Die Grundlagen der Arithmetik §§82–83
... a natural number and that any successor of a natural number is a natural number follow immediately from the definition of “natural number”; 78.5 says that P is functional and one-one. So apart from the easily demonstrated statement that nothing precedes zero, by the end of §81 Frege can be taken to ...
... a natural number and that any successor of a natural number is a natural number follow immediately from the definition of “natural number”; 78.5 says that P is functional and one-one. So apart from the easily demonstrated statement that nothing precedes zero, by the end of §81 Frege can be taken to ...
A logic-based theory of deductive arguments
... the reasons and the conclusion of an argument though we do not indicate the method of inference since it does not differ from one argument to another: We only consider deductive arguments, hence the method of inference for each and every argument is always entailment according to classical logic. Mo ...
... the reasons and the conclusion of an argument though we do not indicate the method of inference since it does not differ from one argument to another: We only consider deductive arguments, hence the method of inference for each and every argument is always entailment according to classical logic. Mo ...
Proofs
... Let f be the identity map from A to B. Then f is an injection (and we conclude that | A | | B | ). Define the function g from B to A as g(x) = x/4. Then g is an injection. Therefore, | B | | A |. We now apply a previous theorem which states that if | A | | B | and | B | | A | then | A | = | ...
... Let f be the identity map from A to B. Then f is an injection (and we conclude that | A | | B | ). Define the function g from B to A as g(x) = x/4. Then g is an injection. Therefore, | B | | A |. We now apply a previous theorem which states that if | A | | B | and | B | | A | then | A | = | ...
THE PARADOXES OF STRICT IMPLICATION John L
... s e s to do with one another, if, that is, A and B are totally disparate in meaning," It cannot be denied that there is a strong temptation to identify implication with a relation between meanings. However, we must be more explicit about just what this relation is. Let us begin with the case of anal ...
... s e s to do with one another, if, that is, A and B are totally disparate in meaning," It cannot be denied that there is a strong temptation to identify implication with a relation between meanings. However, we must be more explicit about just what this relation is. Let us begin with the case of anal ...
An argumentation framework in default logic
... corrected in specific circumstances: people reason with defaults as if they were true, until they give rise to an inconsistency. The attractiveness of this idea is that if nonmonotonic reasoning is regarded as a kind of inconsistency handling in classical logic, no new logic needs to be developed. F ...
... corrected in specific circumstances: people reason with defaults as if they were true, until they give rise to an inconsistency. The attractiveness of this idea is that if nonmonotonic reasoning is regarded as a kind of inconsistency handling in classical logic, no new logic needs to be developed. F ...
On two problems with the Theory of the Creating Subject
... our minds are taken to be essential to what a mathematical construction is, and others are not. The stance that Brouwer assumes is of a kind with Turing’s, who devised his theoretical analysis of (mechanical) computation in terms of an idealised human, not a machine; Gandy proposed the term ‘comput ...
... our minds are taken to be essential to what a mathematical construction is, and others are not. The stance that Brouwer assumes is of a kind with Turing’s, who devised his theoretical analysis of (mechanical) computation in terms of an idealised human, not a machine; Gandy proposed the term ‘comput ...
PPT - UBC Department of CPSC Undergraduates
... WLOG, let a and b be algorithms. Assume a is generally faster than b. Based on the definition of generally faster, then: there is an i such that a is faster than b for all n > i. We now need to prove that b is not generally faster than a, that is that there is no i2 such that b is faster than a for ...
... WLOG, let a and b be algorithms. Assume a is generally faster than b. Based on the definition of generally faster, then: there is an i such that a is faster than b for all n > i. We now need to prove that b is not generally faster than a, that is that there is no i2 such that b is faster than a for ...
PPT
... WLOG, let a and b be algorithms. Assume a is generally faster than b. Based on the definition of generally faster, then: there is an i such that a is faster than b for all n > i. We now need to prove that b is not generally faster than a, that is that there is no i2 such that b is faster than a for ...
... WLOG, let a and b be algorithms. Assume a is generally faster than b. Based on the definition of generally faster, then: there is an i such that a is faster than b for all n > i. We now need to prove that b is not generally faster than a, that is that there is no i2 such that b is faster than a for ...
