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Graham Priest: Logical Theory Choice

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okay thanks arrested and thank you very

much inviting me to come and talk to you

I hadn't been back to Edinburgh for a

number of years now so it's always a

great pleasure to come to this city and

I know a few folks in the audience but

not many so it's a pleasure to meet new

people so let me tell you what I want to

talk about and this is an epistemology

talk but it's a talk about the

epistemology of logic now the word logic

means many things it's highly ambiguous

compared with the word dynamics so we

talk about the dynamics of the earth

which are actually mean the way the

earth moves but we'll also talk about

Newtonian dynamics which is a theory of

how things moved okay for the word

dynamics is ambiguous it can be a theory

or it can be the stuff itself what a

word logic is similarly ambiguous it can

mean what really follows somewhat or it

can mean a theory of what follows from

what and I'm concerned with logic in the

sense of riches of the theory okay so if

you look at the history of Western logic

in the last two and a half thousand

years there have been many different

theories of what follows from what I'm

not going to go into history and a look

into the way that if you want to but

there have been many theories in the

last two and a half thousand years and

it's pretty clear that they disagree

with each other on many issues so we

have a multiplicity of theories and if

you have a multiplicity of theories then

there's obviously a question of how you

decide which is the best one which is

the rationally preferable one and I

guess the art is not obvious okay that's

why I wanna talk about now um

elsewhere I have proposed a method for

rational evaluation of theories in

general and logical theories in

particular and what I want to do today

is apply that in a case study so you can

see how it works okay so what the

essence of today's talk is is I'm

showing you how to apply a sort of

simple model of favourite choice to a

particular example a few choice in logic

now the where we're going is this and

this is the oh so okay oh all right I

can point okay so and this is really

where I do the case study okay but I

can't expect you to understand the case

study unless you understand the case okay

okay

so the first half of the talk

preliminaries so it's in the

preliminaries first of all I'll explain

how the model of theory choice works

then I'll talk about the particular case

study that I want to apply to and then

when we've got to that then we can see

how to apply the model to the case study

now this bit is necessary otherwise you

won't understand this bit but the fact I

could do this first means that this is

somewhat longer talk but I would like to

give so apologies for that but what I'll

think I'll do is break at particular

points to see if you've got any

questions so I don't think for an hour

without a break which is not good news

alright so that that's where we're going okay

okay

I have to say that get up and ask me

whether we can extend it little bit the

decision day so so that was a kind of

pre introduction all right so let's

let's go to the introduction I'll give

you the model of theory tries in a

moment but let me tell you a little bit

first of all about the case study and it

confirms cata factual's now have a look

at these counterfactuals if you

intuitional our intuition is Blodgett

recollect correct an explosion will be

value so explosion is a principle of

inference that contradictions imply

everything so from a and it's negation

you can infer B which of course valid in

classical logic that it's also valid

than the intuitionistic logic

so if intuitionist modular correct

explosion will be valid that seems true

but let's now say if intuitionistic

logic were correct explosion would not

be valid well that seems false right

because explosion is valid an

intuitionist logic or if Hobbes had

squared the circle all the features in

the Andes would have been interested

well ok the antecedent is logically

impossible right because you can't

square the circle but that's not very

like like a very plausible conditional

right because the signal and the Andes

wouldn't have known that loan cared okay

so assume that intuition is logic is not correct

correct

these conditionals are both are well

they both have necessarily false

antecedents now there is a dispute

currently going on in logic about

whether or not counterfactuals with

necessarily false antecedents must be true

true

some people like to in Williamson think

that they are vacuously true so a

vacuous is someone who thinks that

counterfactuals with impossible

antecedents are true vacuously through

whereas a non vacuous is someone who

thinks that some are true some our

thoughts so this is a debate that's

currently going on about counterfactuals

and this is the debate that I want to

focus in on in the as an application for

the theory of the method of theory

choice and the there are proponents on

both sides of the debate the main

proponent at the moment on the vacuous

side at Tim Williamson in these books of

his the main proponents of the book at

some main proponents of non vacuum are

these guys I guess I'm one of them so

you can see which side of it about I'm

going to come down on ok that's not a

surprise and you know I'm going to give

you some arguments right however that's

not the main point of today's talk the

main point really is to show how you can

apply the model of theory choice which

I'm going to give you to this dispute

hopefully so you can see how to make

sense of it ok make sense of some of the

arguments used pro and con trap all

right so that's the real interaction now

let's move to the perimeters and I need

to tell you what the model of Theory

choice is which I'm going to apply now I

think the model of rational Theory

choice is pretty much the same whenever

you theorize about so we theorize all

the time in science and metaphysics in

ethics and aesthetics and in logic

and how you sort of cash out the exact

details of food clothes may depend for

example accuracy numerical accuracy to

the data is pretty important in science

it's not so clear that numerical

accuracy is works in logic because we

don't have really many numbers so the

how exactly how you implement the theory

may change depending on the area in

which of theorizing however I think the

method itself is pretty general

okay so when we theorize in the first

place what what a theory is form in the

first place theories are there to

explain something a certain kind of data

so you might have empirical data you

want to explain you might have morals

later you want to explain or you might

have logical data you'll want to explain

so okay you're in Rome if you're angry

Rome in Italy so you're in Italy that

looks pretty good right you're in Italy

if you're in Italy then you're Rome

throw in Rome not so good okay so we

have all kinds of data about what sorts

of inferences are valid and what sorts

of reopens you like invalid now the data

is soft theorization is always dealing

with data reduce off so you know data

can be overturned if you have a good

reason but generally speaking we have

all this fallible data that we want to

theorize so a theory of validity must

account for which inferences are good

which imprints are bad and why and we

want to do a good job of explaining the

data that we have so far so good but of

course it's very rare that any theory

will explain all the data and I suppose

