Lecture 3. Metavocabularies of Reason. Pragmatics II: Normative Bilateralism and Reason Relations

Okay, oh well, uh, I wanted to start with a brief recap of the story I told last time. There are five important pieces of conceptual machinery that I put on the table last week that I want to build on this time.

this time so the first one is the idea of a pragmatic meta vocabulary uh that's a a language a metal language that is a language for talking about language uh but for talking specifically about the use of the language about discursive

So the first one is the idea of a pragmatic metavocabulary. That's a language, a metalanguage, that is a language for talking about language, but for talking specifically about the use of the language, about discursive practices. The notion of a metalanguage started off with Tarski's notion, which was the notion of a semantic metalanguage. Carnap, thinking of Hilbert, talked about syntactic ones. Semantic metalanguages let you talk about meanings. Pragmatic metalanguages let you talk about the use, the practices of using language.

languages let you talk about the use the practices of using language and the second point was the idea that uh uh we may need to use normative vocabulary in order to give a pragmatic metavocabulary pragmatic meta vocabulary may need to essentially depend on a

The second point was the idea that we may need to use normative vocabulary in order to give a pragmatic metavocabulary. Pragmatic metavocabulary may need to essentially depend on a normative vocabulary. I didn't really argue for that. I invoked a tradition from Kant through Frege to Wittgenstein, and on to Kripke's Wittgenstein, which pointed us at a literature about that. I didn't really argue for it. We can think of that as a metatheoretical methodological commitment that I'm undertaking. I'm going to be developing normative pragmatic metavocabularies.

think of that as a a metaphoretic methodological commitment that I'm undertaking uh I'm going to be developing uh normative pragmatic metabocabularies foreign and the third idea then was that we should use a two sorted normative pragmatic metavocabulary instead of just having some binary

The third idea was that we should use a two-sorted normative pragmatic metavocabulary instead of just having some binary opposition: is that appropriate or inappropriate, is that correct or incorrect? There are substantial expressive benefits to having a two-sorted deontic vocabulary, and I suggested two of those that I'm employing. They're not exactly intertranslatable, but usually you can transfer what's said in one idiom into the other. For official purposes, the notions are commitment and entitlement, and unofficially, in motivating that, talking about responsibility and authority.

transfer what's said in the one idiom into the other and that's uh for official purposes uh the notion of commitment and entitlement and unofficially in motivating that talking about responsibility and Authority oh fourth point was using that preferred

The fourth point was using that preferred idiom of commitment and entitlement. I talked about how practices of assertion are intimately tied up with practices of reasoning. Making a claim is essentially doing something that involves undertaking the responsibility to offer reasons, entitling you to that commitment, at least if you're appropriately challenged. That is, if someone makes a claim that offers a reason against what you said, then your entitlement to that commitment is put at risk, and to redeem it you need to give reasons for it. Now, secondarily, one way of redeeming that entitlement, vindicating that entitlement, is to invoke someone else's testimonial authority, the authority of their assertion. But entitlements can't all be handed around just by testimony. There has to be another way of redeeming them, by reasons. In connection with that, the story about how practices of asserting and practices of rationally defending and rationally challenging, by giving reasons for and reasons against, are all part of one package means that assertion can really be thought of as essentially a move in a practice, a game of giving and asking for reasons. In connection with that sketch of discursive practice, I recommended thinking of that structure as what makes a practice a specifically discursive practice. I also sang the praises of a default-and-challenge structure of commitment and entitlement, whereby merely undertaking the commitment, making the assertion, brings with it a default entitlement. That entitlement is fragile and defeasible. It can immediately be challenged by giving an incompatible claim. But it's essential, in order that we not be patsies for skepticism, that we do think of entitlements as something that come with assertions until and unless they're appropriately challenged.

commitment at least if you're appropriately challenged that is if someone gives an appropriate makes a claim that offers a reason against what you said well then your entitlement to that commitment is put at risk and to redeem it

The fifth point, which I had already raised in the introduction two weeks ago, is the Harman point. Harman makes a lot of points, but I would call this the Harman point: distinguishing practices of inferring, as a kind of doing, from the relation of implication. He's thinking about deductive implication, logical implication relations, but the point is more general. It's not specifically about logic. It's about distinguishing relations of implication, and, as I'll particularly emphasize today, incompatibility, from the practices that they in some sense normatively govern.

around uh just by testimony there has to be another way of redeeming them by reasons and in connection with that uh story about how practices of asserting and practices of rationally defending and rationally challenging by giving reasons uh against

In the second part of my presentation today, I'll look at John McFarlane's criteria of adequacy for having an adequate account of the sense in which relations of implication or incompatibility normatively govern our practices. But I'll only get to that at the end.

sketch of discursive practice I oh recommended thinking of having that structure as what makes a practice a specifically discursive practice and in connection with that I sang the Praises of a default and challenge structure of commitment and entitlement whereby

So the five things to keep in mind from last week are: the idea of a pragmatic metavocabulary; the idea that it should be a normative pragmatic metavocabulary; the recommendation that we get substantial expressive dividends from having a genuinely two-dimensional deontic pragmatic metavocabulary, two-dimensional in that we use two notions that are not interdefinable, that are independent of one another in the sense of not being reducible to one another; then a sketch of the way in which practices of undertaking a commitment by assertion go hand in hand with, and essentially involve, the idea of vindicating one's entitlement to that commitment, if appropriately challenged, by rationally defending it with reasons; and this Harman point about the distinction between practice and content, inferring and relations of implication.

that we do think of entitlements as something to come with assertions until and unless there appropriately challenged and then the fifth point which had already raised in the introduction two weeks ago uh is the Harmon point I mean Harmon makes a lot of points but

What I want to do today is deepen that discussion by looking at relations among these. But before I do that, maybe I should just stop and ask whether there are questions or comments about those five points, insofar as I've put them on the table so far. We're going to have a lot more to say about them, so anything anybody wants to point to or ask about?

specifically about logic it's about distinguishing relations of implication and as I'll particularly emphasize today incompatibility uh from the practices that they in some sense normatively govern now in the second part of my presentation today I'll look at John

Yes, Taylor?

take away from last week the idea of a normative of the idea of a pragmatic meta vocabulary uh the idea it should be a normative pragmatic meta vocabulary uh the recommendation uh that we get a substantial expressive power expressive

Yeah, I was wondering about the third point, um, C on the handout. So we say you can't just be a one-dimensional binary deontic status, we need two. Is there something to be said for, instead of moving to two dimensions, changing the binariness of the deontic status? Using a single dimension of deontic status but having it be gradable in some capacity, rather than, say, having three values?

and then uh a sketch of the way in which uh practices of undertaking a commitment uh by assertion um go hand in hand with essentially involve the idea of uh vindicating one's entitlement to that uh commitment uh if appropriately challenged by

