So it's my pleasure to reintroduce Lorent Le Fogg, who will continue his course on classifying toposes of geometric theories. Please, Lorent. OK, thank you very much. So I just want to remind the participants that yesterday, I introduced the statement of the existence theorem of classifying toposes. How to associate to any first-order geometric theory a topos which represents the function of models of this theory. So the first part of the lecture was devoted to the meaning of the theorem, of everything which appears in the theorem, and the second part, which we had begun, was devoted to sketching the proof of this theorem, which means to construct from a given theory T category, the so-called syntactic category, and owed with topology, GT, JT, the so-called syntactic topology, such that the associated topos answers the question raised in the theorem. So we had begun the second part. So saying first that we wanted to construct such syntactic category, CT, together with the topology, JT, and it should be endowed with canonical model, MT, which should be universal with respect to the construction of all models in all geometric categories. So then here, we had introduced the notion of geometric category, which is a type of category where geometric formulas in any signature can always be interpreted. And there is not only a notion of geometric category, but also a notion of geometric function. A geometric function is a function between geometric categories, which respects the interpretations of geometric formulas in sigma structures. OK. As a statement of the characterizing property of syntactic categories, endowed with their canonical model, the fact that these categories, that the syntactic category, represents a function of models on geometric categories related by geometric formulas. And then we had proposed the construction of the syntactic category. So by definition, the object of this category are formulas, or geometric formulas, in some variable. And these formulas are considered up to substitution of variables. Then there is a definition of morphism. So morphism are geometric formulas, which are provably functional. And in fact, yesterday, I had forgotten to say that these provably functional geometric formulas should be considered up to three provable equivalents. In fact, one participant made me remark that I had forgotten to say that. So here, it is added in the last line of this slide. So of course, this notion of equivalence, two provable equivalents, refers to what it means to be provable in the theory, just as the notion of provably functional formulas. So this heavily depends on the theory you are considering, not only on the signature. And then there is a formula for the composite of two morphisms. And of course, it has to be verified that this definition defines a category, and this category is a geometric category. OK, as this definition refers to the notion of tip probability, we need it to make precise what it means to be provable. So to be provable in a theory means that it can be deduced from the axioms of the theory using the inference rule of geometric logic. And we had given a full list of the inference rule which can be used. And of course, this list is just the list of deductions, rules which we use all the time when we do mathematics. Even without thinking about that. OK, and by now, as we have this notion of provability, there is an induced notion, which is a notion about the relationship between different theories. So let's consider two theories, T and T prime, with the same signature sigma. So the same language, but different theories considered with different axioms. And then there are elements of vocabulary we introduced. So first, we say that the T prime is a quotient of the T, if any geometric sequence in the signature, so a sequence relating two formulas, phi and psi. So any such sequence, which is provable in T prime, is also provable in T. So you understand that T prime is a quotient of T, when there are everything which is provable in T prime, excuse me, it is the opposite. Here I have made a mistake. I wanted to say that T prime is a quotient of T, when anything which is provable in T is also provable in T prime. So this means that in T prime, there are more provable properties than in T. So for instance, if you think about the theory of rings and the theory of commutative rings, so of course, the theory of commutative rings has more provable properties than the theory of rings. So it means it is a quotient. And we say that two theories are equivalent. If anything which is provable in one of these theories is also provable in the other, so each one is a quotient of the other. Then there are obvious remarks to be made. If two theories are equivalent, of course, the associated syntactic categories are the same. And if T prime is a quotient of T, which means if there are no properties, more sequence provable in T prime than in T, then CT is subcategory of CT prime. And they have the same objects because the objects only depend on the signature, as we have already remarked. OK, so this will be important for later. By now, what we immediately remark is that if two theories are equivalent, associated syntactic categories are exactly the same. OK, so by now, it is important to consider subobjects in syntactic categories. So the notion of subobject makes sense in any category. So in particular, we may wonder what is a subobject of an object in the syntactic category. So let's consider a geometric theory T and its associated syntactic category CT. And let's consider an object of CT, which by definition is a geometric formula, phi of x in some variables, in some context x. And of course, this is considered up to substitution of variables. Then the statement of the proposition tells us that the subobjects of such a formula are exactly the formulas phi 1 in the same context, in the same familiar variables, such that the second phi 1 implies phi is provable in the theory T. OK, so we see that in other words, in this category, the notion of subobject exactly corresponds to the notion of provability between geometric formulas written in the same variables. So this is a categorical translation of the notion of provability. And by now, if we have two subobjects of phi, phi 1 and phi 2, then the inclusion relation of one of these subobjects in the other corresponds exactly to the relation of provability between the formulas. OK, so the second part, of course, is the consequence of the first part because a subobject is included in some other subobject phi. If and only if A is a subobject of phi. OK, so this is very important to have such a translation between the categorical notion of subobject and the logical notion of provability. OK, in fact, this whole theory of syntactic categories is a way to make logic categorical. And when I say logic, once again, you should not understand this word as a particular part of mathematics, but rather as a way to present any mathematical theory in the linguistic way, which we always do when we do mathematics. OK, so then we have to make precise what is the canonical model empty in such a syntactic category. How is it defined? So once again, let's consider such geometric theory T in some signature sigma together with associated syntactic category. And of course, we suppose we are verified that Ct is a geometric category. So this, of course, requires a proof. We don't have enough time to give the proof, but it could be checked. And if you don't know the proof, it is a very good exercise to check it that it is really a geometric category. In particular, it has arbitrary finite limits and so on. OK, so as it is geometric, as this category is geometric, it has a meaning to talk about the models of the theory T in such a category. And then we are to introduce a particular model, which we shall call the canonical model. So a model consists in associating an object to any sort of A, a morphism to any function symbol F, and a sub-object to any relation symbol R. OK, so let's do it. So first, for any sort of A, we decide that the associated object is just the formula code in any variable XA associated to the sort F. Of course, it does not depend on the choice of variable because objects are formulas considered up to substitution of variables. Then if we consider a function symbol F going from a list of sorts A1, An to a sort of B, then by definition, the associated morphism in the model we are constructing is given by the formula, which is written there. So it is just the formula is just that the variable XB in the codomain is equal to F of the variables X1, Xn in the domain. OK, so this is just the formula we are used to when we want to define a function. But here, by definition, such a formula is a morphism. Here, we just have to check that this formula is probably functional, which of course is completely of use. And lastly, for any relation symbol R in the context of a family of sorts A1, An, we decide that the associated subject of true in the variables X1, Xn is just the formula R in X1, Xn. So R in X1, Xn is, of course, a subformula of true of X1, Xn. And here, we are using the fact that in the syntactic category, the formula true in the variables X1, Xn is the product of the objects represented by the formulas true in X1, true in X2, true in Xn. OK, so this, of course, defined a sigma structure. And here, there is something to be verified, which is the fact that this is a model of the theory T. So in order to do that, we have to consider the interpretations of geometric formulas in this model. So let's consider such a geometric formula phi in some variables X. And by now, we have a lemma that the interpretation of the model of such a formula phi of X is just the subobject defined by this formula. So just remember, here, we had said that the subobject of formulas consist in formulas in the same variables, which probably imply the ambient formula. OK, so here, the ambient formula, the context is the formula true in the variables X1, Xn. And it contains the subobjects formula phi X. And so the statement of the lemma is that this formula phi of X, considered as a subobject of the formula true in X, is exactly the interpretation of the formula phi of X in our canonical model empty, in our canonical sigma structure empty. And if we combine this lemma with the previous proposition here on the interpretation of the relationship between provability and inclusion of subobjects, we get as a corollary that a second is a geometric sequence, a sequence relating two geometric formulas phi on psi. Is t provable? Is provable in the theory t? If and only if, considered as a subobject of the object true in X, the first one is included in the second one. And this, by definition of a model, means that such a model, it means that the sigma structure empty verifies the second phi implies psi. So you see that here we have an equivalence. We are seeing that the second is provable in t. If and only if it is verified by the sigma structure empty. So an equivalence, of course, means we have an implication in two directions. So in the first direction, we have that if a second is provable, in particular if it is an axial, then it is verified by the sigma structure empty. So this means that empty is a model. But here we see that it also works in the other direction. If the canonical model empty verifies this second, then verifies a second. It means that this second is provable in the theory t. OK? And by now, we have a theorem, which is, so this theorem exactly tells us that the category we have constructed is an answer to the question we addressed. So let's consider the syntactic category just constructed of a geometric theory t together with its canonical model empty. So then, as for any model, there is for any geometric category c, from the