just occasionally it could be the case that

that

two different theories explain all the

data equally well so adequately - the

data cannot be the sole criterion Theory

choice okay and those of you who work in

the philosophy of science will know that

there's a bunch of other criteria which

we deploy in rational theory choice so

just for the sake of today the crimes

here we're going to consider at Absolute

of the data and then consistency

simplicity power unifying power and so on

so when we evaluate a theory

even though adequacy to the data is the

most important of the criteria we have

to take the other into account as well

and it's not difficult to see that the

criteria may well pull in different

directions in different theories so for

example stand a bit of history or at

least you know the bow derives version

of it if you look at early Copernican

astronomy and Ptolemaic astronomy they

were pretty much equally good in

adequacy to the data they both did

pretty good jobs but Copernican

astronomy was simpler not really didn't

use echo cycles it did didn't use the

equina is when you dissenter the center

of rotation it's no longer the center of

the circle so it's generally regarded up

in terms of simplicity Copernican theory

was better all right but it was sadly

lacking in unifying power because the

standard theory of the day in the early

16th century was Aristotelian and you

couldn't explain why the earth moved it

dynamics so Ptolemaic astronomy which

said that the earth is stationary fit it

much better with the current dynamics of

the day so simplicity pulls in one

direction and unifying power pulling the

other so you have the criteria can pull

in different directions

all right so given that how do you

determine which is the best very overall

well what you're looking for is the one

that sounds best kind of all things

considered now I know that survey okay

let me try to make the little more

precise let me give you a sort of a time

model of how this works so I want to

make the thought that I just explained a

bit more accurate by giving you a former

model a theory choice so and we've got a

mind works yeah you're right

alright so we we've got a number of

criteria so you won through seeing and

we want to evaluate how well a theory

operates according to each of those

criteria so um we need some kind of

measuring scale and this is kind of

arbitrary conventional but just for

taking argument let's suppose that it's

some integer between plus and minus 10

so plus 10 is best minus 10 is a list

and you need a measure function which

measures how well a theory behaves on

each of the criteria so it's going to

map but if you've got a criterion C mu C

is going to map the theory to something

in that scale and not all criteria are

equally important okay I've already said

that adequacy to the data is going to be

the most important one but you might

think that power is more important than

simplicity maybe not but anyway not all

criteria are equally good so we need to

assign a weight to each criteria and we

might as well take that to be measured

on the same scale okay

so that's a little bit of basic

technical apparatus and with that you

can define the rationality index of a

theory so the rationality index with you

is just the weighted sum of how well the

theory performs on those criteria so you

just measure the theory on each of the

criteria you then multiply it and some

with the criteria appropriately weighted

and when is a theory rationally

preferable well if you've got a bunch of

theories from which you have to choose

then you know size is the one with the

highest rationality index if you've got

two equal equally top contenders well we

can argue about what you do maybe you

can choose at random maybe you can go

either way rationally doesn't really

matter but computing the rationality

index of something is a way you

determine which theory is rationally

preferable now I'm not suggesting that

when scientists or theoreticians

actually to try to figure out which

theories rationally best they do this

okay I think they probably do it in

colored lis but I think something like

this is the kind of encode procedure

that goes on when theorists choose which

theory they find

rationally preferable all right so

that's the first half of the prep

preparatory material it's the theory

sort of formal theory a theory choice so

let me pause for a second and see

whether you want to ask any questions

about this yeah about why you choose to

No oh hang on actually you're right

that's good yeah yeah so um you it's

fine to have a zero point in your scale

but you want it to be the point of

indifference yeah thank you okay any

more complex than the postal works meta

conceptually just cause you've got an

extra bunch of concepts right but the

extra complexity is not really get hard

I mean the vacuous semantics it took me

three slides to explain the impossible

world I covered in half the slide okay

so yet it's more complicated

conceptually but the extra concepts are

not themselves terribly complex so okay

the vacuous position is a bit simpler

than the non vacuous position but not

that much ontological all right it looks

very small difference here because after

all both theories have possible worlds

and the non vacuous Theory also has

another kind of world complete quite

different in possible worlds so at this

moment of time if you're with your dad

or would crying you'd fall of your perch

because you're not only introducing

these horrible youth you're only

introducing these new kinds of creatures

there are the kind of revolting

creatures be then as it may you are

introducing a second kind so you know

come to Occam's razor you've got just

one kind of world for the vacuous and

two kinds of worlds for the non back

twist and one if simpler than two okay

so that's pretty clear yeah um there's a

cardinality of the world can be can be

anything I just found a model theory right

okay right this is sense I'm seeing

weekly impossible world's vastly more

numerous than the possible ones because

it is a bit of these randomly assigned delivery

delivery

it depends on the size of the look in

mobile semantics or the counterfactual

antics the cart down to the set of

possible worlds can be as large as you

like and the cardinality of the set of

impossible worlds in interpretation can

be as big or as small as you like so

there's nothing about the model theory

which constrains the size of the worlds together

together

you know interrupts take me one world

you can have interpretation it took me

out of note worlds that's not this home

by the model theatre is arbitrary all right

right

so we'll talk about ontological

simplicity and I've pointed out that you

know we've only got one kind of entity

in the possibly some antics you've got

to in the impossible so pretty clear

that the vacuous semantics is simpler be

careful though what we're applying here

and another name is Occam's razor

Occam's razor says that you shouldn't

multiply entities beyond necessity not

to each other multiplied necessities so

nothing should multiply entities period

you shouldn't multiply entities beyond

necessity and that's kind of weasel

phrase right because you want to know

what the 15 means in this context so if

it turns out that other considerations

are pushing you towards invoking in past

law world Occam's razor if not sort of

destroyed if somewhat blunted however

certainly as far as that's the caveat I

mean certainly as far as the notions of

complicity goes the judgment I think is

pretty clear

the vacuous semantics is how we get there

there [Music]