I don't know. I mean, that would be doing different work than the two-dimensionality is doing. But I suppose if we think about commitment as graded, a doxastic commitment is graded, basically what you get is credences, and we know you get a lot from thinking in those terms. So yes, that's a reason to think that's an intermediate move. I don't think it's an intermediate move, though. It's a different move. But one might then want to combine that dimension with the two-dimensionality and think not just about graded commitments but graded entitlements. That's not something that Bayesianism or the rational choice framework really does. Well, I don't know. We have both the preferences and the probabilities, corresponding to credences. Maybe we really do have two dimensions there. I haven't really thought through what the relations are between the framework I'll be laying out and that way of relaxing the assertable/not-assertable tradition.

among these uh but before I do that maybe I should just stop and ask whether their questions or comments about uh those Five Points insofar as I've put them on the table so far ranting that you know we're gonna have a lot more to

Good thought, Hassan.

ideologic status we need to is there something to be said for um moving instead from instead of moving to two Dimensions to changing the binariness of the deontex status so using a single dimension of Niantic status but having it be gradable in some

Yeah, so maybe I'm rushing ahead here. I don't have it all together. I understand the five points as represented in the second diagram you introduced last week, where pragmatics is doing explan

graded a doxastic commitment is graded basically what you get is credences and we know you get a lot for thinking in those terms uh so yeah that that's a reason to think that uh is that intermediate I I don't think it's an intermediate

move it's a different uh it's a different move but one might then uh want to combine that Dimension with the two-dimensionality and think not just about uh graded commitments but created entitlements uh that that's not something that uh bayesianism or uh the

rational Choice framework uh does is really only one well um I don't know I mean we have both the probabilities and the credences sorry both the preferences and the probabilities corresponding to credences yeah maybe we really do have

um two Dimensions there now I haven't really thought through what the relations are between the framework that I'll be laying out and uh that way of uh relaxing the assertable not assertable uh tradition so you know a good thought

Hassan yeah so maybe maybe I'm rushing ahead here I'm just not uh I don't I don't have have it all together so the the Five Points here um I I understand them as sort of um represented in the the second sort of

diagram you introduced last week where pragmatics is doing explanatory work for for Content or for semantics I guess um one one thing I'm struggling to get is that one thing you mentioned in the first week is that um

with respect to the pragmatic to semantic word of explanation and the the possible semantic to pragmatic order of explanation we want to use we want to like avoid having to choose between them instead focusing on like reasons to to

sort of understand them together how how um is is this just go understanding what one side of that the pragmatics this just understanding the pragmatic to semantic Direction I'm not sure how it fits together yeah I mean you

your initial thought was right that this is sort of okay where we're going but uh the the picture here is uh let's look at uh and we want to look at the relations between the two sides that Harman

distinguishes let's look at the relations between uh the discursive practices that our pragmatic metabocabulary lets us specify and the reason relations you know as I'm calling them of implication and I'll argue of equal status uh incompatibility uh what

are the relations between them uh and we'll look to one program for understanding the reason relations in terms of uh the discursive practices and that's bilateralism um and uh that's roughly the you know sort of the first half of today and the second

half we'll look at the other direction that is how can we understand the reason relations as normatively governing uh the [Music] um a discursive practice of setting standards for assessment of doing that uh of doing that right and the

inferentialist semantic programs has uh if you give me the recent relations I'll give you the meanings uh will uh think about meanings about contents but propositional contents in terms of the roles that things play as uh that uh claimables play as premises and

conclusions of implications uh as things that can be incompatible with one another but we'll see from a semantics first order of explanation if you start with uh the example we'll focus on fines uh truthmaker false maker uh semantics he

has another way of specifying those reason relations sort of the first and most important thing he needs uh truth makers and false makers for is to define a notion of consequence and there's an ocean of incompatibility as well uh and that's going to be

metaphysically uh grounded and I'll claim that we can look at a meta vocabulary for reason relations and see that as amphibious between the pragmatics and the semantics um that's some weeks down the line but that's where we're uh where we're going

to sort of hire uh inferentialism understand your semantics and metaphysical uh representational terms if you like there's still going to be this core of Reason relations that we can approach either from the pragmatics or the semantics so that's that's where we're aiming

so um uh just to clarify the reason relations it's not that they're not a creature of either pragmatics or semantics doing explanatory work for both it's that you can understand them through like sort of each perspective or or whatever right

okay okay so uh as uh I started to say here um I want to think about the relations between the two things that uh Harmon distinguishes the practices of asserting and inferring defending and challenging uh by producing more assertings that are

reasons for standing relations of reasons for and reasons against uh on the one hand and the reason relations uh paradigmatically implication or consequence relations between assertables uh and I think about those as relations and I think about the assertions the

commitments and entitlements those statuses as sort of positions in uh the assertional game in the game of giving and asking for reasons and uh the inferring the giving a reason for giving a reason against defending challenging those are the moves uh that one can make

uh and the reason relations which hold not between the acts or statuses but between uh the assertables or the claimables uh as uh as I'll say ultimately between the contents that are expressed by the declarative sentences that you use to give reasons make

assertions and so on and so first I want to look at one program for moving from uh the practices to the reason relations the way the bilateralists think about it is they're giving us a pragmatic account of what it means to say that some

premise said gamma implies a conclusion a H you know we can write that if you um look at the bottom page two of the handout uh you know we can write gamma implies a there's that funny uh Snake Turn Style I

use that to indicate its substructurality we'll start talking about that next week uh but we can write that a is a consequence of uh the premise set Gamma or is implied by it uh but what does that mean uh what does

it mean to say that that reason relation holds and the bilateral is going to give us an account of that in a normative pragmatic metavocabulary um and so what one way of thinking about this is uh the reason relations articulate

what sellers called the space of reasons um the space of reasons his reasons as standing in relations of consequence or incompatibility relations of being a reason for or Reason against uh uh other contents and we're asking what's the relation between

the space of reasons that uh is invoked and thinking about Davidson as well as about sellers that blimps large uh in John McDowell's where what's the relation between the space of reasons and the game of giving and asking for

reasons or practices of making claims and challenging and uh defending them and I want to tell that part of the story in two parts uh I want to look at rest all Ripley bilateralism which is a few uh that looms large and

contemporary philosophy of logic uh but that in fact is addressing reason relations more generally it doesn't have to be logical consequence that they're giving an account of so that's uh what they're focusing on uh and look at their normative pragmatic

uh account of what it means to say that a reason relation holds that an implication holds and then second I want to show uh in the second part of my discussion of uh this move uh I want to show how we can add a

further level of fine structure to that bilateralist account by rendering it in an explicitly deontically two-dimensional pragmatic meta vocabulary of commitment and entitlement uh which their account invites but doesn't actually uh give us how and then in part so so that's basically

going to be an account of the first arrow in the mandala of um meta vocabularies uh of reason the one that goes from the pragmatics vertex to the inner triangle of Reason relations oh and then uh in the second part after the

break uh I'm thinking uh we'll look at McFarlane basically worrying about the arrow that would go in the other direction saying suppose you'd give me these uh meaning relations give me a consequence relation uh you tell me that

