural to think that time can be represented by a line. But a line has a shape. What shape should we give to the line that represents time? This is a question about the topology, or structure, of time. One natural way to answer our question is to say that time should be represe…

   blog/plato-stanford-edu/time.md

10. 10 · blog0.717

    Yet this way of thinking is misleading in at least one respect: the relevant category of belief is not restricted to beliefs about one’s geographical or temporal location. If the talk of “self-location” is not to be misleading, we have to understand “self-location” quite broadly—in the messy shopper case, Perry’s problem may be a failure to properly self-locate, but it’s not a failure to properly spatiotemporally self-locate. When Perry realizes what’s going on, he locates himself among the (widely spatiotemporally dispersed) messy shoppers of the world. Perry’s new belief state is one of self…

    blog/plato-stanford-edu/self-locating-beliefs.md