how is that what it is ah when you go

out of you don't leak with your fingers

because okay I'm not going to experiment

in the middle of a lecture right okay so

the second criterion was simplicity and

the judgment is pre-cleared the vacuous

semantics is simpler right at least

somewhat okay um power ok now this comes

back to your point P it looks as though

no in this hope that most of the

are going to be invalid in the non

vacuous semantics even you know things

like this if I if I am B with a K phone

I'll be the case because if you I mean a

and B may be an impossible condition in

which case it takes you to impossible

ones where they may not be true if

nothing exposing the impossible words if

a conjunction is true one of the

contracts is through so it looks as

though very non vacuous semantics is

very low on power in the sense that it's

not going to validate many inferences

okay you've got identity you've got

modus ponens nearly everything else is

going to go so prima facie it looks as

though you've moved there quite powerful

logic to a very anemic logic okay if

that's the case then of course the

vacuous semantics is much more powerful

however matters are not that simple or

not that straightforward a number of the

issues when look at have replies and

counter applies and this is a case in

point where there's a counter applied

because if you add provided you've got

this constraint being Tegrity the

passport even though that are not valid

if you stick the possibility at the

antecedent in as an extra premise then

this is valid because if the anti thing

is possible you stay within the domain

of possible worlds okay so everything

behaves as you're used to and quite

generally if you've got any inference

that's valid in the vacuum of semantics

it's going to be ten it's going to turn

out to be valid in the non vacuous

semantics provided you add the extra

premises expresses that the all the

conditions you're dealing with have

possible antecedents so in other words I

mean if you think that the vacuous don't

like vacuous semantics is right then the

non vacuous does not need to disagree

with that because the non back ships

will say hey you know you're any

thinking of possible worlds and if we

just think it possible my theory is

exactly the same so in a fast rate it

might have seen that a lot of power is

getting lost but once you look at it

you're not because the new theory the

impossible theory retains the power of

the old theory because as long as you

stick to possible world the same

theories of fame of the old theory now

there's a counter counter apply I might

say that I'm taking all these arguments

from the papers I showed you original

I'm not making them up okay the

dialectic of the reply counter apply

sometimes get a bit gets a bit complex

but I'm not going to follow every

argument down the tortured part and got

to keep things as simple as possible to us

the point so come ok so the non vacuous

reply is hey if you've got this

constraint IP define a counter apply it

would be well okay I peer that hug

because add hotness is a not a good

method logical time reply not so because

just think about it's actually motivated

by the very meaning of the accessibility

relation right if you're in a possible

world and if you're dealing with a

possible condition which world's would

you expect to be cared for as parables

the same as this world except that that

condition holds possible ones in a

possible world and you did with

impossible condition then the things

that are caetera spiral is the same

except that condition is true it expect

to be possible by very meaning of the

accessibility relation so reply the IP

is not at hot because it's motivated by

the very meaning of the accessibility

relation okay so fires asthma then it

might have seemed at first that the

vacuous semantics was much more powerful

because you lose all the universe but

we've also seen that propagate and once

you look carefully at what's happening

there's nothing much to choose between

them in terms of power alright so final

other constraints unifying power there's

a lot to be said about this but let me

say it very very briefly impossible

worlds have applications in all kinds of

areas when modal semantics with many

possible Wells Creek okay

so if you use possible worlds for

example to give a theory of intentional

verbs like belief desire and so on

if you only got possible worlds then

it's going to turn out that you believe

and desire everything that's necessarily

true that's certainly not the case for

real people or if you want to give a

theory of content in terms of words and

you've only got possible worlds then

every to necessary truths have the same

content every to necessarily falsehoods

at the same content and that's kind of

implausible to all right

Fermat's Last Theorem does not have the

same content as a lovely city middle so

if the impossible worlds find a very

natural application in the semantics of

intentional verbs in a semantics of

content and so what a fear of impossible

worlds allows you to do is unify these

disparate almost a desperate maybe

that's it's very disparate areas of

semantical inquiry you know so

counterfactuals intentional states

content okay if you've got impossible worlds you unify these areas by one

worlds you unify these areas by one single technique okay you cannot do the

single technique okay you cannot do the same with it with possible worlds there

same with it with possible worlds there are things you can do but they make

are things you can do but they make matters much much more complex so in

matters much much more complex so in terms of unifying pair up it's clear

terms of unifying pair up it's clear that the impossible world semantics are

that the impossible world semantics are better just because they much stronger

better just because they much stronger to do a number of jobs and so they unify

to do a number of jobs and so they unify the Triglav counterfactuals

the Triglav counterfactuals intentionality and so on alright so I

intentionality and so on alright so I haven't dealt with adequacy to the data

haven't dealt with adequacy to the data yet that's the one other thing that we

yet that's the one other thing that we need to do but let me just sort of

need to do but let me just sort of summarize the state of play

summarize the state of play so we haven't talked about attitudinal

so we haven't talked about attitudinal data

here are the other criteria and I've assigned sort of rough weights to these

assigned sort of rough weights to these criteria now you may disagree with how

criteria now you may disagree with how I've assigned these weights in gain

I've assigned these weights in gain nothing much is going to turn on them

nothing much is going to turn on them but I think most people would agree that

but I think most people would agree that you know power unifying power pretty

you know power unifying power pretty important consistency but the sake of

important consistency but the sake of today let's say that's really high okay

today let's say that's really high okay and simplicity well I mean I think this

and simplicity well I mean I think this is good but how is better so as you can

is good but how is better so as you can see at the moment there's really not

see at the moment there's really not much to choose between the two theories

maybe no vacuum has its nose ahead but you wouldn't want to sort of hang too

you wouldn't want to sort of hang too much on that so everything really is

much on that so everything really is going to depend on this final critique

going to depend on this final critique which you know is the most important

which you know is the most important after all

after all yes the main point of a theory is to

yes the main point of a theory is to account for the data okay so the last

account for the data okay so the last thing I'm going to do is talk about this

thing I'm going to do is talk about this last criterion which is the most complex

last criterion which is the most complex of the moon so let's just pause for a

of the moon so let's just pause for a second there and see if you've got any

second there and see if you've got any questions about this stuff do you want

questions about this stuff do you want to come back about power and redefine

to come back about power and redefine power okay okay so any other question

power okay okay so any other question about this stuff yeah yeah okay good

about this stuff yeah yeah okay good point

point and no you're dead right and sometimes

and no you're dead right and sometimes excess power can be a bit of advice so

excess power can be a bit of advice so for example a classical logic with a

for example a classical logic with a material conditional is much more

material conditional is much more powerful than say a power consistent

powerful than say a power consistent logic or irrelevant logic and one of the

logic or irrelevant logic and one of the gripes that real auditions have against

gripes that real auditions have against task logic is precisely this extra power

task logic is precisely this extra power is vicious so your point is data right

is vicious so your point is data right so

so you have to understand this talk of

you have to understand this talk of parents a lot more nuanced way we do

parents a lot more nuanced way we do reason count using counterfactuals quite

reason count using counterfactuals quite often and the loss of power that you

often and the loss of power that you appear to get if you've got impossible

appear to get if you've got impossible walls was pretty devastating it seems to

walls was pretty devastating it seems to get rid of virtually every inference

get rid of virtually every inference okay so even if you think that some of

okay so even if you think that some of them you shouldn't want anyway you've

them you shouldn't want anyway you've lost the whole bloody lot okay so okay

lost the whole bloody lot okay so okay [Music]