B follows from a or that a implies B now what does that mean about what I'm allowed to do normatively uh and he has a very carefully worked out uh account of what the space of possibilities is For

answers uh of that uh that article of his has been very influential uh oh and anyone then use that as the uh measure of success of the account of the deepened bilateralism so the two bits of um influential contemporary philosophy

Each of which has a significant literature around it that we'll talk about is uh the bilateralist account of consequence relations and uh McFarlane's question you know he says it's turns out to be surprisingly difficult to say what the normative significance

of uh a consequence claim uh is so that'll be looking moving from the pragmatics to reason relations and then seeing how the recent relations uh inform uh the pragmatics so the rest all and Ripley bilateralism and uh this

problematic uh of McFarlane's okay okay how so the basic idea that restful Ripley is Greg restall uh and Dave Ripley uh rest all just recently moved to Saint Andrews [Music] um and uh Dave Ripley is still in Monash

they're both Australians will come across them again when we look at logic uh and contrast what they call negation on the Australian plan and negation on the American Plan um and the original idea is vestals in the article that I put

um uh in the supplementary reading uh for today uh Ripley who's one of wrestles uh students uh applied that to thinking about the semantic paradoxes and I'll mention something in passing about that uh really uh later on the

first observation of theirs is that there's uh a fundamental uh by valence in uh Speech hacks and the attitudes that they express now one can assert but one can also deny oh the assertion uh expresses a practical attitude

of accepting uh acclaimable and the denial expresses a practical attitude of rejecting it uh ristol and Ripley just talk about assertion and denial because they want everything to be out in the public Light of Day of of our

doings uh and they don't want to have any Commerce with potentially spooky inner uh uh attitudes uh but I don't think these practical attitudes are mysterious and I'm perfectly uh happy to keep two sets of books on the Practical attitude and

uh the expression uh of it now so we we can line up uh assertion as expressing acceptance uh denial is expressing rejection oh these are the pragmatic analog of the semantic bivalent relation between truth and falsity between the

true the two truth values uh with which semantic semantics first orders of explanation uh begin and we can see a connection between these because uh accepting a claimable that is something that can be asserted or denied uh accepting a claimable

we can paraphrase that as taking it true as taking true that blameable taking it to be true and we can paraphrase rejection what's expressed by denial of a claimable as taking false and in a semantics first order of explanation one

might give an account of Truth and falsity first uh fine we'll say uh the beginning of the semantics is to talk about what it is for some state of the world to be a truth maker for a claim so that if the state is

actual then the claim is true or to be a false maker uh for it one of the reasons uh that we'll be talking about the truth making framework as our semantic model uh is that it is I think

uh also one of the reasons that it's been so successful uh this hypertintentional truthmaker framework is that it's genuinely two-dimensional it says uh don't think that you can do with just truth making or false making uh and Define the one in terms of the

other uh you need two potentially independent uh Notions but in a semantics first uh order of explanation which is something like what the tradition has um uh worked with since Fraga you get some sort of a grip on truth and

falsity and that's your route to the Practical to understanding the Practical attitudes of taking through and taking faults but in a pragmatics uh first uh order of explanation uh one's going to start with assertion and denial acceptance and

rejection and on Down the Line we'll look for what illumination we might get about oceans of Truth or falsity exploiting the idea that accepting is taking true but thinking if we can get an independent grip on accepting what's

expressed by asserting that then we can get a handle on true as what we're taking things to be the property that we're taking them to have when we accept or assert so uh the bivalence with which the bilateralists begin is basically the

same um by valence with which the semantic tradition uh begins it's just uh they're going to focus on the pragmatic side rather than the semantic uh side of it so bilateralism is going to be a strategy for uh a pragmatics first uh

order of explanation um and their second idea is that by valence is the key to understanding the reason relation of implication this is the really deep idea uh that they had uh and I I think it's it's a

new it's a new idea um that the bipolarity the my valence uh that shows up in the opposition between assertion and denial how corresponds to the two sides of the implication relation that's the bilateralism they call it latera are the signs

so if we have our turnstile expressing the reason relation of implication as I say for reasons to be clear later I use the funny snake uh Turn Style but it doesn't matter what we use uh they're saying that opposition

between assertion and denial acceptance and rejection corresponds to the two sides of the implication relation to the premises and the conclusion that uh the premise side of an implication relation is associated with assertion or acceptance and the conclusion side is

associated with denial with rejection oh now obviously a lot turns on what associated with means I mean how we fill in that uh notion but as I say this was an original idea oh and I and I think it's a genuinely

deep uh idea to to line up oh assertion and denial with the two sides of the implication relation um I say I think this is a deep idea what we're going to be uh sort of digging down Excavating

um sort of following out uh that depth I hope to to convince you that this is a deep uh an important uh uh idea now we'll see over on the uh [Music] when uh of locals isomorphism result gives us

a root to move back and forth between uh pragmatic bilateralism and finds truthmaker framework we'll see that this corresponds to thinking of consequence in terms of the truth of the premises and the falsity of the conclusion oh now that's not an idea that fine has

uh even though I'll argue that that's actually the key to seeing what uh finds uh achievement is but just bracket that thought and not today going to be talking about the true false uh version of that uh but the key connection between the

premise side and assertion and the conclusion side and denial is not obvious oh that this was a hard idea but it's really important so the way they're connected is to treat assertion and denial by available each of them is a is one of of a pair of

speech Acts attitudes along with assertion goes with denial acceptance with rejection uh to treat the implication turnstile bilaterally to think about oh the position you're in if you assert all the premises and deny the conclusion and they call that a position

it's a constellation of I'm going to say commitments commitments to accept and commitments to reject those attitudes are themselves uh normative statuses of the commitment uh kind and then the the third element of uh restful Ripley bilateralism uh is to use a global or holistic

normative binary uh to apply to those positions and what they say is um gamma implies a says that the position you're in if you assert all the premises and deny the conclusion is out of bounds that's a bad

position you've made a mistake and what you should do is try and get back inbounds but uh in keeping with the Harmon point uh the implication doesn't tell you how to do that all implications says is that if you

find yourself asserting all of the premises and denying the conclusion uh your out of bounds and so are normatively obliged to do something to get Back in Balance so what the reasons relations tell us is how to distinguish between

constellations of attitudes that are inbounds or out of bounds they use that global um that global normative assessment I'm going to paraphrase that by saying oh that a position is a constellation of commitments in the case where we have an implication

relation the position we care about is a set of commitments to accept all the premises and the set of combined with the set of commitments to reject the conclusion and it being out of bounds is saying you can't be entitled to those

commitments um their inbounds out of bounds I'm going to say inbounds think of entitlement but now to the whole holistic set of uh commitments and being out of bounds is well you can't be entitled to uh all of those

so I'm going to take over oh all those ideas uh in particular those three uh to think about the bivalence of Acts and attitudes assertion denial acceptance rejection uh understanding the implication relation bilaterally in terms of these uh

sides how and then uh applying uh a normative assessment a binary normative assessment inbounds out of bounds entitled not entitled to the whole constellation of commitments I'll say to the whole position that you've adopted oh they say you know

