Pokrewne
- Strona Główna
- Barker Clive Powrot z piekla
- Heath Lorraine Najwspanialsi kochankowie Londynu 01 Odzyskana miłoÂść
- Wharton William Tato
- Ludlum Robert Krucjata Bourne'a
- Stanislaw Lem Glos Pana (2)
- G.G. Marquez Kronika Zapowiedzianej Smierci (4)
- Nowe Wyznanie Egzorcysty
- Carroll Jonathan Kosci ksiezyca
- 194
- eBook Business Killer Internet Marketing Strategies
- zanotowane.pl
- doc.pisz.pl
- pdf.pisz.pl
- zsz5.keep.pl
[ Pobierz całość w formacie PDF ]
.Logical forms on this level allow for a variety of transforma-tions that show the deductive consequences of our speech and mental acts, butdo not themselves represent such acts.Deductive transformations also allowfor the study of the consequences of scientific hypothesis, or of mathematicaltheories, which in general are not intended or designed to represent features ofcognition.On this level, there is no basis for allowing (Hyper1) (Hyper3) asdeductive principles, and in fact given the above argument there is good reasonto reject these assumptions altogether.Finally, we should note that there are other, equally important reasons whywe must distinguish an initial level of analysis regarding the cognitive structureof our speech and mental acts from a second level at which deductive trans-formations are allowed to occur.These other considerations have to do withconceptual realism s theory of reference and the deactivation of the referentialexpressions that occur as the direct objects of transitive verbs.We will returnto this issue in section nine of chapter seven. 118 CHAPTER 5.FORMAL THEORIES OF PREDICATION PART II5.5 Summary and Concluding Remarks" As a way of avoiding Russell s paradox, the theory of simple logical typesdivides predicate expressions and their corresponding abstract singular termsinto a hierarchy of different types, and then imposes a grammatical constraintthat nominalized predicates can occur as argument- or subject-expressions onlyof predicates of higher types." The grammatical constraints of type theory exclude as meaningless manyexpressions that are not only grammatically correct in natural language but alsointuitively meaningful, and sometimes even true." The logical insights of type theory, and in particular the asymmetry be-tween predicate and subject expressions, can be retained while mitigating thegrammatical constraints of the theory.Within standard second-order predi-cate logic with nominalized predicates as abstract singular terms we need onlyimpose a constraint on complex predicates (»-abstracts), namely that theybe restricted to those that are homogeneously stratified in a metalinguisticsense." By retaining the full comprehension principle (CP" ) of second-order pred-»icate logic with nominalized predicates, but excluding »-abstracts that are nothomogeneously stratified, we obtain the system »HST", which is equivalent tosimple type theory and consistent relative to Zermelo set theory." »HST" can be taken as a consistent reconstruction of Frege s and Russell searly 1903 form of logical realism." For Frege s extensional ontology, an extensionality axiom, (Ext"), can beadded to »HST".This extensionality axiom is Frege s Basic Law Vb.Theother direction, Basic Law Va, is an instance of Leibniz s law in »HST".ThusFrege s basic law V is consistent in »HST"." By replacing standard first-order (possibilist) logic by free logic, »-abstracts,whether homogeneously stratified or not, can be allowed in the comprehensionprinciple (CP" ).Russell s paradox then only shows that the »-abstract for the»Russell property, when transformed into an abstract singular term, must failto denote.A new axiom schema, ("/HSCP"), is added in order to include»the objects denoted by nominalized »-abstracts that are homogeneously strati-fied.The resulting system HST" is equivalent to »HST"and can be taken as»a better reconstruction of Frege s ontology, but not also of Russell s." The difference between the systems »HST" and HST" shows in a clear»and precise way one of the important differences between Russell s and Frege sformal ontologies." The concepts of conceptual realism are rule-following cognitive capacities inthe use of predicate expressions and as such have an unsaturated nature similarto but also different from the unsaturated concepts and relations of Frege sontology.It is the unsaturated nature of a predicable concept that informs aspeech or mental act with a predicable nature." Unlike Frege s ontology where nominalized predicates denote the extensionsof concepts, in conceptual realism nominalized predicates denote the intensionalcontent of concepts if in fact that content can be object -ified.The object - 5.5.SUMMARY AND CONCLUDING REMARKS 119ification of the intensional content of a concept is an abstract intensional objectthat represents the truth conditions determined by that concept." The intensional content of most concepts can be object -ified, i.e., pro-jected onto the level of objects, as abstract intensional objects.But the in-tensional content of the concept that the Russell predicate stands for, as wellas certain others, cannot be object -fied, i.e., the nominalized predicates thatstand for those concepts must be denotationless." The system HST" can be taken as the core part of the formal ontology»for conceptual realism as well as of Frege s form of logical realism.Frege s log-ical realism differs from conceptual realism in having the extensionality axiom,(Ext"), as part its core as well." The principle of rigidity (PR), which is discussed in the next chapter, isvalid in logical realism but not in conceptual realism.This is another importantdifference between the two formal ontologies." Logically equivalent formulas do not in general preserve truth when inter-changed in intentional contexts, and only a hyperintensional logic will sufficefor that purpose." One objection to the systems »HST" and HST" (and the theory of sim-»ple types as well) is that they do not adequately respect the fine-grained, or hyperintensional, structure of such intentional contexts as belief, desire, etc.This is because formulas provably equivalent in these systems do not in generalpreserve truth when interchanged in such contexts.The claim is that only ahyperintensional logic will suffice for that purpose [ Pobierz caÅ‚ość w formacie PDF ]