category of geometric functors from city to city, to the category of t models in c. And this functor associates to any functor from city to city, the transform of the model empty by the functor f. OK? And the statement of the theorem is that for any such geometric category c, this functor is an equivalence. So the category of geometric functors from city to city is equivalence through this functor to the category of models of city. And not only it is an equivalence, but we can also construct the reverse equivalence. So the reverse equivalence has to associate to any model of the theory t in c, a geometric functor from the syntactic category city to city. So how is defined this reverse equivalence? So we have to associate to any object of city an object of c. And we have to associate to any morphism of city a morphism of c. So what is an object of city? By definition, it is a formula. It is a geometric formula up to substitution of variables. And what we do is just to consider its interpretation in the model m. And this, by definition, will be the image of this formula considered as an object of city by the functor fm. So the image of such a formula considered as an object of city by the functor fm is just defined as the interpretation of the formula phi of x in the model m. And by now, let's consider a morphism of the syntactic category. So it is a provably functional formula, theta in two families of variables, x and y. And this is such a provably functional formula up to three provable equivalents. And so what you have to do is abuse. You consider the interpretation of this formula. So the interpretation of this formula is a sub-object in the product of the interpretations of the formula phi of x on psi of y. But because the formula theta is provably functional, you get that this sub-object in the product is the graph of a morphism. And so you define the image of this morphism theta by the functor fm to be the unique morphism whose graph is the interpretation of theta. Everything has been defined so that all of this makes sense. OK, so the theorem tells you that these are two equivalences which are in this one to the other. OK, so of course, it has to be verified. But the verification is, in fact, is quite easy. It is more intricate to verify that the category city is geometric. Once you know this, everything goes through very easy. OK, by now, we have constructed the syntactic category together with its canonical model. And we know that the syntactic category represents the functor of models on geometric categories. But by now, we remember that what we want, in fact, is not a geometric category. We want a topos, which is a much more geometric object. And in order to get a topos, we need to define topology on the syntactic category. So we need to define when a sieve on an object in the syntactic category will be considered as a covering. And here is the definition we propose. We decide that the sieve on an object's psi of y is a covering. If it contains a family of morphisms, you see some domains phi i to the co-domain psi. And these morphisms are defined by probably functional formulas, theta i's. And so we decide that such a sieve has to contain such a family of morphisms, which is globally epimorphic. So this means globally epimorphic is, once again, a categorical notion. But because images and unions of sub-objects are well-defined in the geometric category city, the property to be globally epimorphic just means that the union of the images of this morphism is equal to everything, is equal to psi. So this is an inclusion property. And the inclusion property, I remind you, is equivalent to property of t probability. So in fact, it means exactly that the following sequence psi implies the union over the indices i of the images. The images are just given by the existential quantifier on the variable x i's. So this sequence has to be t provable in the theory. So this exactly means, so this is a logical translation, a translation in the language of probability of the categorical property for a family of morphisms to be t provable. And so we decide to define in this way the notion of covering sieve. And of course, it can be checked that this is indeed grotendic topology, which means it verifies the three grotendic axioms of maximality, stability, and transitivity. So maximality is obvious. Stability comes from the fact that both arbitrary unions and images, which means existential factors, commute with best change. So for unions, it is a so-called distributivity rule. And for the existential quantifiers, it is the so-called Frobenius rule. OK, so this means these are parts of the usual inference rules, deduction rules of the object. A remark we can make here, an important remark, is the fact that this topology is defined by the categorical structure of the syntactic category. You see a family of morphisms is covering when it is globally epimorphic. So this property is purely categorical. So it means, in particular, that if you have two syntactic categories which are equivalent, then they have the same topology. Because the topology is deduced from the categorical structure in that case. OK, so let's just think where we are. So we have constructed a syntactic category. And we have proved that it is universal with respect to models of the theory T in geometric categories. But by now, we want to move to a universality property with respect to toposies and to morphism of toposies. So this means we have to move from geometric factors between geometric categories to morphism of toposies between toposies. And these two things are different. And the relationship between the way to go from geometric morphism to morphism of toposies is given to us by Diakonescu's equivalence, which was already stated yesterday afternoon by Olivia. So here it is, so I repeat it again, just in the case when the category we are considering has finite limits, which, of course, is a simple case. In fact, yesterday, Olivia stated Diakonescu's equivalence in general. But for today, we only need Diakonescu's equivalence in that particular case. So let's consider such a small category with finite limits together with topology. And let's consider the canonical function from the category C to the associated topos. So the canonical function L is just the composite of the Yoneda embedding followed by the Shiffication function, J upper star. And let's consider an arbitrary topos. Then here is a statement of Diakonescu's equivalence. First, for any morphism of toposies from E, from this arbitrary topos E to the topos defined by the site C, J, then the composite of the canonical function from C to the topos C at J with the point-back component F upper star of the toposmorphism from E to C at J. So this component verifies the two following properties. So first, it is a flat functor, which means here that it respects finite limits. So the notion of flat functor exists in a much more general setting without any hypothesis on C, as Olivia explained in her lectures yesterday afternoon. But in that particular case where C has arbitrary finite limits, it just means that this functor from C to E respects finite limits. And the second property verifies is the fact it is J continuous. So this means that it transforms any J covering family of C into a family of morphism of E, which is globally epimorphic. So this is the first part of the statement. So the second part of the statement is the fact that the functor we have just defined from the category of morphism of toposies from E to our toposm is an equivalent to the category of functors from C to E, which are both flat and J continuous. So here, I remind you, flat just means that it respects finite limits. And J continuous means it transforms the coverings into globally epimorphic families. OK, so this is a general statement of Diacones Cruz equivalence. And by now, we have to apply it to syntactic categories. But for this, we need a lemma. So let's consider geometric theory, the associated syntactic category on an arbitrary toposm E. And let's consider a functor from C to E. And then the statement is that such a functor is geometric. If and only if it is flat, which means it respects finite limits. And it is JT continuous, which means it transforms globally epimorphic families of Ct into globally epimorphic families of E. I remind you that the topology of Ct, the syntactic topology of the syntactic category, was defined by deciding that a family of morphism is covering when it is globally epimorphic. So here, JT continuity just means that such a functor has to transform globally epimorphic families into globally epimorphic families. OK, on the earth, lemma, which is easy, tells us that such a functor from the syntactic category to E is geometric if and only if it is flat on JT continuous. But according to Diacones Cruz equivalence, it just means that such a functor defines morphism of toposis in the reverse direction. OK, also, we get the following corollary for any geometric theory. And if we denote by E, the cushion topos of the topos of pre-shifts on Ct by the topology JT. So we consider this topos on an arbitrary topos E. And then we have a composite functor which goes from the category of morphism of toposis from E to ET to the category of flat JT continuous functors from Ct to E. OK, so this first functor is Diacones Cruz equivalence. So it is an equivalence. But by now, we just said by the previous lemma that a flat JT continuous functor is the same thing as a geometric functor from Ct to E. And then we have already proved that the category of geometric functors from Ct to E is equivalent to the category of models of E. So here, we take the composite of two equivalences of categories. So it is an equivalence of categories. And we have proved that our topos is a classifying topos for the theory. For any topos E, to consider a toposis morphism from E to ET is the same thing as to consider a model of the theory T in the topos E. In particular, if you take for E the topos of sets, you get that the point of the classifying topos ET is the same thing as a model of T as a set theoretic model of T. OK, so here, of course, we have, as for any topos defined by your site, of course, we have a canonical functor from the syntactic category to the topos ET. But yesterday, Olivia introduced in her lecture a notion, a property which can be verified by these canonical functors. It is a property to be a fully-faced full embedding. This property is not always verified, but it is verified by some sites. And here, so the definition is the following. You say that topology on a category C is subcanonical. If the canonical functor from C to the associative topos, to the quotient topos by J, so if this canonical functor is fully-faced full. So it is a definition. And in fact, you can prove that this is equivalent to say that the unedited embedding of C into C at factorizes through the topos considered as a subcategory. In other words, it means that any representable functor on C is a shift for the topology J. OK, so it is a definition, a general definition, which was given yesterday in Olivia's lectures. And then we have a lemma, which is the fact that the topology GT on the syntactic category Ct is always subcanonical. Whatever the theory T. And so this means that Ct is embedded into ET as a fully-faced full category. And of course, this fully-faced full embedding also respects finite limits. So this is always the case because the unedited embedding respects arbitrary limits. And the shiftification functor respects finite limits. So the composites, the canonical functor, always respect finite limits. And so this functor respects finite limits. In particular, it respects subobjects. And it is fully-faced full. And as a corollary of this lemma and what we already proved, we get the following