I'm going to have more things to say about consequences of this uh but uh the most the first thing to see about it is uh they're offering an explanation in a normative pragmatic meta vocabulary of what the reason relation of

implication or consequence is they're saying we can define that uh what it is for gamma to imply a just is for uh the position that anybody's in if they assert all of gamma and deny a to be out of bounds

that's what we're going to mean by saying that a follows from Gamma or is a consequence of gamma or is implied by gamma that last is a reason relation is the sort of thing that we semantic inferentialists are then going to use and say oh give me

those and I can tell you what propositional contents are but this is an account in a normative in a pragmatic meta vocabulary of uh assertion and denial uh the way they have it which is something you do in the

practice it's a normative pragmatic meta vocabulary because we've got inbounds and out of bounds uh here and it's bilateral because it uses the bivalent relation between assertion and denial and lines those up with the two sides of uh

the implication relation on the premise side and the conclusory side so the most important thing to see about it I'm saying is that it's an account of what a reason relation is uh what that turnstile is expressing what we mean by saying that one set of

claimables implies another in a normative pragmatic meta vocabulary no so let me stop there do you see how this is supposed to work a few years ago there was a a big collection from Oxford University press called the concept of logical

consequence uh sort of asking what do we mean by logical consequence uh and bilateralism uh I think gave by far the the best answer to that uh question there are a number of the essays in there um uh taking a bilateralist point of view

uh and they had a straightforward so here's what we mean by uh logical consequence uh in a way that that I think the rivals the Rival theories can't uh can't match let me mention two points in the vicinity of

uh this bilateralism oh the first is uh what do Restylane Ripley want it for and this is something that um they want it for different reasons um and let me mention rest all first and then uh and then Ripley

uh so we will hear a lot more about what I'm about to wave my hands uh very generally at uh in our two two weeks on logic but oh the logic we're going to be concerned about uh is sequent calculi that were invented

by Genson uh which is what happens when you take a statement like gamma implies a he called that a sequent says one thing follows from another sequel uh follows and you treat those as mathematical objects treat those implication statements as

mathematical objects and see how you can manipulate them a sequent calculus is a set of meta inferential principles uh meta-inferential in them they say if this is a good sequence then so is this other one uh or if this collection of sequence

holds then so does this other one so for instance uh a meta-inferential principle and a secret calculus might tell you uh that if a Turn Style B is good and b-turn style C is good then a Turn Style C

is good that's a meta-inferential principle of transitivity um so Genson formulated uh logic in the form of sequence calculi and as I say in a couple weeks we'll talk more about these I'll tell you everything you need to know about them fear not

but one of the astonishing uh features of genson's sequent calculi formulations of logic is um in the battle between classical additions and intuitionistic logicians they had focused on the very different treatments of negation uh in the two settings

so notoriously you don't have the law of excluded middle and intuitionism uh the treatment of the conditional is different um and a lot of excluded middle is is about disjunction as well as negation they said well these particular features

of what rules hold for the connectives that's the way people thought about the opposition between classical and intuitionist logic which for most of the 20th century were the two rivals people argue which was the correct uh is the correct logic

a bad question I will argue later on but it much exercise people but they thought it's the rules for the connected it's how we understand negation uh disjunction that's where the dispute is an astonishing feature of genson's uh

secret calculus formulation is he uses the same rules for the connectives the same set of meta inferences govern are used to introduce all the propositional connectives uh and he gets classical logic in one formulation and its missionistic logic

and the other formulation and the only difference between them is whether you allow more than one conclusion on the right side of the turnstile now if you only allow a single conclusion on the right side of the turnstile then his connective

definitions defining those the connectives paradigmatically negation and the conditional in terms of meta inferences involving sequence with them his connectives if you restrict yourself to a single conclusion gives you intuitionism uh but if you allow multiple conclusions on the right side those very same

connective definitions give you classical so this suggests that that the difference between them was in the turns file uh not in the connective definitions and that was a huge uh conceptual shift in thinking about the difference between these Logics and we've learned a

tremendous amount uh from that shift in uh in perspective and this is something that you know when we actually are focusing on logic in a couple of weeks I'll talk about some more but uh right from the beginning there have

been questions about what so if you only allow one conclusion the jargon for that is it's a single succident system so we have the sequent uh is gamma turnstile a and if a only a sentence not a set of sentences can go on the right

that's a single succident um called the conclusion this accident of the sequent um the other is antecedent the sequence uh singles accident implication people sort of thought okay you can draw this conclusion and sort of understand that but multi-succident

sequence what does that really mean oh if we say gamma Turn Style a comma B and we can think of gamma as just just normally set up with a bunch of commas separating the sentences in it uh well on the left

in the premise side The Comma just means and and the rules for conjunction show that but in the multi-succident one the comma is disjunctive if you have gamma Turn Style a comma B that means that either gamma implies a

or gamma implies B um and philosophers of logic looking at multi-succident uh schemes said I don't really understand those multi-sexident conclusions that that's not the way we reason we reason to single conclusions so rest all is a believer in the sequent calculus

and In classical logic so he's a believer in multi-succident uh implication bilateralism was his way of explaining to people who don't understand it what that conclusion means so if you look at the very bottom of page two uh on the handout

gamma implies Delta the set of sentences gamma implies the set of sentences Delta means on the bilateralist account anyone who asserts all the elements of gamma and denies all the elements of Delta is out of bounds you get bilateralism gets the effect

of the comma on the left being conjunctive and the comma on the right being disjunctive by having a universal quantifier but there's a sort of implicit negation in the denial side and that de Morgan turns you know denying all of Delta

is destructive to deny all of them uh only one of them has to be true um sorry sorry only one of them has to be rejected um so um wrestle could say I can give you a uniform explanation

of single success and multi-succident implications oh it's assertion on the left and denial on the right it's uh asserting everything on the left and denying everything on the right in effect saying everything on the left is true and not everything on the right

is true or something on the right is false that's the disjunctive uh version if you assert every element of gamma and deny every element of Delta then you're out of bounds so from restyle's point of view uh bilateralism gave him away of

making good sense to monsterably good sense of multi-succident uh sequence in exactly the same terms that he could do single succident uh sequence so that was uh a bombshell in the philosophy of logic to have uh an account like that that's why Resto cared

about it his student Ripley cared about it because he was concerned with the semantic paradoxes and he wanted to say if we look at the liar we see that from the liar we can see that the there's an argument

uh uh that the liar implies its own negation and the negation of the liar implies the liar and I could walk through the argument for it a couple of steps in a sequence calculus and he wants to say both of

those are good oh understand them bilaterally and the conclusion you come to is uh if you either assert or deny the liar this very sentences false you're going to be out of bounds so the only way to be inbounds is

neither to assert nor to deny the liar and that is compatible with accepting both of the implications the liar imposes negation and the negation of a liar implies to liar you can accept both of those um uh implications in the bilateralist

sense and you've still got the option of neither asserting nor denying the liar that's the only way you won't be out of bounds and he thought that was a good solution to uh The Wire I'm waving my hands over what you can

imagine is a very uh intricate and sophisticated discussion but that's roughly uh that's roughly how it goes okay so that's one sort of side comment I don't know placing the bilateralism in uh philosophical space uh neither of those motivations has

anything to do with what I'm going to go on to do with uh bilateralism so you know I'm saying this to uh to acknowledge some of these issues we'll come up later when we talk about logic the other thing is you'll see I've been

careful to talk about rest all Ripley bilateralism RR bilateralism I sometimes uh abbreviated here that's because it's not the only bilateralist game in town there also is uh smiley rumfit bilateralism uh oh Rumford was Smiley's student uh this