PPT - UBC Department of CPSC Undergraduates
... WLOG, let a and b be algorithms. Assume a is generally faster than b. Based on the definition of generally faster, then: there is an i such that a is faster than b for all n > i. We now need to prove that b is not generally faster than a, that is that there is no i2 such that b is faster than a for ...
... WLOG, let a and b be algorithms. Assume a is generally faster than b. Based on the definition of generally faster, then: there is an i such that a is faster than b for all n > i. We now need to prove that b is not generally faster than a, that is that there is no i2 such that b is faster than a for ...
preprint - Open Science Framework
... CS1: If n is in the past, the subject inspects its perfect memory; if n is in the future, it can postpone its decision for the finite number of stages required and then check again. CS2: This just makes the presence of perfect memory explicit. When Brouwer made his first remark about the ideal mathe ...
... CS1: If n is in the past, the subject inspects its perfect memory; if n is in the future, it can postpone its decision for the finite number of stages required and then check again. CS2: This just makes the presence of perfect memory explicit. When Brouwer made his first remark about the ideal mathe ...
Logic for Gottlob Frege and Bertrand Russell:
... is necessary for the combinations of truth-value assignments to q’s component propositions displayed in t to be just the possible ones). 5. If presupposition p is a proposition, then truth-table t is a proof that q has the modal status displayed in t only if p is also shown to be true. 6. This raise ...
... is necessary for the combinations of truth-value assignments to q’s component propositions displayed in t to be just the possible ones). 5. If presupposition p is a proposition, then truth-table t is a proof that q has the modal status displayed in t only if p is also shown to be true. 6. This raise ...
A Yabloesque paradox in epistemic game theory
... Based on this framework, it was shown that not every configuration of beliefs and assumptions are representable in belief models, such as the BK paradox (Branden- ...
... Based on this framework, it was shown that not every configuration of beliefs and assumptions are representable in belief models, such as the BK paradox (Branden- ...
An introduction to ampleness
... (C2): If A ≤ M is finite and A ≤ B ∈ C0 , then there is an embedding f : B → M with f (B) ≤ M and which is the identity on A. Moreover M is uniquely determined up to isomorphism by these two properties and is ≤homogeneous (meaning: any isomorphism between finite self-sufficient substructures of M ex ...
... (C2): If A ≤ M is finite and A ≤ B ∈ C0 , then there is an embedding f : B → M with f (B) ≤ M and which is the identity on A. Moreover M is uniquely determined up to isomorphism by these two properties and is ≤homogeneous (meaning: any isomorphism between finite self-sufficient substructures of M ex ...
PPT - UBC Department of CPSC Undergraduates
... Aliens hold the Earth hostage and demand that we help them get started proving: x D, y E, z F, P(x) Q(y) R(x,z). Problem: Propose four different, promising solution strategies that are each as complete as possible (given the available information) and could be used to address this theor ...
... Aliens hold the Earth hostage and demand that we help them get started proving: x D, y E, z F, P(x) Q(y) R(x,z). Problem: Propose four different, promising solution strategies that are each as complete as possible (given the available information) and could be used to address this theor ...
Document
... the paper, we show that a supersimple ω-categorical structure which is CM-trivial is of finite SU-rank. More precisely, we show that a finitely based CM-trivial regular type in a simple ω-categorical theory is non-orthogonal to a type of SU-rank 1. We shall assume familiarity with the basic notions ...
... the paper, we show that a supersimple ω-categorical structure which is CM-trivial is of finite SU-rank. More precisely, we show that a finitely based CM-trivial regular type in a simple ω-categorical theory is non-orthogonal to a type of SU-rank 1. We shall assume familiarity with the basic notions ...
1. Proof Techniques
... We begin our study of proofs by recalling the following notations: R: the set of all real numbers Z: the set of all integers Q: the set of all rational numbers ...
... We begin our study of proofs by recalling the following notations: R: the set of all real numbers Z: the set of all integers Q: the set of all rational numbers ...
Chapter 5 - Stanford Lagunita
... that a sentence Q is a logical truth, then you may assert Q at any point in your proof. We already saw this principle at work in Chapter 2, when we discussed the reflexivity of identity, the principle that allowed us to assert a sentence of the form a = a at any point in a proof. It also allows us t ...