that a geometric sequence of the theory T, so an implication between two geometric formulas, phi and psi, is provable in the theory T if and only if it is verified by the universal model of T. So the universal model of T is the image of the canonical model in CT by the canonical functor L from Ct to ET. So here we really have, you see, a wonderful relationship between syntax and semantics. So we have that any property is provable in the theory if and only if it is verified by the canonical model of the theory in its classifying topos. OK. And I already mentioned as a side remark that if you apply that to so-called coherent theories, so here it corresponds exactly to theories whose classifying topos is coherent in the sense of topos theory as already introduced in FGA4, then what we get is that Godel's completeness theorem is the same thing as the theorem of the linear on coherent opposites having enough points. So this is a really wonderful fact because it tells us that a logical, most important theorem of logic is, in fact, the same thing as this purely geometric theorem of the linear. OK. So by now, an important remark we have made is it is a reverse direction, which is the fact that if we start with an arbitrary topos, then there are infinitely many geometric theories whose classifying topos is equivalent to the given topos. And here I just write a sketch on the idea of the proof of this proposition. So you start from an arbitrary topos is, so by definition, a topos is a category which is equivalent to the category of sheaths on some site, Cj. OK, so by definition, a topos is a category equivalent to some Cj hat, where C is a small category. And we can even suppose that C has arbitrary finite limits. And J is a topology on C. And by now, of course, there is a notion of a flat G continuous functor from C to an arbitrary topos. And this notion, of course, defines a theory. There is a theory of flat G continuous functors. And you can check that this theory is, in fact, a geometric theory. And then when you consider the geometric theory T, so you see the geometric theory of flat G continuous functors. In other words, you can say that this geometric theory is really the theory of points on the topos associated to Cj, according to Diaconix whose lemma. This theory is a theory of points of the associated topos. So it is a geometric theory. And then you prove that its classifying topos is equivalent to the topos of sheaths on Cj you started with. So here you see that any presentation of the topos in terms of a site gives rise to a presentation of the topos as a classifying topos of some geometric theory. So here you already see that there is an incredible diversity of presentations of topos by geometric theories. And so the fact for here there is an induced definition, you say that two geometric theories are so-called morita equivalents when they have the same equivalent opposites. So maybe it could be suggested to call this equivalent semantic equivalents. In fact, we have already there is also a notion of syntactic equivalents. It was mentioned yesterday when I answered the question. You say that two theories are syntactically equivalent when their syntactic categories are equivalent. But here there is another notion of equivalents, which is induced by the abuse one, but which is much more rich. It is a notion of semantic equivalents or morita equivalents. It means that two theories are the same associated topos. And it really means that two theories, which possibly are completely different languages, have the same mathematical content. So it gives rise to, it is the beginning of a theory of, I would say, of relationship between the contents. It is a theory of relations between the mathematical contents of different mathematical theories. And this theory, in fact, was introduced and developed by Olivia from her PhD thesis. And she has called that the theory of topos theoretic bridges. And she already talked about it yesterday. And today I will introduce some consequences of some consequences, some applications, some bridges, and some consequences of some concrete bridges. So here is the definition. Two theories are called morita equivalents if they're associated, the classifying topos are equivalent. And then, as a remark, we have the fact that the syntactic equivalents between two theories which means the existence of an equivalent of syntactic categories implies an equivalence between the associated topos. This is because the topologies, the syntactic topologies and syntactic categories are induced by the categorical structure. And here, a very important remark is that the converse is not true. Some theories are semantically equivalent or morita equivalent without being syntactically equivalent. So the relationship of semantic equivalence is much more subtle. OK. And by now, what I want to do in the third and last part of the lecture is to present some basic results which allow to get some first applications of the theory of classifying toposes. So these results I am to present are from the PhD thesis of Olivia on their book Theories, Sites, Toposes. OK. So a general principle for getting these results will be to use bridges. So a bridge, once again, is an equivalence between two toposes presented in two different ways. And the general principle of bridges, of toposteritic bridges, is to consider invariance of toposes, which means some informations which can be extracted or informations or structures or whatever type of properties of geometric or mathematical objects which can be constructed from toposes using the language of categories and which are invariant under equivalences of categories. And when we consider such an invariant, general principle is to try to express these invariants in terms of presentations of the toposes under consideration. Here's the first invariant we are to consider is the category, in fact, the ordered set of sub-toposes of given topos. So the way any topos, it is possible to associate an ordered set, a set with an ordering, consisting of its sub-toposes. And then we may wonder how this invariant can be expressed in terms of different presentations of the toposes we consider. So first, we need a definition. In fact, the first part of the definition was already introduced. So what is an embedding of toposes? It is a morphism of toposes consisting in a pair of adjoint factors, j upper star, j lower star, such that the right adjoint component, j lower star, is fully faithful. And this is equivalent as these factors are adjoint. It is equivalent to requiring that the composite factor, j upper star composed with j lower star for this composite factor, identify with the identity factor of E prime. So you see it really corresponds to E prime being a sub really embedded in E. And the pullback component from E to E prime has to act on objects of E prime without changing them. So in some sense, there are fixed points of this factor. So this is the definition of an embedding. And then a sub-topos is an equivalence class of embeddings. You decide that two toposes, two embeddings of toposes E1 and E2 into an ambient topos are equivalent if they can be related by an equivalence of categories which transform the first embedding into the second embedding up to isomorphism of functions. So this is the notion of sub-topos. And then there is a first result which, in fact, it is already in SGA form. So it is the fact that if we consider a sub-topos of a topos E, which is presented as a topos of sheaves on some site, then to consider a sub-topos of this topos is the same thing as to consider another topology, J prime on the same category C, which is bigger than the given topology, J. So of course, in one direction, it is abuse. If you have on C topology J prime, which is bigger than J, of course, it induces, it defines a sub-topos C at G prime of C at. And the embedding of C at J prime into C at factorizes through the sub-topos C at J because J prime contains J. So this means that any topology G prime bigger than J induces a sub-topos of our topos E equal C at J. But the proposition is that this map is one to one. So to consider a sub-topos is the same thing as to consider a topology. And here, as we can take for C, a small category, it means that as a consequence, it implies that the sub-toposis of a given topos E together with inclusion relation of sub-toposis is a set. It is a set ordered by inclusion. OK, so it is a corollary of this proposition. And by now, we can wonder about the translation of this property of this invariant, the invariant of consisting in the ordered set of sub-toposis in terms of theories. So by now, we consider a geometric theory of signature sigma. And we suppose that we are interested in sub-toposis of the classifying topos of T, in sub-toposis of E T. And here is a statement. So first, start from a theory T, which is a quotient T prime of T. So this means it has the same signature, the same language, and it has more provable sequence. There are more properties. There are more axioms in T prime than in T. And then the first part of the statement is that in that case, E T prime, the classifying topos of T prime, identity is a sub-topos of the classifying topos of T. And the second part of the statement is that this map, which goes from quotient theories T prime of T, considered, of course, up to equivalence, the map from these quotient theories to the order set of sub-toposis of E T. So this map is one to one. So to consider a quotient theory of T is the same thing as to consider a sub-topos of E T. So this means that this invariant, consisting in the order set of sub-toposis of a given topos, has an extremely nice expression, both on the sides of topologies and on the side of theories. OK. So maybe we can sketch or at least give an idea of the proof. So on one side, we have the quotients. And the other side, we have the topologies. But what we need to do is to define a map in one direction and then in the other direction. So start from quotient T prime of T and consider an axiom of T prime. So it is a second phi implied psi. And of course, this sequence defines a monomorphism in the category C T. So the monomorphism just corresponds to the object phi conjuncted with psi on the object phi. Of course, phi on psi is a sub-object of phi in the syntactic category. And then you decide that this monomorphism has to be a covering for the topology J associated to T prime. And you define J as the smallest topology of C T, which contains a canonical topology, J T, on these coverings. OK, so it is a topology generated by G T and by this family of coverings associated with all axioms of T prime. And in the other direction, when we have a topology J on C T, which contains G T, we want to associate to it a quotient T prime of T. So in order to do that, what you do is to consider an arbitrary J covering family of morphism of C T. So such a family of morphisms, of course, is a family of T-provable functionals. OK, and you can consider, of course, the images of this morphism. So this corresponds to taking an existential quantification. And then we consider the union of the images, which corresponds to the disjunction sign we have written there. And by now, what we just introduced this second five implies this property. And what we really want is this family of morphism to become a covering. And so, excuse me, it is a covering. So we want this family of morphism is a covering. And we want to translate that in the language of provability. So we decide that any segment of this form gotten from a covering has to be an axiom of T prime. And we define T prime as a quotient of T defined by this family of axioms. And so the theorem is that these two maps are inverse one to the other. So you see that it is constructive in both directions. OK, and before we