Ian rum fed and uh who Locus classicus for him is his recent book uh the boundary stones of thought which is his philosophy of logic book that works in uh this other bilateralist tradition now Smiley and rum fit

uh found themselves in the following uncomfortable position oh they thought that the secret calculus was the right way to do logic uh they were committed to classical logic being the correct logic and they took it that multiple succident

uh sequence were unintelligible and the trouble is the original Genson result was you get classical logic in a sequence Calculus if and only if you allow multiple conclusions but they wanted classical logic they had independent grounds to think that was

right and they couldn't make any sense of multiple succident sequence and yet they thought sequent calculus was the right way to formulate things and what Smiley realized and rumfit developed this thought is if you associate a valence with each

premise and each conclusion uh well they want to do it in a single section case so and the conclusion If instead of just having P1 through PN Turn Style Q how if each one of those comes with a

plus or a minus that says whether you accept it or rejected whether you assert it or deny it and so does the conclusion that they can get a single succident uh version of classical logic they call this bilateral because they're

building in explicit acknowledgment of the bivalence of each of the claims but uh it's not really though they use the term bilateralism because it sort of starts in the same place that wrestle and Ripley do it's not really by

lateralism in that the polarities are associated with the particular sentences rather than with the two sides of the turnstile so proper bilateralism restyl Ripley bilateralism says oh the bivalence goes with the turnstile one side is the assertion side and the

other side is the denial side and uh Smiley and rum fit oh associated bivalence with each uh uh with each sentence so in Smiley rum fit scheme it makes sense to talk about a premise set that is asserting some things and

denying others whereas in uh restaurant Ripley uh bilateralism the premises are all ones you accept they can't make any sense of uh you're making you're having as premises of an implication some things that you deny denial is something on the other side of

the turnstile so uh there's a lively uh debate in the philosophy of logic um about you know these two ways of going it was a remarkable achievement of smiley and rumfit to get a single succident sequent calculus that gives

you classical logic so they showed that going by valid really does give you something that you didn't have before and if you are concerned with understanding the significance of that original Genson result singles accident calculus will give you intuitionism and

a multi-succident sequence calculus will give you classical logic with the very same rules for connectives if you want to understand that then you really need to worry about and you really need to think hard about this uh Smiley rum fit

uh result now we're not actually going to worry about that when we get to when we get to logic but I wanted you to our discussion of uh logic right gonna worry about this highly rum fit uh version but I wanted

you to know it existed and to to put the restful Ripley bilateralism into uh philosophical context in this way okay so having said that that restaurant carries because of um multi-sexident and in a way so do smiley and Rumford uh I don't propose to

say anything more about that that's just for uh contexting but uh let me stop there in case this some question it was a uh raised by that I say that's I'm writing rough shot over really intricate uh discussions but I

hope you get the general eye of the land there okay then I want to go on and uh deepen uh the bilateralist account by putting it explicitly in a deontically two-dimensional context of commitments and entitlements and let me

say at this point that where uh I hope I sufficiently fairly advertised that the logic we're going to look at is due to Dan Kaplan and wolf Lobel and the semantic treatment is due to them as well um

uh so that in our book this pragmatic part is the only part that I'm seriously responsible for and here uh there's another one of our role group the logic group the research on logical expressivism Ryan simonelli uh just defended his dissertation in

philosophy at the University of Chicago um how who is the one who taught me about um how to think about these bilateralist issues and though the way he goes in his own thinking and in particular in his dissertation uh is a smiley rum fit

uh version uh whereas I'm going to push the rest all uh I couldn't at this point uh separate uh which ideas were Ryan's and which were mine in thinking about how to extend uh the Russell Ripley bilateralism in

the way I'm going to uh suggest we've just been talking about this for years and this is what came out of it uh we'll re actually read a piece and recite an argument of Ryan's about a completely different topic

um later on uh actually next week um okay oh The Logical tradition has not sufficiently appreciated that in addition to implication or consequence there's another similarly fundamental and equally irreducible reason relation namely incompatibility or its generalization is incoherence of

a set of propositions uh I gestured earlier at [Music] um the distinction between doing negation on the Australian plan and doing it on the American Plan uh roughly doing it on the Australian plan is understanding negation in terms

of incompatibility rather than uh the other way around and the basis for uh my variant of the restful Ripley bilateralism is the notion of incompatibility and this uh which as I say it it and um implication are co-evil and co-equal uh I want to say

um this is hidden in traditional logic because a series of technical tricks let people notationally encode incompatibility in the consequence relation so for instance uh in tarsky's 1930s paper on the concept of logical consequence uh he's able to

introduce negation and deal uh with that uh because he can use as a substitute for the notion of uh a set being incoherent so every element of it is incompatible with the rest of it uh saying oh that's what you get if the

consequence of that set is the whole language uh so an incoherent set in his setting an inconsistent set uh he's just one that has the whole language as its consequence that is he used explosion to um encode uh incoherence or incompatibility

in the consequence uh relation and Genson in the single well in in both um uh systems uh uses the notational conceit of an empty right hand side he says if a premise said has if the sequent that has gamma on the

left the turnstile and nothing on the right if that's a good uh sequent then gamma is incoherent and in both uh intuitionism and classical logic everything follows from it so if gamma implies nothing then you can throw anything in on the right side and

that sequence will be a consequence of the original sequence that meta inference will be a good one um now those are your notational conveniences it means they can just work with one Turn Style I'm going to use the pound sign in place

of the Turn Style to Mark uh incompatibility um but incompatibility is the Paradigm of a case where uh we see the expressive dividends paid by Deonte two-dimensionalism as opposed to a merely binary scheme in originally in making it explicit I

