How Do You Know What the Right Logic Is?fitelson.org/bridges2/priest.pdf · 2015. 9. 20. · Graham...

How Do YouKnow Whatthe RightLogic Is?

Graham Priest

Some CrucialDistinctions

A LittleHistory

A Model forTheory-Choice

Comments onthe Model

A Problem forthe Model?

Conclusion

How Do You Know What the Right Logic Is?

Graham Priest

September 17, 2015

Graham Priest

A LittleHistory

Conclusion

Introduction

1 Some Crucial Distinctions

2 A Little History

3 A Model for Theory-Choice

4 Comments on the Model

5 A Problem for the Model?

6 Conclusion

Graham Priest

A LittleHistory

Conclusion

1 Some Crucial Distinctions

Graham Priest

A LittleHistory

Conclusion

Pure and Applied

Geometry

Graham Priest

A LittleHistory

Conclusion

Pure and Applied

Geometry

Graham Priest

A LittleHistory

Conclusion

2 A Little History

Graham Priest

A LittleHistory

Conclusion

Darapti

All As are BsAll As are C s

So:Some Bs are C s

Graham Priest

A LittleHistory

Conclusion

Explosion

No As are BsSome Bs are As

So:All As are As

Graham Priest

A LittleHistory

Conclusion

3 A Model of Theory Choice

Graham Priest

A LittleHistory

Conclusion

Criteria of Goodness

adequacy to the data

simplicity

consistency

avoidance of ad hoc elements

Graham Priest

A LittleHistory

Conclusion

A Formal Model; Components

Criteria: {c1, ..., cn}.Measuring scale: [−10,+10] ⊆ Z.Measure function: µc

for any theory, T , µc(T ) ∈ [−10,+10].

Weights: wc

for any criterion, c , wc ∈ [−10,+10].

Graham Priest

A LittleHistory

Conclusion

A Formal Model. Definitions

Rationality index: ρ

ρ(T ) = wc1µc1(T ) + ...+ wcnµcn(T )

If the theories on the table are T1, ..., Tk , the rationallypreferable one is that with the highest rationality index.

Graham Priest

A LittleHistory

Conclusion

A Formal Model. Definitions

Rationality index: ρ

ρ(T ) = wc1µc1(T ) + ...+ wcnµcn(T )

If the theories on the table are T1, ..., Tk , the rationallypreferable one is that with the highest rationality index.

Graham Priest

A LittleHistory

Conclusion

An Example

From traditional logic to classical logic

Graham Priest

A LittleHistory

Conclusion

4 Comments on the Model

Graham Priest

A LittleHistory

Conclusion

Comments

Rational reconstruction

Fallibilism

Situatedness

Graham Priest

A LittleHistory

Conclusion

Comments

Fallibilism

Situatedness

Graham Priest

A LittleHistory

Conclusion

Comments

Fallibilism

Situatedness

Graham Priest

A LittleHistory

Conclusion

Comments

Fallibilism

Situatedness

Graham Priest

A LittleHistory

Conclusion

John is in Rome.If John is in Rome he is in Italy.

John is in Italy.

John is either in Rome or in Florence.If John is in Rome he is in Italy.If John is in Florence he is in Italy.

John is in Italy.

Graham Priest

A LittleHistory

Conclusion

Intuitively Invalid Inferences

John is either in Rome or in Florence.John is in Rome.

If John is in Rome he is in Italy.John is not in Rome.John is not in Italy.

Graham Priest

A LittleHistory

Conclusion

Another Intuitively Valid Inference

Mary is taller than John.John is taller than Betty.

Mary is taller than Betty.

For all people, x , y , and z , if x is taller than y and y istaller than z , then x is taller than z .

Graham Priest

A LittleHistory

Conclusion

Another Intuitively Valid Inference

Mary is taller than John.John is taller than Betty.

Mary is taller than Betty.

For all people, x , y , and z , if x is taller than y and y istaller than z , then x is taller than z .

Graham Priest

A LittleHistory

Conclusion

5 A Problem for the Model?

Graham Priest

A LittleHistory

Conclusion

A Problem?

Logic is required to revise logic

How much logic?

What can go wrong?

Graham Priest

A LittleHistory

Conclusion

A Problem?

How much logic?

What can go wrong?

Graham Priest

A LittleHistory

Conclusion

A Problem?

How much logic?

What can go wrong?

Graham Priest

A LittleHistory

Conclusion

How do you know what the right epistemology oflogic is?

Graham Priest

A LittleHistory

Conclusion

How do you know what the right epistemology oflogic is?

How Do You Know What the Right Logic Is?fitelson.org/bridges2/priest.pdf · 2015. 9. 20. · Graham...

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