make a break, I want to state the following consequence, which is the equivalence between the language of provability, between the notion of provability, and the notion of grotendic topology. So here, we combine the two translations of this invariance that had been computed on the one hand in terms of topologies, and on the other hand in terms of theories. So consider a geometric theory. And suppose it's classifying topos, ET is presented as a topos of sheaves on some site. So this site may be the syntactic site, but it also may be any site, any representation which you know. And then there is a correspondence, a one to one correspondence between on the one hand the theories T prime, which are quotients of T, and on the other hand, the topology is J prime on C, which contains J. So here, this is, as Olivia says here, we have a bridge, so the invariance is the invariance consisting in the sub-toposis of the considered topos. And we are considering two representations of this topos at the same time, on the one hand in terms of a theory P, and on the other hand in terms of a site Cj. And we express the same invariant on the two sides. And in this way, we get a correspondence. And so by now, this corollary has very striking consequences. So the first one is written there. Of course, when you have a theory given by your family of axioms, the first thing you want to know about this theory is whether it is contradictory or not, whether it is contradictory or consistent. And in general, it is a very subtle and difficult question to answer that is, in general, it is very difficult. But here, consequence of this corollary is that when the classifying topos of ET is presented from a site Cj, and j prime is the topology corresponding to t prime, then t prime is contradictory. If only if the topology j prime is maximal. And maximal means that the NTC is covering for any object. So this is a geometric translation of the property to be contradictory. And so this means that if, in the category C, there is at least one object which is not covered by the NTC, then the theory t prime is not contradictory. OK. And here, there is the last slide before the break, which is also, I think, very, very interesting. So it is just an obvious consequence of the previous result. So it is the following. Consider an arbitrary geometric theory of signatory sigma. And then consider an arbitrary geometric sequence.  Is it a consequence of the axioms or not? So in mathematics, usually, you want to prove results. So a result is always an implication, which has to be a consequence of the axioms of the theory.  This is exactly what you want to do. But then, formally, you can do the following. You just introduce t prime, the Cushion theory of t, which is defined by adding this axiom. And so the question is, is t prime equivalent to t or not? T prime equivalent to t just means that this sequence is a consequence of the axioms of t. It is provable in t. So on by now, let's consider the classifying topos of t, so ET, written, we suppose, as the topos of shifts on some sites. And let's consider the topology, j prime on j, which is defined by ET prime. In fact, we know how this topology is defined. We just consider the sequence phi implies psi. We consider the associated monomorphism, phi on psi implies phi. And j prime is just the topology generated by j and by this morphism considered as a covering. So the monomorphism from phi on psi implies psi. Okay, so this means j prime is constructed by just generation from j by one covering. And by now we have the following equivalences. We have that our sequence is provable in the theory. If and only if the caution theory t prime of t is in fact equivalent to t, and this is equivalent to j prime equals g. So in other words, is some topology generated in some way, is it equal to g or is it bigger? This is a question. So this is really wonderful because it means that all the inference rules, you remember there were maybe 10 or 12 inference rules which were the deduction rules of geometric logic. On the earth, they are just replaced by the rules, by the axioms of growth and dik topologies. And there are three axioms, so the maximality axiom, which is trivial, and then the stability and transitivity axioms. So in fact, the axiom of growth and dik topologies here appear as completely equivalent to the deduction rule, the deduction rules of geometric logic. And any problem of probability in a geometric theory can be translated in a problem of knowing whether some family of morphism in a category belongs to the topology generated by family of covariance. Okay, so of course it doesn't make the problem trivial, but it is a translation of one part of mathematics. It is really here in some sense an embedding of logic into topology. Okay, and so here in fact, I think something very, which has to be done is to try to implement that in the computer systems. I really think here there is an important subject to be explored. Okay, so I stop there for the first part. We make a break. Okay, thank you.


It's time for another pack opening Yo, what's going on the ufnation asleep for back again and welcome back to the channel like I said today We are back with another pack opening and we are hoping for some very good pulls So it is Wednesday at the time of recording this which means a new team of the week has dropped So let's look at the new team of the week. It's actually pretty insane We have as you can see an 88 dry settle 87 stamp coast 83 willy knee lander Connor garland mccann 86 cane we got parron Grandland crider and then a bunch of like oh a jellies We have surga chest cider merino Riley and then in that we have mr. Jack Campbell So we do have a rival rewards. We didn't place too well in rivals. I didn't play too much But don't worry next week's pack opening is gonna be better as you can see I'm close to diamond So we have seven an open packs So let's get right into it to gold players pack. We're gonna start off with this We're hoping for a purple pull. We did take untradable pox this week So we're hoping for something good something that can make the team maybe a couple x factors I've yet to pull an x factor in a pack Which I find absolutely crazy Hopefully we do that today Even a power-up icon would be huge So let's see if we can get a thousand coins will definitely take that because the coin total is a little bit low right now All right onto the premium pack. We get two gold players in this who knows an x factor would be great I think this is our best chance of getting an x factors in a premium pack But Probably not so let's keep it going here What can we get Freda coach or Freda coach a pure angle being the best player that we have and that'll be the best one In that pack moving on to a prime pack We got 10 items in this pack at least five players with at least three gold players and two NHL players So let's see what we can get in these prime packs I don't know if I've opened up a prime packet this year So we'll see what we can get these are untradable by the way These are my rival rewards here. So let's see what we can get here nothing above an 80 yet 81 Jason Zucker and That is that for that pack. I don't expect too much from these prime packs to be honest We're waiting for these jumble NHL player packs. Those are gonna be the big boys. I think hopefully anyway So here we go. Last of the prime packs here. That's what 500 coins will definitely take that. We pull a gold player yet We did Something good here, man 84 Victor headman. That's actually not bad. We will definitely take that if I get his ex. Oh, I have his 88 So I don't know how I feel about that. But if we were to get his ex factor, that'd be very nice So we'll take a Victor headman And that is it. So we'll take Victor headman not too bad 84 overall Moving on to the jumble NHL player packs here 20 items all gold NHL players with at least 10 of them being 80 plus overalls Let's get a purple in this pack or a power-up icon will be very nice. Arendelle not not ideal here So let's keep it going Curtis Lazar Jordan Greenway, I don't know how many times I pulled the greenway this year JT Miller at an 82 overall. Come on Kevin Lankan in. All right Come on, man. Let me see that purple team of the week Jared McCann. So we pull one of the new team of the weeks the It's a leaf legend Not really but Jared McCann at an 82 overall We like that not too bad pretty cool team of the week pull Tim Stutzla Come on. We still got a little bit of this pack left Alexander Kerfoot like I said a purple would be great a power-up icon Even an X factor another team of the week we pull a Mort Sider team of the week. That's actually a pretty cool one with With applesauce. I don't think we'd use him, but that's not too bad Tave Lutera Vyman Thomas Tatar and Alec Martinez. So a decent pack All right last jumble NHL players pack. We're gonna open this one with our nose here Come on Let's see a purple in this one Robby Fabry's not a purple neither is Andreas Jonson Nick Letty. Oh my goodness We're wasting my 80 overalls on 80 overalls. Come on. Give me an 80 plus here Nick Suzuki Braden Shen.   He might even make the team now at an 84 We will take a kill my car.  Welcome to the team buddy Anyways guys, that's going to be it for today's pack opening video I know it's a shorter one. We didn't have too many packs to open But we got some decent pulls and kill my car and Victor headman upgrades to the team for sure But guys if you enjoy this video be sure to drop a like on it figures and you run here Make sure hit the subscribe button down below And hit the notification bell as well, but like I said guys that is it for today's video Thank you guys very much for watching


Thank you for having me. It's it's really good to be here and and it's it's You know as I was telling Colin and Emma, I think I'm neither a law person nor am I a tech person. So I'm trained as a rhetorician and which means I'm interested and I guess the ways in which some of these issues intersect around language and how the language that we use And the arguments that we develop in the metaphors that we use to develop those arguments how they really can affect Limit and open up possibilities for social movements and so on So I'm going to be talking specifically about the book our space but primarily about The last case study that I that I engage in the book and that is about creative commons, which as you know Was grounded here and and I'm sure some of you are still involved and so again as far as issues of intellectual property and and So on I know that I'm in a room full of people that probably know more about these issues than I do So so I'll look forward to your thoughts and comments And hope that the added value that I bring to the table is is some thoughts about the language that we use and so on so the central task of the book is just to give you a little bit of background on that to kind of tee up What I want to talk about which is the last argument in the book But the central task of the book is to investigate the constitution and Inventional possibilities of publics in an age dominated by the rhetoric and logics of the market That is how are publics made and what can they do in the book? I examine how social movements like culture jamming seek to undermine the rhetoric of multinational corporations specifically through practices such as media pranking and That some of the examples that I look at in the book is the work of a group out of San Francisco called the Biotic baking brigade if you're not familiar with them Their mission to pie pompous people in here is they've pied Bill Gates here. They pied Milton Friedman And I talk about at some length media pranking as a strategy in other chapters of the book and Sort of good old-fashioned ad busting which you're probably familiar with