Define uh two claims A and B as incompatible in uh antic score keeping terms kind of pragmatic meta vocabulary if commitment to one precludes entitlement to the other [Music] um this is genuinely uh two-dimensional uh it depends on commitment and entitlement

not being interdefinable um incompatibility is you know a demonstration of what um two-dimensionalism gets you oh it lets you define oh another kind of uh implication relation uh and I exploited this in my lock lectures in between saying and

doing uh you can treat one sentence as incompatibility and tailing say another just in case everything that's incompatible with the consequent is incompatible with the antecedent so Pedro is a donkey implies Pedro is a mammal in the sense that everything

incompatible with Pedro being a mammal for instance being a prime number or not having a spine oh you know not being a vertebrate everything incompatible with Pedro being a mammal is incompatible with Pedro being a donkey and uh

that's a particularly strong kind of entailment and in between saying and doing I use that to interpret modally robust uh implications necessitated um implications um now this notion of incompatibility plays a particularly important role in thinking of the game of giving and asking for

reasons it emphasizes the difference the structural difference between commitments and entitlements commitments are atomistic I can take one on and Give It Up by asserting or by denying oh and you can't stop me from for instance undertaking inconsistent commitments

I claim that the so you know single colored Swatch is blue and I claim it's red and there I am those are incompatible claims so being committed to the one means I can't be entitled to the other so I'm not entitled to either of them

but I can still commit myself to them in this normative framework this is how we can understand people having incompatible beliefs that's incompatible commitments they're not entitled to both of them but so be it um but entitlement isn't like that

entitlement is a holistic matter you have to look at all your commitments in order to know whether you're entitled to any of them because even though I may have been say default entitled to this claim oh if I'm also committed to something

incompatible with it that undercuts the commitment I might otherwise have been able to testimonially inherit entitlement to a claim that you asserted from you uh you licensed me to reassert it by asserting it your inheritance your entitlement was in

principle heritable by me but uh it's a two-phase process one uh do I have a prima fascia entitlement either by default by testimony or because I've given a reason but then second we have to test whether that prima facie entitlement gets

undercut by commitment to something incompatible so if we think about uh implication as a matter of commitment inheritance if you're committed to the premises you're committed to the conclusion we'd say oh well there's a variant of that which is entitlement

preserving uh implications where if you're committed and entitled to the premises then you're entitled to the conclusion this would be a sort of analog if you think of commitment preserving implications as an analog of deductive logical relations then entitlement preserving implications

would be an analog of inductive or abductive um implications but all you can inherit that way is a primification entitled because if you're committed to something incompatible with that conclusion then you're not entitled to that conclusion anymore that the incompatibles undercut

it it's this feature of entitlement the Global or holistic character of Assessments of entitlement that is expressed in the rest Hall Ripley um bilateralism by saying you have to assess the whole position to see whether it's inbounds or out of bounds

because we're looking at whether you can be entitled to all those commitments they don't use commitment talk but that scale paraphrase oh what they say so implicitly I want to say this notion of incompatibility where one commitment can preclude

entitlement to another this is implicitly the motor of Resto Ripley bilateralism and mind you oh it's incompatibility that articulates the critical dimension of practices of giving and asking for reasons how if you claim the Q and I ask you why

and you give a reason for it you say well pee and that's a good reason for it if he implies Q but if you say Q and I challenge it by giving a reason against it I say but

r well that reason against it is something that's incompatible with it if you're committed to R you can't be entitled to pay if they're incompatible that's what it that's what it means it's an incompatible reason relations of incompatibility

stand to reasons against and so to speech hacks of challenging as implications stand to reasons for and practices of Defending of rationally defending your claim that's why you have to have both kinds of Reason relations the one informed

reasons for that you use to justify your claims to defend them against challenges but it's the incompatibles that it's incompatibility that defines reasons against a reason against is an incompatible commitment which it won't matter if you're not entitled to the incompatible commitment

but if you are then you can't be entitled to you know that commitment precludes entitlement to the thing it's a reason against so incompatibility relations are needed in any practice that has this critical uh rational structure that you can

challenge someone's commitment remove their primification entitlement by making incompatible plane and then we have to argue about which one of these is one entitled to the the reason against or what it's a reason against in the uh draft of chapter one uh

I quote from this wonderful essay by Hugh price called why not why do we need negation which is really an argument in favor of incompatibility um and he imagines uh what it would be like if there were discursive practices that

were purely dogmatic in that you could only give reasons for claims but there were no incompatibilities in it uh he's in asking why not he's using the principle that the way we make explicit incompatibilities is by introducing negations

and we'll talk about that when we talk about logic in the way that the way you make explicit implications is to introduce conditionals that's where we're going with logic but really what he's talking about is what it would be

like if you had dogmatists who couldn't be critical couldn't give reasons against uh and he offers this nice dialogue uh me Fred's in the kitchen and I start to go off to the kitchen you wait Fred's in the garden

me I see but he's in the kitchen so I'll go there and I said oh you you lack understanding the kitchen is Fred free me is it really but Fred's in it and that's the important thing and I leave

for the kitchen foreign if you're a dogmatist if you can't give reasons against I say Fred's in the kitchen and you say wait Fred's in the garden if that's not incompatible okay then I'm going to reason the same way I was before I see

but he's in the kitchen so I'll go there no no you lack understanding the kitchen is Fred free is it really another but that's not incompatible with him being in uh the kitchen if I'm a dogmatist so uh in a much less

theoretically Laden framework uh price is arguing look this critical function you've got to have this Collision uh possible one claim ruling out another well ruling it out ruling out entitlement you can undertake these incompatible commitments it's just you

lose the entitlement to them uh and look this is the idea of the idea behind uh Shannon information Theory uh but before we get quantitative about how much information there is in a signal uh he says the the information

content of a signal is how much it cuts down the Alternatives that you had before you received the signal so you had a bunch of options you get the signal um you know one if by land two if by C

you see there's one Lantern there okay now then then that means we you know Mount up to a horse the information is a matter of it cutting down ruling out some of the Alternatives before you got the message you were entitled to any of

these once you get the message you're only entitled to some of them the message is incompatible with some uh of the Alternatives you had before and it's information content consists in what it rules out and they say that's before we go binary

and say oh in a bit is one that cuts in half um okay oh now I've talked about two sorts of bipolarity uh the bivalence of assertion and denial or acceptance and rejection or as far as that goes proof and falsity