[Music] any other questions okay

so file texture of the talk adequacy to later now this is the most complex of

later now this is the most complex of matters so I'm going to take it in two

matters so I'm going to take it in two parts because prima facie this is an

parts because prima facie this is an open-and-shut case all right look if

open-and-shut case all right look if intuitionist logic is correct the law of

intuitionist logic is correct the law of excluded middle is invalid that's true

excluded middle is invalid that's true because we know exit the middle thousand

because we know exit the middle thousand intuitionistic logic if you intuition is

intuitionistic logic if you intuition is logic is correct explosion is invalid

logic is correct explosion is invalid false has explosion is valid any Jewish

false has explosion is valid any Jewish mystic logic we don't know yet where the

mystic logic we don't know yet where the Goldbach's conjecture is true or false

Goldbach's conjecture is true or false it inside the true or false and so one

it inside the true or false and so one of the claims that you can prove gold

of the claims that you can prove gold but conjecture or you can refute

but conjecture or you can refute Goldbach conjecture has got to be

Goldbach conjecture has got to be logically false so here a couple of

logically false so here a couple of conditionals and just choose the

conditionals and just choose the antecedent which is logically false

antecedent which is logically false either prove or refute right if you were

either prove or refute right if you were to prove or a few Goldbach's conjecture

to prove or a few Goldbach's conjecture you have become a famous mathematician

you have become a famous mathematician for sure if you were to prove or refute

for sure if you were to prove or refute Goldbach conjecture I would give you my

Goldbach conjecture I would give you my life savings no now look here are some

life savings no now look here are some examples and some of them are true some

examples and some of them are true some of them are false this is the kind of

of them are false this is the kind of data

data a part of the data with a theory of

a part of the data with a theory of counterfactuals should answer to and

counterfactuals should answer to and it's fairly clear they call this data

it's fairly clear they call this data vacuum ism it's seriously wanting okay

vacuum ism it's seriously wanting okay that the prima facie case now there's a

that the prima facie case now there's a reply as I pointed out earlier whenever

reply as I pointed out earlier whenever you theorize the data is soft and so a

you theorize the data is soft and so a possible reply here is hey this is your

possible reply here is hey this is your data and it's all wrong because really

data and it's all wrong because really when you understand what's going on all

when you understand what's going on all these things are true of course if you

these things are true of course if you just say that it's really ad-hoc however

just say that it's really ad-hoc however it's not ad hoc if you can give an

it's not ad hoc if you can give an independent explanation of your

independent explanation of your intuitions that these some of these are

intuitions that these some of these are false and that's exactly what's in

false and that's exactly what's in Williamson does in one of these papers

Williamson does in one of these papers so if this yeah these are really all

so if this yeah these are really all true now I'll tell you why you get the

true now I'll tell you why you get the impression that's having on the false

impression that's having on the false well it's because ah this so this is Tim

well it's because ah this so this is Tim innocence story when we evaluate when we