the work of ad busters magazine This is kind of a play on this Campaign that the gap ran in the late 90s, which was you know different counter cultural figures wearing khakis to kind of position khakis as you know sort of the rugged individualist pant choice and of course Yeah, so they this obviously turns it into sort of mass conformity writ large So ad busting things like billboard liberation write people like the billboard Liberation front who go out in the middle of the night and do some things as sophisticated is actually Rerouting neon and turning off parts of signs and so on sometimes. It's just sophisticated computer graphics that alter existing advertising messages and so on Or copyright and trademark infringement and you're probably familiar with a lot of that work people that are just trying to Steal hijack, you know corporate imagery in order to either comment on the kind of litigiousness of Corporate culture around their brands and their brand imagery Or just to make a case for for public domain in general. I'll talk a little bit more about some of that But among the questions that the project raises is whether so-called Resistance as traditionally conceived has reached its limit as a diagnostic category for critics interrogating struggles over cultural messages in the global economy So in the book I provide a taxonomy of contemporary Anticorporate activism that I break down in the following way and first our Our activists engaging in what I talk about as sabotage And that's an explicitly dialectic Reputation of the rhetoric of consumer culture It's a strategy that begins from the premise that we have become merely consuming publics, which is the original title of the book by the way That we become merely consuming publics publics who consume Sabotage is a direct attempt to thwart what activists see as the repressive Disciplinarity of the spectacle and to wake the citizenry from their stupor. So it's a very kind of wake up Shake the masses and to sort of bring them to reality in some way The rhetoric of sabotage is probably best exemplified by ad busters magazine and I look at them in some length in the book And their approach to commercialization as a monolithic machine or image factory that must be stopped or slowed down So this is culture jamming in a very oppositional way In fact in their culture jammers manifesto that they publish in ad busters and also in their founder Kelly Lassen has a book called culture jam Their culture jammers manifesto says we're going to bring the imagery to a shuttering the image factory to a shuttering halt And I talk about that it's very telling that they use this very industrial revolution factory metaphor as a way of Talking about the enemy And in fact, they talk about themselves as contemporary saboteurs and they use the language of sabotage quite a bit Sabotage for those of you that may not know etymologically comes from the word Sabo, which means wooden clogs and during the industrial revolution when workers wanted to Literally stop the machine of industry. They would show throw their clogs Where we also get the metaphor to clog They would throw their clogs into the machinery into the factory machine in order to stop work for the day and as a means of protest Part of what I suggest in in the book is that Although sabotage has its time in place and it certainly had its time in place in the face of industrial capitalism And sometimes today in certain parts of the world in the fact I challenge the notion that we can really look at today's consumer culture and today sort of Swirling scintillating barrage of images as a factory I wonder about the limitations of that very 20th century or 19th century metaphor for how capitalism functions Secondly, I examine culture jamming strategies that rather than Sanitizing commercial culture attempt to appropriate it toward new ends. So through practices of pranking like I showed you that the Pies in the face and I look at a variety of sort of people who commit pranks in order to get themselves on Television and so on and also copyright pirates. I put in this group These appropriation artists attempt to take seriously consumer culture on its own terms and engage it accordingly So it's less oppositional And more sort of taking advantage of some of the resources that commercial culture provides However, I suggest that appropriation artists in their celebration of the criminal artist do tend to perpetuate although less So maybe than saboteurs a dialectical or oppositional relationship with commercial culture by positioning themselves as outlaws I argue that appropriation artists risk validating the very codes they challenge This strategy begins from another premise that the dictates of markets have so successfully turned us into mere consumers That the only response is the citizen as criminal That is post-industrial capitalism with its tendency to turn products into brands and brands into the vernacular of everyday life Has consumed publics so markets are consuming publics rather than just turning us into consumers Publics in that sense are being consumed. So I conclude the book and this is what I want to talk about today I conclude the book by looking at a third set of responses to commercial culture Responses that do not so much attempt to thwart brand giants nor liberate small pieces of culture from their clutches Rather by actively promoting the concept of the commons these activists augment and intensify certain aspects of markets So importantly the strategy is unavailable to those who see markets and publics as mutually exclusive Rather than saying no to consumer culture as the antithesis of healthy thriving publics An intensive a care intensification strategy says yes and to the tools that markets afford This strategy begins from the premise that publics are everywhere that they are all consuming It is this third strategy that I want to discuss today and it comes from the final chapter Of the book which is inventing publics kairas and intellectual property law so just a bit about some and Contemporary theories on sort of the notion of how publics function One of the more popular in the recent studies of publics and publicness has been Michael Warners publics and counterpublics in Warners model Publix do not exist a priori their text their textual interpretation and sorry Interpolation before they are called into being by the rhetorics that speak them as such publics are kinds of fictions Albeit fictions with identifiable properties and very real material effects Publix's Warner begins his book our queer creatures. You cannot point to them count them or look them in the eye You also cannot easily avoid them. They have become an almost natural feature of the social landscape like pavement However is even a cursory read of his argument illustrates Warners publics are really nothing like pavement They are shaped by the temporality of circulation. Those are his terms And ebb and flow of discourse is demanding our attention and building on one another Their rhythms are shaped and punctuated by an endless systolic and diastolic pulsing of newspapers Hollywood films 24-hour news channels sitcoms movies of the week, etc. etc The texts of our everyday lives that constitute the teeming and multi citational field in which Publix are made So for Warner, I think he really foregarns this notion that Publix are created through the circulation of texts So so questions of intellectual property law and how is it that text circulate have a direct effect on what we can understand is as public What does invention which is a primary concern for rhetoricians like myself or creativity? Maybe put more plainly Invention of a foundation of rhetoric. What does it look like in such a model? How can Publix thrive and create under these conditions? One response a very common response one that I'd like to resist Would would be to begin from the premise insisted upon by people like Juergen Habermas that the public flourishes in the absence of control That healthy Publix enjoy absolute freedom from say governmental or commercial constraints Warner's metaphor such as circulation and dissemination might indeed lend themselves to the position that the circulation of texts that constitute Publix Must be protected from rules or obstructions of any kind So in my analysis, I look at I'll kind of speed through some of this kind of public theory stuff One of the concerns is that that Certainly that intellectual property law is acting as a tourniquet It's choking off the circulation of texts on which Publix depend right that again if Publix completely depend on The the free circulation of texts then there's this concern that intellectual property law copyright Regimes and so on are kind of acting as it as a tourniquet So for many at the heart of the debate is our freedom of speech and our capacity to create new and innovative works And at stake for many of those evolved a course is the conditions for creativity itself So some who might agree with the notion that Publix depend upon the circulation of texts see the regime of intellectual property law Again is increasingly threatening this dynamism on which Publix thrive acting as a tourniquet So my goal is to contribute to the conversation about Publix by suggesting that Kyros the Greek concept of Kyros Which I'll talk about in a little bit or a kind of making do is an Inescapable component of text making and indeed public making this conception encourages in the case of contemporary intellectual property law responses that improve on What is rather than mourn a fantasy of what was I argue that if we look at the strategies of some Anti-cop copyright activists many of them are fighting for a deregulation of the discursive field for a lightning of the burden of intellectual property Their approach correlates to an understanding of Publix that would assume that because circulation is what Publix require The appropriate strategy of resistance ought to be to lift regulations that bind them To decentralize power and to return to the notion of ideas as common property Toward this end many anti-copyright activists act as modern-day Robin Hoods by artistically pirating or hacking Copyrighted and trademarked material in an effort to reinvigorate a sense of the commons As I argue then the copyright pirate model of resistance Despite its good intentions perpetuates and solidifies the most harmful assumption girding current intellectual property law That is that intellectual materials can and should be exclusively treated as property as an alternative to the notion That ideas and concepts are property. I suggest that the most compelling approach comes from the so-called free culture or creative commons movement Unlike other copyright activists those who ostentatiously pirate Corporate intellectual property in effort to make a case for deregulation the creative commons sharing model embraces a thoughtful and detailed increase in Regulations agreement that emerge the emergence specific and ever-changing encounters between texts the law and Publix Ultimately, I argue perhaps Controversially that a conception of rhetorical invention based on the classical Greek ideal of Kairos rather than property Offers a way of reimagining the public as being made more robust not less by regulations I'll be at regulations of a different kind Kairos in the sense that I want to propose it here is a rhetorical art for which Karen in Carolyn Miller's words quote the challenge is to invent Within a set of unfolding and unprecedented Circumstances and action rhetorical or otherwise that will be understood as uniquely meaningful within those circumstances, and I'll talk about it a little bit More now now again, I don't want to rehearse issues that people are well familiar with so I'll just Maybe abbreviate here a