Reflections in a glass Darkly of uh these this pragmatic uh by valence but now I've talked about a bipolarity of Reason relations there's implication and there's incompatibility what's the relation between those two pairs between the bivalence of Acts and attitudes

on the one hand and the two flavors of Reason relation on the other hand I said implication lines up with reasons for incompatibility with reasons against well the connection is that reasons for are reasons to assert and reasons against her reasons to deny

so there's an intimate connection between the bivalent statuses the acts and attitudes on the one hand and these two flavors of Reason relation on the other so if you look at the proposal at the bottom of page three

oh gamma implies a gamma turnstile a says the commitment to accept all the elements of gamma polar premises precludes entitlement to reject a I'm just doing the single section you'll see that you can tell how one would do a multi-saxon it

that's implication but now in the same terms we can do what Restylane Ripley didn't do and explain incompatibility and furthermore see how they are to two sides of one coin gamma is incompatible with a using the pound sign for that

says the commitment to accept all of gamma precludes entitlement to accept a accepting gamma precludes entitlement to accept hey that's the notion of incompatibility that I gave you and it's exactly parallel to the definition of implication oh that we get in Resto Ripley

bilateralism if we put it in terms of commitment and preclusion to an uh to entitlement and the fact that we're using preclusion of entitlement is what makes me say that incompatibility is the basic idea here it's the commitments preclude

entitlement to other commitments but you get reasons for if what they preclude is entitlement to reject and you get reasons against if what they preclude is entitlement to accept and then here for how a final move let's see well now wait a

minute I thought implication idea we came in before you made all of these fancy distinctions was if you're committed to the premises then you're committed to the conclusion and to accept the conclusion and incompatibility would be if you're

committed to the premises and they're incompatible with the conclusion uh then you're committed to reject the conclusion is wasn't that the intuitive idea we started with I say okay we can make sense of that because we can define a notion of

pragmatically implicit attitudes uh and say that if you're precluded from entitlement to reject a as you are in the implication that's implicitly being committed to accept it because acceptance is the only attitude that you could ever be entitled to

you're precluded from being entitled to reject it so the only option open to you the only one you could be entitled to is to accept it now you don't need to take a stand you don't need to accept or reject that's

important to Ripley and that's why this is only implicit commitment your options have been narrowed so the only option that you could be entitled to would be acceptance and similarly uh to be precluded from entitlement to accept a As You Are by something

incompatible is to be implicitly committed to reject a because accepting a has been ruled out you can't be entitled to that the only thing you could be entitled to is rejection so we can say oh if we're speaking

strictly about uh what your what commitments you're entitled to implications has commitment to accept all of a precludes uh entitlement to a commitment to reject a but implicitly that's committing you to accept a there's space between the explicit and

the implicit here you might not take a stand uh at all how so this finer grain bilateralism that I'm proposing models both of the reason relations on incompatibility oh I guess there's one other thing uh I want to say before we take our break

how isn't it if you imagine Smiley or Rum fit looking at this they'd say haven't you expressively restricted yourself all of you are our bilateralists who are bilateralists about the turnstile haven't you expressively restricted Yourself by only allowing commitment to

accept premises on the left side now shouldn't we want to know what uh follows in either these sense what the reason relations are of a mixed set of acceptance and rejections of commitment to accept and commitment to reject

uh after all in our uh single succident Smiley rum fit systems uh we get a lot of mileage out of that and all I can do is issue a promissory note make a gesture here and say we're going to Define logical negation

from incompatibility if gamma is incoherent sorry if if gamma is incompatible with a oh then it implies nowaday it's basically uh going to be the principle and using that we can get the effect of uh having commitments to reject in the

premises by having commitments to accept negations and we'll see that we don't get anything new that way so it actually will be possible to prove that we don't lose any expressive power by only considering relations of implication and incompatibility that are

exclusively have its their premises commitments to accept okay I want you to chew that over a little in the Break um will come back at 2 51.

welcome back everybody so um the story that I told was how one can deepen and give a finer grained bilateralist account not only of implication but of its sister recent relation incompatibility in a way that shows the parallel between

them uh why uh the the bivalence of attitudes and acts uh brings with it a bivalence of Reason relations of reasons for and reasons against uh that those two uh by valences are two sides of one coin they

come together in this uh conceptual framework which connects commitments to preclusions of entitlement to Commitment which is the fundamental uh incompatibility structure now in the appendix to one of the chapters in between saying and doing uh I offer uh

an incompatibility semantics for an S5 modal logic oh I now think that what I was crudely reaching for there is this uh sense in which uh incompatibility uh is the pragmatic core of Reason relations but I appreciate that was a lot of

material coming at you fast are there questions or comments at this point before we go on to McFarlane okay oh so I said that you know we're going to look at a sophisticated version of bilateralist explanation of Reason

relations in terms of uh oh a normative pragmatic meta vocabulary that's that first arrow in the mandala but that then uh McFarlane asks about the other question he said suppose we were just given by an oracle uh facts about what followed from what

he's not thinking about incompatibility but you know the Paradigm is implication suppose we were just given those uh Harman tells us we've got to separate that from Norms governing what we should do in the way of the attitudes that we uh adopt

this is all Downstream from the harman point but what exactly is the sort of constraint normative constraint that we should understand reason relations by term not his um facts about what follows from what the validity of implications he says uh

just what arms of reasoning what normative significance do they have so he sort of wants to go the other way suppose we were given the reason relations and this is a good test for the account we've given if the

account in the direction we pursued is a good one then it ought to satisfy any reasonable uh set of constraints in going the other way oh let me mention in passing last week I recommended Hannah ginsburg's treatment of the normativity of concept

use um she like McFarlane long time Berkeley uh professors they reach each served as chair there McFarlane unlike uh Ginsburg is a proud Pittsburgh product uh he wrote I supervised his dissertation um this is all you know long after that uh

McFarlane has uh an enviable and unusual position in contemporary philosophy he barely publishes his papers you really have to beg him to do it he just puts him on his website and they're important enough that everybody talks about them

uh and that this is uh a version of uh I don't know how the uh how the future could be without our needing to go through uh the various um um bottlenecks that there are otherwise but there's only a few people who can uh

count on getting an audience um uh that way uh so he says he's talking about logic in what sense is logic normative for thought but nothing actually turns nothing in this argument turns on the notion of consequence or implication

that he's using being logical consequence or implication uh so we can see it as being about reason relations in general um and here I've put the um oh main parts of his argument on the handout so his state to the question how do

facts about I'd say the goodness of implications rather than the validity of inferences uh relate to Norms uh for reasoning let me say in passing that uh validity was originally introduced as an English translation of cons gulting kite which

means the the bindingness of uh the goodness of uh of something and has come to mean necessary truth preservingness of uh in a logical context uh and so people often use that term validity uh I think it's better just to

talk about the goodness of it and logical validity is a way in which implication can be good so uh I should say that this uh essay of macfarland's is a paradigm of one way to write a superb philosophy uh paper he

sets out a botanization a systematic motivated buttonization of the alternatives lays out a list of criteria of adequacy for a solution and systematically measures everything in the botanization all the options against these criteria of adequacy with discussions of the

issues that come up along the way and comes up with well this is what seems to survive and meet these criteria of adequacy so this is a tour de force in a way uh altogether admirable so he says we need a bridge pro

principle of the following form if a b turns style C he uses the uh equal sign instead of my friendly sake but uh it it doesn't matter then normative Claim about believing a b and c now believing that's not cutting is fine

as what we've got uh but if you look okay um but if we look at polarity uh that's uh one of the one of the parameters that he's varying are these obligations permissions reasons to believe or merely not to disbelieve

and he says disbelief is not just not believing it's an actual attitude you might need to believe nor disbelieve uh really belief is standing in for commitment here and disbelief sorry commitment to accept uh and disbelief for a commitment to