innocence story when we evaluate when we take a counterfactual if a then B to be

take a counterfactual if a then B to be false it's because we evaluate its mate

that's true and then we apply this heuristic but if this is true this is

heuristic but if this is true this is false

false now Tim knows very well that this is

now Tim knows very well that this is only heuristic it's not correct but he

only heuristic it's not correct but he thinks it's a plausible heuristic and it

thinks it's a plausible heuristic and it thinks that this is how we get

thinks that this is how we get conclusion that some of these

conclusion that some of these conditionals are false because we

conditionals are false because we evaluate yellow one first and then apply

evaluate yellow one first and then apply this heuristic

this heuristic okay this really does not work and it

okay this really does not work and it does not work for at least a couple of

does not work for at least a couple of reasons

it would seem that the batteries run out see what we can do ah thank you

see what we can do ah thank you it is alright in Luna severe on me yeah

it is alright in Luna severe on me yeah well done

well done okay this pendulum sense exploration

okay this pendulum sense exploration really won't work because it assumes

really won't work because it assumes that we evaluate one of the pair first

that we evaluate one of the pair first and get true and then we evaluate the

and get true and then we evaluate the other one to get false but there's no

other one to get false but there's no reason why we should value either one of

reason why we should value either one of these things first okay so come back to

these things first okay so come back to you know if intuition logic is great LEM

you know if intuition logic is great LEM is valid and why should I evaluate that

is valid and why should I evaluate that before

before if intuition is watching this correct

if intuition is watching this correct nem is not valid or if the intuition is

nem is not valid or if the intuition is logic is correct explosion is valid if

logic is correct explosion is valid if interest logic is correct explosions not

interest logic is correct explosions not valid I mean I can't attend both of

valid I mean I can't attend both of those are vacuously rule

those are vacuously rule so which one comes out to be up here be

so which one comes out to be up here be false will depend on which one our value

false will depend on which one our value at first and there's no reason I should

at first and there's no reason I should go one way or the other but that's not

go one way or the other but that's not really getting the heart and matter

really getting the heart and matter because maybe on some occasions we do

because maybe on some occasions we do apply tim's heuristic but generally

apply tim's heuristic but generally speaking we do not we evaluate

speaking we do not we evaluate counterfactuals in exactly the same way

counterfactuals in exactly the same way over the time so for example if

over the time so for example if intuitionist logic is correct

intuitionist logic is correct nem is invalid how do we evaluate that

nem is invalid how do we evaluate that what we go those scenarios where

what we go those scenarios where intuitionistic logic holds we know what

intuitionistic logic holds we know what those are like we know about Crickley

those are like we know about Crickley semantics we know about all the other

semantics we know about all the other semantics strange mystic logic and we

semantics strange mystic logic and we know that if we go to a world where

know that if we go to a world where intuitionistic logic holds then LEM

intuitionistic logic holds then LEM fails there so we go to the appropriate

fails there so we go to the appropriate worlds and we see that the conclude the

worlds and we see that the conclude the consequent is false how do we evaluate

consequent is false how do we evaluate this guy exactly the same way

this guy exactly the same way so we've done in those worlds where

so we've done in those worlds where interest intuitionist logic is correct

we know what interest exit logic is like we know that at those worlds were

we know that at those worlds were intuition is logic holes explosion does

intuition is logic holes explosion does not fail so we evaluate these two

not fail so we evaluate these two conditionals in exactly the same way we

conditionals in exactly the same way we do not apply the heuristic in fact it's

do not apply the heuristic in fact it's really that mode of evaluation of CAM

really that mode of evaluation of CAM factual's which determines the correct

factual's which determines the correct result provided of course you have got

result provided of course you have got worlds where intuitionistic logic is

worlds where intuitionistic logic is correct and I'm assuming for the purpose

correct and I'm assuming for the purpose of today's talk that it is not all right

of today's talk that it is not all right so this is a nice attempt to explain why

so this is a nice attempt to explain why the data is wrong and I do not think it

the data is wrong and I do not think it works

works ah so the original data

ah so the original data I reckon stands all right that's the

I reckon stands all right that's the first half of the story second out of

first half of the story second out of the story is this

the story is this hey but there's some more data out there

because something you want a theory of counterfactuals to do is explain how it

counterfactuals to do is explain how it is we get away with certain kinds of

is we get away with certain kinds of counterfactual ISM this comes back to

counterfactual ISM this comes back to your question

your question so another argument by two is this

so another argument by two is this according to non vacuum ism this

according to non vacuum ism this inference fails a equals B if a then P a

inference fails a equals B if a then P a so if a then P B so substitutive

so if a then P B so substitutive identicals right now I didn't give you

identicals right now I didn't give you the somatic so identity because I didn't

the somatic so identity because I didn't want to sort of here hanging millstone

want to sort of here hanging millstone around your neck but the point is right

around your neck but the point is right if given an appropriate semantics for

if given an appropriate semantics for identity in the non vacuous case this is

identity in the non vacuous case this is going to be invalid so I mean you can

going to be invalid so I mean you can just hear Tim saying now where I write

just hear Tim saying now where I write here nothing too bad but I mean you can

here nothing too bad but I mean you can tack Apple well all right so let's see

tack Apple well all right so let's see um there's a reply an obvious reply and

um there's a reply an obvious reply and it's pretty it is pretty obvious if you

it's pretty it is pretty obvious if you follow me thus far

follow me thus far alright don't lie Tim's example sorry I

alright don't lie Tim's example sorry I should've told you this if the rocket

should've told you this if the rocket had continued on its course it would

had continued on its course it would have hit Hesperus so pretty powerful

have hit Hesperus so pretty powerful rocket I guess um Hesperus is phosphorus

rocket I guess um Hesperus is phosphorus so if the rocket has continued on its

so if the rocket has continued on its course it would have hit phosphorus okay

course it would have hit phosphorus okay Perce whistles phosphorus right it not

Perce whistles phosphorus right it not like about inference and you know we've

like about inference and you know we've just said that the inference is right

just said that the inference is right invalid but the reply is pretty obvious

invalid but the reply is pretty obvious namely assuming you've got the integrity

namely assuming you've got the integrity of the possible then the inference if

of the possible then the inference if you add the extra premise that a is

you add the extra premise that a is possible this inference comes out valid

possible this inference comes out valid and again I didn't give you this magnet

and again I didn't give you this magnet for identity so I haven't shown you that

for identity so I haven't shown you that but trust me on this if you if you don't