little bit but Part of what I suggest in the book again, which is for a more general audience than what I have here is Talking about you know the notion that ideas don't operate based on notions of scarcity And so on which a lot of anti-copyright activists and others Um readily say right and they often quote Jefferson is his metaphor about sort of if I light your candle with mine It's you know Mine isn't darkened and so on people people use those metaphors, but at the same time There continues to be a lot of rhetoric Such as John Oswald's notion that if creativity is a fence if creativity is a field Trademark is the fence which is an oft quoted as you probably know Comment about the the influence of intellectual property on creativity Similarly Yeah, I'll talk about it talk about that in a minute, right? So there's this great resistance to this notion of You know trademark is being the fence presumably that cordons off Creativity and so on so of course in response A number of scholars and activists and so on have advanced then this metaphor Maybe it's maybe the metaphor is new in the right way of putting it This notion of the commons, right kind of echoing Habermas's fears about the monopolizing tendencies of private enterprise Communication scholar Kimberl McLeod for example Wonders in his book owning culture in this environment How in the world are people supposed to critique ubiquitous privately owned texts that help shape our consciousness without being able to reproduce them so growing of Growing number of so-called appropriation artists responding by invoking a kind of pirate ethic as I've mentioned before By unabashedly using copyrighted and trademark material in their own work They attempt to call attention to the asymmetrical control over our cultural materials in doing so many activists have sometimes unwittingly Provoked major major corporations into high-profile legal battles which directly affect the future shaped shape of what counts as the public domain So illustrating this kind of art of theft those who pirate and hijacked own materials Attempt to free information and so on from what they see as the prison of private ownership and a couple examples of Well-known cases. This is the food chain Barbie series by Forsythe Tom Forsythe and This is probably a familiar case for some people the artist Starbucks took him to court realized that they didn't have a case based on Copyright because his this was considered fair use its political commentary and so on but they kind of did an end run and got him on trademark dilution Which is increasingly as some of you probably know used by corporations Against political commentators when I think that it's meant to be a protection against other corporate Marketers and so on competitors So a concern for the Commons is a concern that the text that create publics are being strangled again by the control of copyright So part of you know, and again, this is kind of a couple chapters that I go over Sort of the notion of appropriation by both pranksters and and pirates But part of the critique that I have as as productive and sometimes Appropriate these kinds of strategies are again as as somebody who studies rhetoric my position is always that That you need to pick a strategy based on the situation in which you find yourself so So no strategy is universally good nor no strategy is universally bad But one of the limitations that I think that appropriation art has in the face of its perceived enemy is that I Want to suggest that the restrictions posed by intellectual property are more prohibitive if we accept the notion that intellectual material can only be Imagined as property and I worry that the appropriation artist strategy of stealing copyright materials so-called stealing As an act of subversion is too limited that is if we perpetuate romantic notions of an anti Anti-copyright activists as pirates or Robin Hood stealing from monolithic corporate landlords We leave uninterrogated the founding premise that ideas are property that can be hoarded or denied The most crucial argument of terrain is seated from the start That is I say in the book that that it's like stealing bits and pieces from the kingdom while leaving the monarchy intact so Yeah, so I'm gonna sort of leave that because I think that hopefully That critique is clear but but together with with The notion Oswald's notion that trademark is the fence of in creativity in a field of creativity Likewise, David Bollier's position serves as another example of this kind of call for again the lifting of restrictions He says quote any sort of creative endeavor, which is to say progress Requires an open white space in which experimentation and new construction can take place. There must be the freedom to try new things So in his book silent theft he describes a monolithic corporate takeover of our commonly shared resources that diminishes the variability to progress as a culture He idealizes an open decentralized train for civic invention that is unsullied by the interests of private enterprise As he says quote an argument for the commons then is an argument for more white space So part of if I could just kind of I guess get to the the nub of Where I come down on this after and I won't Kind of rehearse as I as I might talking to a different group Rehears kind of how creative commons functions and and and what its role is and and so on Part of the argument that I make is that it's this isn't a creating more white space It's not about lifting the fence from a field of creativity it's in fact an intensification of certain Aspects of copyright and so on right that it's a layered added layer of augmentation or added layer of nuance That in fact can increase the circulation of texts rather than decrease them, which is which is often the fear and I go about this through among other things the concept of kairas and Let me talk just a little bit about that so that you know where I'm coming from So if we allow a notion of publics that that recognizes that circulation is not necessarily the dialectical opposite of Regulation again, so it's not just about lifting regulation. I think the creative commons case sort of shows that That an added Level of regulation can actually speed up and free up texts Then we remain open to the ways in which the intensive Intensification of regulatory categories Can actually increase the circulation and vitality of creative publics So in the book I propose that for those interested in promoting a robust and democratic Democratic commons the ancient rhetorical concept of kairas serves as a more appropriate rhetorical resource than property In the golden age of greece philips aporia tells us kairas was quote typically thought of as timing or the right time Although its use went far beyond temporal reference So unlike kronos or kronos, which was associated with a linear qualitative Quantitative time, excuse me kairas was better understood as a moment of a particular quality The word carried a number of meanings including symmetry Propriety occasion do measure fitness tact decorum convenience proportion profit and wise moderation So it's all about sort of um It's a meaning about taking advantage of the particular moment in which one finds themselves And I go to some links in the book to in my analysis of creative commons that um The that the fact that you can tailor licenses and agreements Based on each text and based on each instance Allows for kairas to thrive or that it capitalizes on the sort of kairotic moment So that it's not this blanket zero sum sort of code that gets a priori mapped on to every transaction Instead a kind of creative commons really makes use of that kind of um in the moment in every sort of specific situation You to negotiate the the rules of the road Between creators and users and so on So so I just want to conclude my comments with the strange notion that rhetorical invention may work like a pinball machine So I encourage us to collaborate on alternatives to models of rhetorical resistance in which publics Let me let me reword this I encourage us to collaborate on alternatives to models of rhetorical resistance That they move away from the notion in which publics are perpetually on the losing side of an endless cat and mouse game with the corporate establishment That is it's probably clear hopefully that i'm um that i'm not willing here to Um To conclude that yes intellectual property always stifles creativity right that that's that that's um how it works Right so certainly corporations invoke an even lobby for laws so that they can thwart certain kinds of critique And it's true that copyright laws were never intended to be used ideologically to silence political dissent However, as may always be the case when some chirotic moments are undermined others are foregrounded That is that the current state of intellectual property law is the chirotic moment in which we find ourselves It provides the conditions from which um challenges can emerge So I offer here the strange supposition that the field of rhetorical invention may be something akin to a pinball machine I invoke that image because in response to bolier's position that the creative that creative progress requires more open space I want to suggest quite the opposite Just as a pinball would gather no momentum no speed no direction without bumpers and pins to respond to Neither is rhetorical invention possible without constraints and obstacles that define its chirotic encounters So with this perhaps juvenile example in mind I would like to return to john oswald's assertion that create that trademark is the fence in the field of creativity Oswald's description is quite useful. Although maybe not in the way that he intended language is funny that way Intellectual property is not merely a fence that confines and makes discreet a piece of stagnant property In an impenetra impermeable boundary along which powerful corporations successfully post their no trespassing signs Rather it is a fence that gives shape and substance to specific fields of discourse Importantly fences can be straddled. They can be climbed under over and through they can be extended and reconfigured into playful mazes They can be walked on like a tightrope and that ability to walk delicately and precisely in a state of in between Is precisely what defines chiros perhaps the most crucial component of rhetorical invention So the mythical figure of chiros was um Minor god in the greek pantheon and he was depicted as a well muscled wing footed figure perched on a Stick or ball balancing a set of razor a set of scales on a razor Almost as if walking along a fence He is also often depict depicted with winged feet presumably for those moments when like a pinball hitting a bumper He is propelled off in some new and unknown direction Perhaps the ancient mythical figure of chiros like the contemporary mythic figure of the who's tommy Knows that creativity is about becoming the part of becoming part of the machine and learning how to play it So with that I'll stop the formal talking at you business and um, and I just kind of wanted to Put a question out there and and people can take it and and run with it as they want to or pose other questions, of course um, but I guess one of the things that I um, still try to think about again if if my interest anyway is about, um Creating a robust public Culture and how to go about doing that and how to sort of keep as many and interesting texts in circulation as possible um if um What I'm saying is true in that regard then then That that's that circulation of text is central to culture Then what would it take for an open commons to really serve as an alternative? That might actually enjoy a level of circulation that could actually compete with the kind of more hegemonic corporate owned