Variations on a Montagovian Theme
... Let me be a bit more precise than I have been so far. We will be concerned with theories of knowledge, belief, apriority or some other “modality”. Until further notice, I assume that a theory of this kind can be identified with a logically closed set of sentences in a first-order language L . As usu ...
... Let me be a bit more precise than I have been so far. We will be concerned with theories of knowledge, belief, apriority or some other “modality”. Until further notice, I assume that a theory of this kind can be identified with a logically closed set of sentences in a first-order language L . As usu ...
x - Koc Lab
... Example: Show that if x and y are integers and both x∙y and x+y are even, then both x and y are even. Proof: Use a proof by contraposition. Suppose x and y are not both even. Then, one or both are odd. Without loss of generality, assume that x is odd. Then x = 2m + 1 for some integer k. Case 1: y is ...
... Example: Show that if x and y are integers and both x∙y and x+y are even, then both x and y are even. Proof: Use a proof by contraposition. Suppose x and y are not both even. Then, one or both are odd. Without loss of generality, assume that x is odd. Then x = 2m + 1 for some integer k. Case 1: y is ...
Second-Order Logic of Paradox
... Truth values of compound formulas are derived from those of their subformulas by the familiar “truth tables” of Kleene’s (strong) 3-valued logic [9, §64], but whereas for Kleene (thinking of the “middle value” as truth-valuelessness) only the top value (True) is designated, for Priest the top two va ...
... Truth values of compound formulas are derived from those of their subformulas by the familiar “truth tables” of Kleene’s (strong) 3-valued logic [9, §64], but whereas for Kleene (thinking of the “middle value” as truth-valuelessness) only the top value (True) is designated, for Priest the top two va ...
MATH 311W Wksht 1 • A logical statement is a phrase that is
... both. For example in everyday English, “He will have Coke or Pepsi” usually does not include the possibility of having both, but in mathematics: the following statements are true: The number 7 is positive or prime. (True, it is both). The number 2 is even or prime. (True, it is both). • Truth Tables ...
... both. For example in everyday English, “He will have Coke or Pepsi” usually does not include the possibility of having both, but in mathematics: the following statements are true: The number 7 is positive or prime. (True, it is both). The number 2 is even or prime. (True, it is both). • Truth Tables ...
PARADOX AND INTUITION
... What does it really mean that some consequences of a given theorem are counterintuitive? Does it imply that there is something wrong with the axioms we have accepted? Or may be, there is something hidden in the arguments (rules of inference) applied in the proof of (allegedly) counterintuitive theor ...
... What does it really mean that some consequences of a given theorem are counterintuitive? Does it imply that there is something wrong with the axioms we have accepted? Or may be, there is something hidden in the arguments (rules of inference) applied in the proof of (allegedly) counterintuitive theor ...
Propositional Logic and Methods of Inference
... We can add simple causal reasoning to our rule by defining additional rules such as: (2) IF the battery is good THEN there is electricity (3) IF there is electricity and the sparkplugs are good THEN the sparkplugs will fire (4) IF the sparkplugs fire and there is gas THEN the engine will run (5) IF ...
... We can add simple causal reasoning to our rule by defining additional rules such as: (2) IF the battery is good THEN there is electricity (3) IF there is electricity and the sparkplugs are good THEN the sparkplugs will fire (4) IF the sparkplugs fire and there is gas THEN the engine will run (5) IF ...