... that a sentence Q is a logical truth, then you may assert Q at any point in your proof. We already saw this principle at work in Chapter 2, when we discussed the reflexivity of identity, the principle that allowed us to assert a sentence of the form a = a at any point in a proof. It also allows us t ...
Chapter 2, Logic
... are P, so that ‘No animals are unicorns’ entails ‘No unicorns are animals. If we allow that to entail ‘some unicorns are not animals‘ we should be committed to the existence of unicorns at the same time we assert that there are none. The matter is more easily discussed with the help of modern logica ...
... are P, so that ‘No animals are unicorns’ entails ‘No unicorns are animals. If we allow that to entail ‘some unicorns are not animals‘ we should be committed to the existence of unicorns at the same time we assert that there are none. The matter is more easily discussed with the help of modern logica ...
POSSIBLE WORLDS SEMANTICS AND THE LIAR Reflections on a
... Now, Kaplan’s argument shows that the principle of plenitude is incompatible with assumptions commonly made in possible worlds semantics. Here is how the argument goes: (i) There is a set W of possible worlds and a set P rop of propositions. (ii) There is, for every subset X of W , a corresponding p ...
... Now, Kaplan’s argument shows that the principle of plenitude is incompatible with assumptions commonly made in possible worlds semantics. Here is how the argument goes: (i) There is a set W of possible worlds and a set P rop of propositions. (ii) There is, for every subset X of W , a corresponding p ...
Infinity 1. Introduction
... On the other side, Brouwer’s philosophy of intuitionism, and other schools of constructivism, view actual infinity with suspicion and attempt to found mathematics solely on potential infinity; they would regard this as in the spirit of best mathematical practice. Their views will be discussed in §3. ...
... On the other side, Brouwer’s philosophy of intuitionism, and other schools of constructivism, view actual infinity with suspicion and attempt to found mathematics solely on potential infinity; they would regard this as in the spirit of best mathematical practice. Their views will be discussed in §3. ...
Logical fallacy
... beautiful women, draped across the dashing red sports car... there is no logical connection between the two, but the advertiser would like to imply a premise that there is. If the advertiser came out and said "Buy this car and you will have more sexual satisfaction" it might be easier to reject as a ...
... beautiful women, draped across the dashing red sports car... there is no logical connection between the two, but the advertiser would like to imply a premise that there is. If the advertiser came out and said "Buy this car and you will have more sexual satisfaction" it might be easier to reject as a ...
Basic Proof Techniques
... Theorem 5. Let a,b,c,d be integers. If a > c and b > c, then M AX(a, b) − c is always positive. Proof. Assume that a > c and b > c. We know that a > c and b > c, but we cannot say for certain if a > b or b > a. Therefore we proceed by cases. 1. Case 1: Assume that a > b. Because a > b we know that ...
... Theorem 5. Let a,b,c,d be integers. If a > c and b > c, then M AX(a, b) − c is always positive. Proof. Assume that a > c and b > c. We know that a > c and b > c, but we cannot say for certain if a > b or b > a. Therefore we proceed by cases. 1. Case 1: Assume that a > b. Because a > b we know that ...
Weak MSO+U over infinite trees
... a subtree with b-factors of unbounded size. It follows that all the nodes with label a form a connected set, call it X, which contains the root. There must be b-factors of unbounded size below every node from X, however every such b-factor must be finite, and have bounded size b-factors in its subtr ...
... a subtree with b-factors of unbounded size. It follows that all the nodes with label a form a connected set, call it X, which contains the root. There must be b-factors of unbounded size below every node from X, however every such b-factor must be finite, and have bounded size b-factors in its subtr ...
a. p
... Valid and Invalid Arguments Testing an Argument Form for Validity 1. Identify the premises and conclusion of the argument form. 2. Construct a truth table 3. Look at the row when all the premises are true. If the conclusion is true, it is a valid argument. Otherwise it is invalid ...
... Valid and Invalid Arguments Testing an Argument Form for Validity 1. Identify the premises and conclusion of the argument form. 2. Construct a truth table 3. Look at the row when all the premises are true. If the conclusion is true, it is a valid argument. Otherwise it is invalid ...