Culture so in other words, how does something like creative commons or um, or the sort of free culture movement more largely? um And the content that it produces Translate if if you think it should at all and maybe maybe you don't um into the mainstream and not remain this kind of countercultural outlier That focuses that that's um driven by and focuses on um A group of people who are interested in specifically these issues that is is it is it to remain kind of a cultural space where people debate issues of um of um Copyright and intellectual property and people who are concerned about those issues should that remain the content of the thing Or is there a way for it to kind of translate into people who don't necessarily have an interest in those issues at all Can see the value and take advantage of its resources and and so on um So with that I think I'll just kind of put that out there and see what people think as well about anything else that people would like to discuss I have I have a a vocabulary point that uh from my field to yours and a question from your field to mine I am in the law inducement intellectual property law and one of the Underlying distinctions of things like copyright is often that the idea at any rate that there is some sort of separation between The idea and the expression of the idea that what is prevented being used is the expression than not the idea And in your talk you repeatedly talk as though you use you say, you know Copyright law constrains ideas and and you may be using ideas in a somewhat different way But but at least in the very technical way that lawyers think about it That's just not what it does the the internal motion is that so so I don't know whether you're doing that intentionally Or whether you just just just are using ideas in a way that it would not be the way we would use it And I would urge you to perhaps at least take that on board Yeah, yeah My my my question in return is is and I'm just unacquainted with with with the field that you're describing And nice to nice to my eyes open. What is a public? In this context you talk about public's is and and it's just not a term I've got any experience with so I would appreciate it if you That's great. I think that the notion of ideas is I'm I guess I'm not trying to to Come down in any way about Sort of what ideas are so much as look at the way that it gets they get talked about or that So I'm looking at the ways that um activists will talk about um That you know that property law is is is sort of Choking off the free flow of ideas, and I think that distinction isn't that's that's actually not what it's doing No, I think that's an important distinction that I think is is absolutely worth making Um, the notion of what is a public is is something that's very much In debate, right? I mean so so for people like um Havana's for example who it coined the term public sphere and um is sort of well known um german philosopher on this topic um For him, it's it's precisely that space that's separate from private enterprise on the one hand and Governments on the other so so the public is that thing that keeps that bay to have a thriving robust public You keep that bay both capitalism on the one side and the state on the other That's not a version of the public that I'm wanting to advance I think that That those I mean that you can't separate out publics from markets and publics from You know the citizenry and the sort of the government and so on so for me publics are Groups that kind of hover around Centralizing texts, right? So they're they're communities that hover around certain sets of ideas um and so on But I mean that you know these things are these things are scurly and debatable for sure So can I um see if I understand that question that you posed at the end um Is it because it's sound to at times it sounded to me as though you were saying what can there be An alternative sort of public alternative mode that is the sort of more creative commons Our space maybe But that to me sounded separate from what we have now rather than sort of an ecosystem where perhaps The center of gravity has shifted From where it is now, which is the vast majority of all people outside this room Are quite content with the status quo or as far as they know And not in the Common's discussion tends to happen within Some sort of other so was it was it a separate was it shifting within Or would you rephrase it in a way that I didn't understand? I think what I'm and again, I'm just kind of trying to think this through too Which is why I wanted to pose the question is that um Is there is there a way for um some of the Values that say you know free culture or a lot of people in this room probably are are committed to is Are those sort of destined to be um this kind of You know rabble rouser from the peanut gallery kind of thing or or is there a potential there For it to to be a kind of major player in terms of cultural production Um and and that would involve people who don't necessarily care about issues of Free expression so on but just see it as a as a good means to an end For getting their work done or for getting their art done So I'm just yeah that helps Please um, I'm gonna throw in an idea from from the global health world Which is the area that I know something about and I was talking about some of these issues with some journalists from Uganda and And uh some public health people from also from Uganda and um At Tanzania and some other places in Africa and they immediately got The importance of creative comments and of net neutrality and of a number of different things I mean I I hardly had to explain anything at all because they saw That that chokehold on information could keep them Backward and and the the least or the less powerful partner You know, you know larger global context and I wonder if I mean I think about some of the Supposed values of global health of open access to Health care of a lot of sharing and and so forth. Is there some way to make an alliance there because I The global health experts that I'm that I know have not yet Cottoned on to creative commons when they talk about making alliances with the business school to create case studies Of what works and what doesn't they don't think about whether or not those case studies are copyrighted Or licensed under creative commons. They don't think about whether it's open software. That's running their e medical records, etc So that's one possibility of of it going beyond the The elites in in this room or or similar rooms That if you if you think we're just specifically talking about Or proposing this whole model for people that are the the jammer so to speak or the more general public because I was thinking if you think about processes of inoculation and Isn't it exactly if you would say that if publics become part of the machine and they have to learn how to play it Although within a creative commons setting Isn't it exactly that that could actually Lift up the whole counterculture Issue that that may be the start of that they start out with So the whole idea of their expression and creativity Becomes part of the system Although it may be creative commons in the sense that it may be easier to express yourself. So I was wondering if how From your talk, I Um, I did not get how you actually see that yourself. What this actually means for These sorts of expressions if it becomes part of the system. I don't know if you can answer that If I'm not understanding the question then then put me back on course, but I think that Part of the problem was some of the more oppositional Strategies that I look at that. I didn't talk very much about now, but I think part of those problems is that they envision themselves as being Outsides for throwing stones Um, and I I find that to be not only counterproductive to what they're trying to do but not realistic as far as You know where they find themselves they constantly. So for example, ad busters constantly finds themselves Um, the subject of critiques By like-minded people who call them sellouts because they're now selling sneakers, you know sweatshop free sneakers and and so on. I think it's it's that it's that position that avant-garde position of of sort of being outside the machine that sets you up for all kinds of For all kinds of frustrations Not the least of which is the fact that Advertising itself the thing that so many of these activists are wanting to challenge Is all about telling you that You'll be an independent avant-garde sort of thinking outside the box person if you buy this or that extreme product So that so the kind of rebel outsider position is the most dominant trope used by advertisers so that so Activists constantly positioning themselves there is is in some ways in the face of Contemporary you know contemporary commercial culture Um seems to be kind of playing right into the hands of you know of marketers um I think that the thing that's interesting one of the many things that's interesting about the kind of more creative commons approach is that It it kind of at least it has the potential and this is I guess one of the things that i'm interested in people's thoughts about I mean at least has the potential to kind of take the wind out of the sales of the big brand giants because it's you know It's not about saying no to mickey mouse or saying no to barbie. It's like barbie and mickey mouse is neither here nor there Right. It's just like about creating this pool um that that Isn't dependent either either in a negative or a positive way um with with corporate culture um But it's not one that can be said to be wholly outside it either right and it's not one that I think Ultimately, I mean it's my position that um any kind of That avant-garde ism In general it doesn't serve and I don't I don't put creative commons in this camp but avant-garde ism like culture like many culture jammers kind of position themselves as Is ultimately rhetorically as a social movement as a model for social movements a dead end Because it so depends on a monolithic enemy that you're sort of that you're constantly critiquing and so on And I think that the thing that's compelling about creative commons is that it doesn't do that It's not about throwing stones at at a monolithic enemy. It's about creating alternatives that don't position themselves outside it But but don't wholly depend on this negative relationship to it either At least in in my estimation. So so I think my goal is or at least in the way I'm trying to think about it is to do away with these kinds of inside outside mainstream counterculture dichotomies anyway because I don't think that they're really very Descriptive of how things really work because we have culture jammers working industry as advertisers, right? I mean that that magazine comes out of the design community the graphic design community and you know that we have You know Andy Warhol, you know was it was making you know Displays for store, you know that that whole movement came out of you know marketing and advertising So I mean these things are so inextricably linked that I think any rhetoric that tries to presume otherwise or to to To pull the two things apart and to to look at them as separate entities Kind of misses opportunities this also mean that Let's say the the creator online just so not the critiquer But let's say someone who does stuff on youtube and miss, you know Do the mashups and stuff with with that kind of personal so fit this kind of model. Do you think or yeah? That's the thing is that um, you know, that's why I find it compelling because it's not one that's dependent on The rebel position, right? It's like i'm just an artist doing you know using this because it's most it's the most It makes the most sense for me to get my work out or to meet me to continue my work