but trust me on this if you if you don't go into impossible world identity

go into impossible world identity behaves as you think it ought to so

behaves as you think it ought to so provided we've got an extra premise

provided we've got an extra premise which says that a is possible then this

which says that a is possible then this is valid okay - again a vacuous can

is valid okay - again a vacuous can explain this inference as just a

explain this inference as just a suppressed premise namely that it's

suppressed premise namely that it's possible

possible Medicus metaphysically possible

Medicus metaphysically possible logically possible but the rocket a

logically possible but the rocket a continuance comes and you can still you

continuance comes and you can still you can imagine say yeah well you know being

can imagine say yeah well you know being you still lose this when the anti thing

you still lose this when the anti thing is impossible don't you yes you should

is impossible don't you yes you should expect you look at an example if

expect you look at an example if Hesperus is not phosphorus modern

Hesperus is not phosphorus modern physics is mistaken it's phosphorus so

physics is mistaken it's phosphorus so if Hesperus is not hazardous modern

if Hesperus is not hazardous modern physics is mistaken no it's not bond

physics is mistaken no it's not bond physics that's mistaken it's modern

physics that's mistaken it's modern logic that's mistaken all right

logic that's mistaken all right so you shouldn't expect to get

so you shouldn't expect to get substitutive identicals if you are once

substitutive identicals if you are once you are dealing with

okay so that's a bit of data that's overturned but there's more okay this is

overturned but there's more okay this is another argument that seduces and reject

