| EPSRC Reference: |
EP/C531485/1 |
| Title: |
Mathematics into Philosophy: analysing complexity theoretic issues in current philosophical theories of epistemology, semantics and truth |
| Principal Investigator: |
Welch, Professor PD |
| Other Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
Springboards Scheme (Pre-FEC) |
| Starts: |
16 November 2005 |
Ends: |
15 November 2006 |
Value (£): |
41,866
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| EPSRC Research Topic Classifications: |
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Philosophers have long been interested in notions such as truth or what could possibly be true in different situations and have tried to develop logic's or ways of reasoning about truth and such situations (which they might call possible worlds ) . A theorem of Tarski (closely related to Goedel'o Incompleteness Theorem) snows that we cannot hope to write down a definition in a formal language that is used for describing/talking about all true arithmetic facts, It is thus impossible to nave a truth definition that works for all sentences about arithmetic. Philosophers such as Kripke have tried to write out 'partial truth definitions that say that 'such and such is true' or 'such and such is false' but leaving the status of many sentences open. These theories nave recently become much elaborated. Kripke analysed his own theory and described mathematically exactly what was going oh. However many philosophical theories since that time remain unanalysed.We nave noticed that some theories nave become sufficiently complicated that their mathematical description can border oh the edge of very difficult problems in the foundations of mathematics. We wish to research into this phenomenon and provide (a) arguments to philosophers that they should be concerned by such theories (b) develop hew mathematical methods of analysing such theories as this as well as the possible world semantics mentioned above for logics that contain expressions for modalities ( It is necessary that P holds , It is possible that Q holds etc etc.)A promising approach seems to be that we should apply the mathematical theory of infinite two person perfect information games in which two players play a game based oh an agreed set A of decimal numbers. They choose alternately integers h_i,h 2,h 3, ... to form an infinite decimal number: x = 0.h_l h 2h_3... If x lies in the set A of decimals we say that Player I wins otherwise Player II wins . It has been known for some while that such games nave winning strategies for one of the players as long as the agreed set A is hot too complicated. Kripke's theory truth can remarkably be analysed in terms of ouch games. The question is whether, or now, the same can be done for the various theories that nave been developed since Kripke's (which dates from 1975). However it is far from clear that this can be done for some of the theories of today.Whilst there are many philosophers of mathematics who study now mathematics 'works and what are its logical underpinnings, there are very few areas where, in the other direction, mathematics seems necessary to get a full understanding of the philsopners' theories. The time is therefore ripe for such an investigation into these areas.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.bris.ac.uk |