Is to to you know take advantage of the resources that are out there Then not to say that it takes the politics out of it. There's always going to be people who are engaging at that at that level And I think that's important Right, just as I think that the people who are fighting just for good old-fashioned fair use is important work to be done But in addition to that Kind of you know more oppositional stuff that has to be done Creating this other pool That just sort of every day people can take advantage of seems to be important I'm I'm not moderating So I it sounds to me as though some of this discussion sort of tracks discussion that's been going on inside creative commons sort of is it a movement or is it uh Uh a tool that can be used by all sorts of movements Is it Just a set of licenses that can be taken by people who agree with one another or by people who disagree Or does it collect all of the activist causes that All of the the license adopters are part of And I think of late it's been trying to Divide those pieces out into the core of creative commons the house of licenses and I commons the meeting place of like-minded activists who use the licenses and then build out projects that go in multiple directions So and I think any social movement works that way right whether you call it a movement or not right that there that there's that kind of The pragmatics sort of The architecture of the things that that um and those people who are kind of Fighting based on ideology or values and so on but yeah, I know I think that that makes sense Yeah, I was just gonna Ask a question about that about this uh you do your attention to The lyrics that p towns and road about being being part of the machine and If I remember correctly, that's maybe halfway through the The cd or the opera and maybe two-thirds of the way through the through the movie and then And I don't want to pretend and I think we all know that that there's not an explicit policy document in you know in Tommy but But okay. Well, maybe there is and I'm wrong again. I'm used to that but um Later on Tommy is no longer blind deaf and dumb, but Can see and there's a process that Creates or miraculously generates that somehow and Among other lyrics, there's also the part where he and people working with them who also may be followers That's to be able Say we're not going to take it and we never did we never will so there's something more oppositional and at the same time there's there's a I think it's fair to say that since Tommy can see he can now have a broader view of He can choose whether to be part of the machine or stand away from it and work with it as a as an agent something like that So anyway, um, does that mean anything with the uh within the context of what you were talking about or is that just my Wacky adolescent musings I think that's that's good I mean part of what I was trying to get out there and and maybe the metaphor works or it doesn't work and and um Now I'm sort of seeing the chinks in the armor of the metaphor. No, no, but I Yeah, yeah, yeah, does it what does that do to that? Yeah Well, how I was trying to think about it and I I when I just when I Talk about this concept of kairos with my students. I'll often Use the example of that. It's it's the difference between And I don't know if this works or not But it works for me There's difference between American football and soccer Right because American football is like a coach designs a play the actors go out onto the field and they enact the play so that the The play exists a priori the enactment of the of the play Um, whereas soccer is much more chirotic in that it's this like a team You know is having to respond in the moment to like where you know that it's it's much less play oriented That the play is much more spontaneous and chirotic and and sort of we are responding to the particular conditions much more So and I know it's not a perfect analogy, but that's what I was kind of trying to get out with that notion of Pinball and sort of Tommy feeling, you know, sort of being part of it to as an extension of himself and so on is a As a better way of thinking of Of production than this kind of You know, I'm here and the content is there sort of thing, but yeah, I like your um Interpretation of it Maybe a limitation on it. I just think about it I just think I feel like I'm still sort of digesting this whole concept. I like the football soccer Description I think that's quite useful. I suspect that there are I mean Going back to the big meta question that you asked I suspect that there are lots of good answers and examples for thought and I guess my gut reaction not feeling like I'm the best informed in this is that There are already movements in in the market of foot that are not value based in a sense of What's the right way to do things or the wrong way to do things because it's you know, some deeply held social Idea, but rather that they're seeing a market opportunity And they're starting to realize and this is maybe having drank too much Kool-Aid But I feel like there are lots of examples whether it's in the space of innovation or anything you're seeing in Kind of the digital media Kind of space where people are started or were industry is starting to realize that the drag that certain aspects of intellectual property place on Using and creating and stuff are Is greater than the benefit that it gives now I mean, it's definitely slow and coming and look no further than the ria to say that it's not you know It's not pervasive By any stretch, but I think there are lots of examples where you're starting to see it And my suspicion is that you you see creative commons fighting in its way and its community And making its points, but that the existing system is going to move quickly to kind of co-opt And to retain its mode of production and you know, and if it's smart and maybe certain entities within it Will be smart. They'll recognize these new opportunities to create to produce and information ideas and cultural products and more And that it will retain this ecosystem I was just talking to one of our faculty directors done date the other day He was talking about how When companies think about marketing now and they think about putting a video or something out into The world it's not a question of whether they will Uh get ridiculed And get spoofed it's a question of how they'll get spoofed and how can they get spoofed in the right way as opposed to the wrong way And that so it's very much become part of how they see their As you know, they're turning over this aspect of the marketing and they're trying to direct it in a certain way So that it makes them look kind of fun and cool I'll be at the butt of the joke, which I thought was terrifically interesting No, that is that is really interesting. I guess, you know, that certain corporations are sort of starting to we were talking about this a little bit less night at the free culture group meeting that That certain companies are seeing that it just makes more sense to take that leap of faith and to to to kind of you know allow for broader collaboration to have a little bit of a less of a proprietary, you know claim on on their content and so on And I mean it seems like again people in this room are going to know much more about this than I do But I mean it seems like when it comes to code and source Stuff that the companies seem to kind of get that it's in some ways more efficient to To allow people to collaborate and so on but I guess the question then becomes What about when you're talking about content? It doesn't it isn't valued based on efficiency, right that you're not trying to solve problems With a film or a song in the same kind of way You know you could argue that you are but in the same kind of way as you are just with a piece of software so Where it where is the um You know the incentive for More mainstream groups that don't necessarily care about The ideological, you know, it's more democratic or any of that right that that's not necessarily the interest How do you show that it is a good? Avenue and I think I guess that's part of my question that content isn't driven by efficiency in the same kind of way Uh There's not necessarily an opposition between the more public a kind of uh Space of operation and and the traditional market kind of space as I think about it The opposition really comes when when people try and move from maybe one domain to the other Because although we all know little bits and pieces of exception By and large most people operate within their their kind of daily personal sphere as though copyright didn't exist I mean I certainly do You know you just you know everybody operates with in that way and you and you quote from books and you send it to your friend and you You know you you write fan Magazine things and you know take off and you post them on on on small websites and all that And we just operate in fact quite quite as though it's irrelevant and every now and then Some thunderbolt comes out of zoos and and we and you know strike somebody dead But but mostly you know people just don't don't pay attention And it's really only when you move into either some kind of very public oppositional role or into that sphere yourself That that suddenly the the gods of copyright take notice of you and and and and and then you have to have to deal with it So I you know I I see this kind of kind of bubbling level of the informal publics if I can use that that term not too bad Where where it's it's not it's not a question And then you get to the more formal levels or the more or the more commercially oriented It's only when you really either want to oppose or or or be part of that that that the commercial interests kind of come down on To to to and it seems like I mean it seems like companies are Trying to really choose their battles around a lot of this stuff because sometimes it behooves them to go after Go after a copyright infringers other times it doesn't write other times. It's just plain bad pr I mean, I think Mattel found themselves in a lot of Trouble in the 90s with going after fan sites and these kinds of things right that I think that this obviously the smarter Companies get that you you want people to have their fan sites You don't want to be going after you know that sort of thing that that you can really hurt yourself in the long run By letting things come out in this kind of David and Goliath way And I think I mean I guess part of the question too is that One difference, I mean, I don't want to suggest that there are no differences between markets and publics whatever that means I just want to suggest that they're not These separate entities either You know one of the difference seems to be that You know the difference between I guess an artist and a content provider You know, whatever that doesn't might be is is that one is is usually in it for profit Right that there's profit is sort of the goal whereas for a lot of people I think who are wanting to take advantage of you know creative commons and other means is You know that the goal can be all kinds of things. It can be the you know reputation It can be you know getting your the pride of getting your work out there It can be earning, you know a certain like credibility among your community It can be you know, there's all kinds of things that drive You know, I mean people are driven to create all the time And so it's just it's interesting to see if I mean, I don't know If something gets lost as corporations just adopt, you know, if they adopt kind of creative commons style Licenses if that does anything Instrumentally to undermine the sort of profit only model we seem to have in terms of cultural production, but I don't know Any final words thoughts reflections? Well in that case, please join me and thank you