another argument that seduces and reject proof in mathematics for example the

proof in mathematics for example the argument that there's no largest prime

argument that there's no largest prime is sometimes put in terms of an argument

is sometimes put in terms of an argument which appears fourth couple of

which appears fourth couple of counterfactuals if people the largest

counterfactuals if people the largest prime and P factorial plus 1 will be

prime and P factorial plus 1 will be crime why because P is the largest prime

crime why because P is the largest prime minute is bigger if people the largest

minute is bigger if people the largest prime P factorial plus one would not be

prime P factorial plus one would not be a prime why because because you can't

a prime why because because you can't divide it by a prime at all

divide it by a prime at all sorry my century okay all right so both

sorry my century okay all right so both these conditions are true and if you dig

these conditions are true and if you dig around with them you get a proof that

around with them you get a proof that there's no largest prime both of these

there's no largest prime both of these things that are vacuously true because P

things that are vacuously true because P whatever it is is not the largest prime

whatever it is is not the largest prime all right so the argument goes well you

all right so the argument goes well you know here's a bit of data that the non

know here's a bit of data that the non vacuous can't account for the use of cat

vacuous can't account for the use of cat factual's in the duchy oprah's and

factual's in the duchy oprah's and notice that we can't make the same kind

notice that we can't make the same kind of ants here because we are dealing with

of ants here because we are dealing with active students which are not much be

active students which are not much be possible however

there is again a different apply but an obvious reply first of all

often when counterfactuals are used by mathematicians there simply Hasan de

mathematicians there simply Hasan de parler we don't often really use

parler we don't often really use counterfactuals in mathematics so so the

counterfactuals in mathematics so so the first can factor was if people the

first can factor was if people the largest prime then P plus 1 is a prime

largest prime then P plus 1 is a prime okay that really in a math in the

okay that really in a math in the context of mathematical proofs that's

context of mathematical proofs that's just like saying suppose P is the

just like saying suppose P is the largest prime ping then

largest prime ping then buh-buh-bah okay it's not a

buh-buh-bah okay it's not a counterfactual it's just counterfactuals

counterfactual it's just counterfactuals are just a cute way of expressing a

are just a cute way of expressing a supposition plus what files are them

supposition plus what files are them that's one argument but I mean actually

that's one argument but I mean actually a non vacuous can account for the truth

a non vacuous can account for the truth those conditionals so this brings us

those conditionals so this brings us back to what we talked about earlier the

back to what we talked about earlier the difference between logical validity and

difference between logical validity and not for truth and truth because suppose

not for truth and truth because suppose you go to a world where P is greatest

you go to a world where P is greatest prime which is Keter asparagus like ours

prime which is Keter asparagus like ours well it ain't going to be a possible

well it ain't going to be a possible world but if it's kept as progress like

world but if it's kept as progress like ours then you know the basic fact about

ours then you know the basic fact about multiplication division addition and so

multiplication division addition and so on are going to be the same so if you go

on are going to be the same so if you go to any possible world where P is the

to any possible world where P is the largest prime but addition

largest prime but addition multiplication and so on do married home

multiplication and so on do married home value the same then the consequent is

value the same then the consequent is going to be true because it just follows

going to be true because it just follows from the facts about

from the facts about prime numbers multiplication and

prime numbers multiplication and addition so again this is um let me

addition so again this is um let me remind you where we are in the dialectic

remind you where we are in the dialectic we're looking at the criterion of

we're looking at the criterion of adequacy to the data and I've pointed

adequacy to the data and I've pointed out that prima facie the non vacuous

out that prima facie the non vacuous wins hands down

we've just been considering a couple of potential replies mainly that there is

potential replies mainly that there is other data that the non vacuous can't

other data that the non vacuous can't handle and I just explained why those

handle and I just explained why those replies don't work alright so the

replies don't work alright so the original evaluation along the path of

original evaluation along the path of addicts we clear data I think stands

addicts we clear data I think stands because the counter applies don't work

because the counter applies don't work all right