reject uh so his talk about belief uh is not as uh indiscriminate as it looks he's got the uh the bivalence of attitudes uh in there he's not discriminating commitments from entitlements though if anyone has a black belt in the uh idiom

of making it explicit it is John McFarlane uh one of the things you'll find on his website is his computer program dogar came of giving and asking for reasons it's just he didn't find that apparatus helpful here so he considers these three dimensions

uh uh parameters that we can vary to get a set of options what's the type of deontic operator uh governing the normative claim uh obligations permission or just reasons so that's going to be the O the p and

the r in his list of options the polarity to believe or not to disbelieve that is to accept or to reject uh we can say here scope of the deontic operator these Norms are in some sense conditional he's thinking of well normative claim

if some something about your attitude towards A and B then something about your attitude towards C but how does that go uh and so he's considering does the oh operator only apply to the consequent if you accept or have some attitude

towards the premises then you ought or have some other attitude towards the conclusion uh or is it both of them you ought if you have this attitude toward the premises have this attitude toward the conclusion oh is that right

yeah or is it the whole conditional so it should be if you have one normative attitude toward the premises should you have another normative attitude toward the conclusion or is there one normative attitude that governs the whole uh the

whole conditional and so in table one he gives us the 18 alternatives that you get deploying those and in fact he doubles those to 36 because he considers uh whether that whether he can throw in a fact of knows that as part of

the attitude uh there I've just divided through by that not that no issues are raised by that but um they don't matter for us that's the minus K I think and then uh the considerations for assessing them uh and now these are

coming from parts of the um he's his starting point his bits of the original Harman discussion that I haven't talked about uh excessive demands um is it completely impossible for anybody to do what uh a given principle would tell them uh to

do one of the versions requires that if you accept the axioms of piano arithmetic you believe all of mathematics um the Paradox of the preface the strictness test I skipped four which is about knowledge and logical obtuseness surely there's

some obligation to you know believe the consequences of uh what you believe now after setting this up obviously there's a lot of philosophical work that's going on in saying how these um you know not just motivating these criteria of adequacy but then assessing

the different proposals according to them uh I'm not going to go through any of that it's in the article look at it there's a huge literature Downstream from this because um a lot of arguments need to be made

and people look at their favorite one and his particular argument against that and say no no I can I can defend that but in the end his own conclusion uh is some combination of these two principles you ought to see to it that

if you believe a and you believe B you do not disbelieve C and you have reason to see to it that if you believe that a and you believe the P you believe that c now uh those those are good good conclusions

oh I want to say those are recognizably versions of already the rest all Ripley um uh bilateralist versions that is uh [Music] the uh deontic operator applies to the whole position that you're in uh as it does in oh rest all Ripley

um and you know the first one is saying if you believe the premises you should not believe you should not disbelieve uh the conclusion that's essentially in his idiom that's essentially the rest I'll Ripley version of um the normative situation that they say is

expressed by uh an implication foreign which has the positive obligation to believe that c that's the version that I described as [Music] that I articulated using the notion of pragmatically implicit commitments that if commitment to accept all the premises

precludes entitlement to reject the conclusion then the only position it's left that you have any chance of being entitled to is accepting it and that's a weaker uh notion than explicit commitment uh but it's a genuine normative status

that you're in the only position left open to you to be entitled to is the commitment now there isn't really a restful Ripley version of that oh but the the short conclusion I want to come to uh uh is that

the version that I've offered of the more deontically fine-grained uh version of rest all Ripley bilateralism uh satisfies the criteria of adequacy that uh MacFarlane has with great Precision extracted from um his large table of uh alternatives as I say he's using slightly different

antic Notions I think in some in some Dimensions cruder ones than I'm using though there may be others along which he's cutting uh finer uh and I would urge as a [Music] recommending feature of the way I've set

things up uh the chaotically two-dimensional version of rest all Ripley uh bilateralism is that the account goes through for the reason relation of incompatibility equally as well as it does for implication uh in keeping with as I said most philosophers

of logic he doesn't explicitly consider incompatibility uh he'd have needed to go through you know all 18 or 36 Alternatives again but the cat I gave is going to be equally responsive to the uh considerations that he's uh that he's offering here

so I think both arrows uh work well so I claim and accordingly that we can trust uh an understanding of Reason relations in terms of uh commitments and entitlements uh of the sort that at the end of part

one there on the bottom of page three uh I've uh offered uh now that obviously you'll have to assess for yourselves uh but I've given you all the sort of raw materials you know McFarlane's argument is there you see

how oh the bilateralism works and how the fancier version of the bilateralism uh works but I take it that you know I'm showing a connection between these two bits of the contemporary literature the bilateralist restful stuff and this

a key move in the discussion of the normativity of logic where uh or of Reason relations so though the particular motivations for the line we're running in the book reasons for logic Logic for reasons is idiosyncratic to us

in fact we're making just the sort of contact with major moves in the contemporary literature that one would hope to so um where we're going with this is uh I claim we're entitled to talk about reason relations of implication and incompatibility

and understand how those are both rooted in and intelligible in terms of practices of giving and asking for reasons making claims defending and challenging those claims by giving reasons for them and reasons against them so we've connected reasons reasoning and

reason relations uh Here and Now I want to turn and look to uh the structure and nature of Reason relations once we've got this topic on the table and begin to assemble the considerations that will let us compare them to logical

relations of implication deductive consequence and inconsistency which is The Logical version of incompatibility you only have inconsistency if you have negation none of the discussion um in these first um two substantive weeks on pragmatics has required the use of any logical

vocabulary we're just talking about um the use of a pre-logical or a non-logical language uh we're still shaping up to introduce logical vocabulary into it the general line as I said in the introduction is that oh what makes something a bit of logical

vocabulary is that you can introduce it into a language that doesn't have that vocabulary to make explicit the reason relations we're making explicit is putting into the form of a claimable of something you can assert or deny something that itself stands in recent

relations to other claims uh so that the very reason relations of implication and incompatibility in virtue of which I want to claim that claimables are the claimables they are have the contents that they do those can be brought into the game of

giving and asking for reasons as things you can give and ask for reasons for and against oh and so it can be the explicit topic of argument logic is the organ of semantic self-consciousness is the slogan that I

will be trying uh trying to fulfill so what we'll be looking at in the next two weeks is what can we say about these reason relations uh before we've got Logic on board but what do we what is it that we're trying

to make explicit we sort of understand them but in particular what structure do they have oh are they transitive are they monotonic and uh so on so that's that's where we're going uh so I claim we're at the end of that

first Arrow the one that takes us into the center of the mandala to the uh reason relations okay well let me pause there okay well this was the first substantive sort of portion of the book manuscript that we

addressed uh and I hope you can see how it's filling in the uh promissory notes that are implicit in that uh in that mandala at least that one Arrow should mean a lot more to you uh now than it did when you first

side and we've got to dwell a little in the central region in preparation for worrying about that next Arrow that vertical okay well then uh be well and I will see you next time