zanotowane.pl doc.pisz.pl pdf.pisz.pl agnieszka90.opx.pl
.Logical forms on this level allow for a variety of transforma-tions that show the deductive consequences of our speech and mental acts, butdo not themselves represent such acts.Deductive transformations also allowfor the study of the consequences of scientific hypothesis, or of mathematicaltheories, which in general are not intended or designed to represent features ofcognition.On this level, there is no basis for allowing (Hyper1) (Hyper3) asdeductive principles, and in fact given the above argument there is good reasonto reject these assumptions altogether.Finally, we should note that there are other, equally important reasons whywe must distinguish an initial level of analysis regarding the cognitive structureof our speech and mental acts from a second level at which deductive trans-formations are allowed to occur.These other considerations have to do withconceptual realism s theory of reference and the deactivation of the referentialexpressions that occur as the direct objects of transitive verbs.We will returnto this issue in section nine of chapter seven. 118 CHAPTER 5.FORMAL THEORIES OF PREDICATION PART II5.5 Summary and Concluding Remarks" As a way of avoiding Russell s paradox, the theory of simple logical typesdivides predicate expressions and their corresponding abstract singular termsinto a hierarchy of different types, and then imposes a grammatical constraintthat nominalized predicates can occur as argument- or subject-expressions onlyof predicates of higher types." The grammatical constraints of type theory exclude as meaningless manyexpressions that are not only grammatically correct in natural language but alsointuitively meaningful, and sometimes even true." The logical insights of type theory, and in particular the asymmetry be-tween predicate and subject expressions, can be retained while mitigating thegrammatical constraints of the theory.Within standard second-order predi-cate logic with nominalized predicates as abstract singular terms we need onlyimpose a constraint on complex predicates (»-abstracts), namely that theybe restricted to those that are homogeneously stratified in a metalinguisticsense." By retaining the full comprehension principle (CP" ) of second-order pred-»icate logic with nominalized predicates, but excluding »-abstracts that are nothomogeneously stratified, we obtain the system »HST", which is equivalent tosimple type theory and consistent relative to Zermelo set theory." »HST" can be taken as a consistent reconstruction of Frege s and Russell searly 1903 form of logical realism." For Frege s extensional ontology, an extensionality axiom, (Ext"), can beadded to »HST".This extensionality axiom is Frege s Basic Law Vb.Theother direction, Basic Law Va, is an instance of Leibniz s law in »HST".ThusFrege s basic law V is consistent in »HST"." By replacing standard first-order (possibilist) logic by free logic, »-abstracts,whether homogeneously stratified or not, can be allowed in the comprehensionprinciple (CP" ).Russell s paradox then only shows that the »-abstract for the»Russell property, when transformed into an abstract singular term, must failto denote.A new axiom schema, ("/HSCP"), is added in order to include»the objects denoted by nominalized »-abstracts that are homogeneously strati-fied.The resulting system HST" is equivalent to »HST"and can be taken as»a better reconstruction of Frege s ontology, but not also of Russell s." The difference between the systems »HST" and HST" shows in a clear»and precise way one of the important differences between Russell s and Frege sformal ontologies." The concepts of conceptual realism are rule-following cognitive capacities inthe use of predicate expressions and as such have an unsaturated nature similarto but also different from the unsaturated concepts and relations of Frege sontology.It is the unsaturated nature of a predicable concept that informs aspeech or mental act with a predicable nature." Unlike Frege s ontology where nominalized predicates denote the extensionsof concepts, in conceptual realism nominalized predicates denote the intensionalcontent of concepts if in fact that content can be object -ified.The object - 5.5.SUMMARY AND CONCLUDING REMARKS 119ification of the intensional content of a concept is an abstract intensional objectthat represents the truth conditions determined by that concept." The intensional content of most concepts can be object -ified, i.e., pro-jected onto the level of objects, as abstract intensional objects.But the in-tensional content of the concept that the Russell predicate stands for, as wellas certain others, cannot be object -fied, i.e., the nominalized predicates thatstand for those concepts must be denotationless." The system HST" can be taken as the core part of the formal ontology»for conceptual realism as well as of Frege s form of logical realism.Frege s log-ical realism differs from conceptual realism in having the extensionality axiom,(Ext"), as part its core as well." The principle of rigidity (PR), which is discussed in the next chapter, isvalid in logical realism but not in conceptual realism.This is another importantdifference between the two formal ontologies." Logically equivalent formulas do not in general preserve truth when inter-changed in intentional contexts, and only a hyperintensional logic will sufficefor that purpose." One objection to the systems »HST" and HST" (and the theory of sim-»ple types as well) is that they do not adequately respect the fine-grained, or hyperintensional, structure of such intentional contexts as belief, desire, etc.This is because formulas provably equivalent in these systems do not in generalpreserve truth when interchanged in such contexts.The claim is that only ahyperintensional logic will suffice for that purpose [ Pobierz caÅ‚ość w formacie PDF ]