all right so up shop so this is the same table as

so up shop so this is the same table as before except that I put in a taxi to a

before except that I put in a taxi to a data and you know I put in non vacu ISM

data and you know I put in non vacu ISM is strongly preferable along the most

is strongly preferable along the most important criterion now you know you do

important criterion now you know you do the weighted sum and you can see what's

the weighted sum and you can see what's going to happen the rationality injects

going to happen the rationality injects of non vacu ISM is higher than the

of non vacu ISM is higher than the rationality indicative vacu ISM so

rationality indicative vacu ISM so conclusion non vacu ISM is the better

conclusion non vacu ISM is the better theory all right um now let me just add

theory all right um now let me just add a few words by way of conclusion I've

a few words by way of conclusion I've given you an argument that vacu ISM is

given you an argument that vacu ISM is better than non vacu ISM and you know I

better than non vacu ISM and you know I stand by that however that was not the

stand by that however that was not the main point of today's talk the main

main point of today's talk the main point of today's talk was to give you a

point of today's talk was to give you a case study in rational theory choice

case study in rational theory choice between different logical theories so I

between different logical theories so I gave you the theory of Theory choice and

gave you the theory of Theory choice and then we've seen how to apply it to this

then we've seen how to apply it to this case study so even if you think that you

case study so even if you think that you know my argument for no vacu ISM is

know my argument for no vacu ISM is wrong it's because presumably you take

wrong it's because presumably you take issue with some of my arguments and

issue with some of my arguments and that's that's fine because you can sort

that's that's fine because you can sort of see how you apply the model of fair

of see how you apply the model of fair choice now

choice now as I said earlier I don't think that

as I said earlier I don't think that when physicists or magicians or whatever

argue that one theories bet another they kind of sit down and they put it in

kind of sit down and they put it in these very decision theoretic terms you

these very decision theoretic terms you don't see that in papers by logicians or

don't see that in papers by logicians or physicists either but I do think that

physicists either but I do think that this is what is informing the kind of

this is what is informing the kind of arguments they give so if you read the

arguments they give so if you read the papers by Tim and by the collective

papers by Tim and by the collective which I was a part you will find the

which I was a part you will find the argument that I've been going through we

argument that I've been going through we don't put them in terms of the decision

don't put them in terms of the decision theoretic procedurally gave you but you

theoretic procedurally gave you but you will find the arguments ok now you can

will find the arguments ok now you can see why they're relevant ok because

see why they're relevant ok because tacitly you can think of these things as

tacitly you can think of these things as addressing the various criteria that are

addressing the various criteria that are evolved in the rationality of futures so

what the case study does is at least illustrate the method but I think it

illustrate the method but I think it does something more than that because

does something more than that because there's a second-order issue here you

there's a second-order issue here you might ask why accept your theory of

might ask why accept your theory of theory choice

theory choice train off question well one reason is

train off question well one reason is that it explains the data ok what data

that it explains the data ok what data were the data that you find physicists

were the data that you find physicists and logicians arguing or using if you go

and logicians arguing or using if you go to the logic journals or the physics

to the logic journals or the physics journals obviously there's a lot more to

journals obviously there's a lot more to be said about that question but you can

be said about that question but you can see today's talk

see today's talk not only as illustrating the method of

not only as illustrating the method of theory choice that I suggested but also

theory choice that I suggested but also as I'm speaking it's favor

as I'm speaking it's favor because it does explain the data of what

because it does explain the data of what you see when you look in logic journals

you see when you look in logic journals or physics journals where these issues

or physics journals where these issues are debated so apologists are for going

are debated so apologists are for going on so long and I don't like to go on

on so long and I don't like to go on this long however the second

this long however the second afterthought would not have been

afterthought would not have been intelligible about the first so thank

intelligible about the first so thank you for your parents for your

you for your parents for your forbearance and the end

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