graham priest on revising logic (youtube)

8/12/2019 Graham Priest on Revising Logic (Youtube)

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Graham Priest on Revising Logic

For each of the three senses of logic there are three questions that follow

o Logica docens (the logic we teach)

o Logica utens (the logic we use)

o

Logica ens (logic itself) The three questions we will ask about each level of logic are:

o (1) Can logic be revised?

o (2) Can logic be revised rationally?

o (3) If so, how?

(1) Logica docens is the logic that we find in textbooks; in textbooks there is pure logic and

applied logic

o Ex. In geometry there are different types and they have different applications for many

different purposes

In Euclid it was supposed to map the spatio-temporal structure of the cosmos

With the rise of non-Euclidian geometry, we want to know which logic is bestused for its canonical application (i.e., its original purpose)

o

Logic has a canonical applicationto chart the structure of reasoning; understanding

the right moves we have to make when we infer

o (a) Can this logic be revised?

Yes, look at the Organon, Kants logic, etc.; Kant said it hadnt been revised but

he was ignorant

Another way of seeing this is that logic is cumulative and we are adding things

that were missing, but that is not true; some things were just removed

Ex. Davapti Syllogism used to be thought as valid

All C are B

All C are A

Some A are B

Where did the idea that contradictions imply anything? The first time we see it

is in Paris in the 12thcentury where we find the argument for explosion

Some A are B

No B are A

All A are A

This all means some things come and go, there is no uniform progress

o

(b) Can logic be revised rationally?

Not all revisions are rational; look at the three great periods of logic

Ancient

Medieval Universities

Modern logic

Sometimes things just get forgotten. During the Renaissance all the advances of

Medieval logic were forgotten since scholasticism fell out of favor


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Do all changes only occur for sociological reasons?

The change for classical logic at the late 19th

century with Frege

o (c) How is logic revised?

Logica docens canonical application is how to reason correctly and every logica

docens is a theory of the correct way to reason

Logica docens is a theory about validity which we use in many different areas;

we want to know what follows from what and why

When we create systems of validity we disagree about what is valid and why it is

valid; looking at the history of philosophy there are many global accounts of this

Ex. The syllogism and supposition account of truth conditions; syllogistic

tells us what is valid and our theory of supposition tell us why it is valid

Ex. Classical logic and give a Tarski account of validity

Ex. Intuitionistic logic can use proof conditions to tell us what validity is

(so we are inferentialists about what validity is)

Each of these try to give an answer to how we reason which inferential steps are

good and which are not and why

How do we choose btw competing theories?

We have many criteria for theory choice which we apply whenever we

theorize in different areas (in logic, metaphysics, physics, etc.) and in

the end we choose which is most rational as what does the best with

the data we have

The revolution of logic in the 19thcentury is driven by mathematics and they

wanted to know what numbers were and to do this they had to look at the

cannons of correct reasoning

Syllogistic couldnt do the job of answering the data so classical logic

was born

There was a backlash by the Thomists, but Aristotelian logic was swept

away

Syllogistic does not do well with paradoxes, non-classical mathematics, tenses,

conditional, etc., and finding validity in those areas

Logica eutens (the logic we use); this is the way that people reason in practice not theory

o This does not have to do with the psychology of reason, about the way that people

actually reason since we know people reason really bad because of many systematic

mistakes

Ex. The Wason selection tasko

What logica eutens is, is the norms of correct reasoning as practice (when it is done

correctly without mistakes)

o (a) Can it be revised?

Yea, we can reason as classical logicians or modern logicians; we could even do

it on different days

o (b) Can it be revised rationally?


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We could be relativists and say intuitionist logic is just as good as classical logic;

what I do on MWF is just as good as TR; this does not follow since logic is not an

isolated game and it meshes with what we do

Some accounts of validity seem to be better than others unless we are

relativists about truth itself and if we are then we dont have an argument

which is going to be persuasive

Because validity engages with truth, some ways of doing validity are better than

others

o (c) How can it be revised?

To find the norms of the best practice is that we try and find out what the best

theory is and bring our practice into accord with it; so we need to find a logica

docens and bring our logica eutens in line with it

Logica ens (logic itself)

o When we make a logia docens we are constructing a theory of something and the

something is the logia ens; it is what we are trying to capture with our logica docens

o

(a) Can it be revised?

Can the facts of validity itself change? We cannot answer this question unless

we have the right account of validity b/c until we do we cannot even approach

the questionso what are different accounts of validity?

(1) An inference is valid if God says soin this account it wouldnt

change

(2) Dentist theorywhat is valid is what 70% of dentists recommend;

on this account it could change

So, until we know what validity is we cannot answer this question

Main theories of validity today

(3) Model theorytruth is defined in a model and validity is truth

preservation of that model

(4) Proof theorydefine inferential rules which govern the various

connectives and a valid inference is one which you can get from

following those rules

On either account, validity is going to be about the relation btw abstract

objects; truth bearers are normally sentences/sentence types and they

are supposed to match up with models (on the model acct) and when

they do this correctly, they are valid

In the proof theory approach, truth bearers are sentence types and wedefine validity in terms of sequences and inferences are valid if we have

the sequence right

Abstract objects cannot change in these accounts, so the facts of logic

cannot change

More complication


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On the proof and model acct we can think of something as giving

meaning conditions of logical connectives

Maybe the facts of validity dont change, but the way we choose to

express these can change

The problem is that meanings interact

graham priest on revising logic (youtube)

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