Statement
... A statement is a substitution instance of a statement form if it can be obtained by substituting statements into the statement variables of the form. The statement "Roses are red or violets are blue" is a substitution instance of the statement form "p or q", because it can be obtained by substitutin ...
... A statement is a substitution instance of a statement form if it can be obtained by substituting statements into the statement variables of the form. The statement "Roses are red or violets are blue" is a substitution instance of the statement form "p or q", because it can be obtained by substitutin ...
4 slides/page
... • epistemic logic: for reasoning about knowledge The simplest logic (on which all the rest are based) is propositional logic. It is intended to capture features of arguments such as the following: Borogroves are mimsy whenever it is brillig. It is now brillig and this thing is a borogrove. Hence thi ...
... • epistemic logic: for reasoning about knowledge The simplest logic (on which all the rest are based) is propositional logic. It is intended to capture features of arguments such as the following: Borogroves are mimsy whenever it is brillig. It is now brillig and this thing is a borogrove. Hence thi ...
Rules of inference
... “It is below freezing now (p). Therefore, it is either below freezing or raining now (q).” “It is below freezing (p). It is raining now (q). Therefore, it is below freezing and it is raining now. “if it rains today (p), then we will not have a barbecue today (q). if we do not have a barbecue t ...
... “It is below freezing now (p). Therefore, it is either below freezing or raining now (q).” “It is below freezing (p). It is raining now (q). Therefore, it is below freezing and it is raining now. “if it rains today (p), then we will not have a barbecue today (q). if we do not have a barbecue t ...
Logic
... Logic is about how to deduce, on mere form, a valid argument. Valid is a semantic concept. Deduction is a syntactic concept. ...
... Logic is about how to deduce, on mere form, a valid argument. Valid is a semantic concept. Deduction is a syntactic concept. ...
A mathematical sentence is a sentence that states a fact or contains
... 1. Given the true statement: “If a person is eligible to vote, then that person is a citizen.” Which statement must also be true? (1) Kayla is not a citizen; therefore, she is not eligible to vote. (2) Juan is a citizen; therefore, he is eligible to vote. (3) Marie is not eligible to vote; therefore ...
... 1. Given the true statement: “If a person is eligible to vote, then that person is a citizen.” Which statement must also be true? (1) Kayla is not a citizen; therefore, she is not eligible to vote. (2) Juan is a citizen; therefore, he is eligible to vote. (3) Marie is not eligible to vote; therefore ...
EVALUATING INDUCTIVE ARGUMENTS
... selection that is thought to be random such that each member of the population from which it has been chosen has an equal chance of being ...
... selection that is thought to be random such that each member of the population from which it has been chosen has an equal chance of being ...
Chapter 2 Notes Niven – RHS Fall 12-13
... If you want to show that a conjecture is false (or disprove the conjecture) you only need to show ONE example where the conjecture does not work. That example proving a conjecture false is called a counterexample. A counter example is a specific case for which the conjecture is false. To show that a ...
... If you want to show that a conjecture is false (or disprove the conjecture) you only need to show ONE example where the conjecture does not work. That example proving a conjecture false is called a counterexample. A counter example is a specific case for which the conjecture is false. To show that a ...
Logic - Disclaimer
... possible way for all premises to be true and the conclusion false all at the same time. • Showing a scenario in which all premises are true, and in which the conclusion is true as well, does not demonstrate validity, b/c there may still be a different scenario in which all premises are true and the ...
... possible way for all premises to be true and the conclusion false all at the same time. • Showing a scenario in which all premises are true, and in which the conclusion is true as well, does not demonstrate validity, b/c there may still be a different scenario in which all premises are true and the ...
Logic
... possible way for all premises to be true and the conclusion false all at the same time. • Showing a scenario in which all premises are true, and in which the conclusion is true as well, does not demonstrate validity, b/c there may still be a different scenario in which all premises are true and the ...
... possible way for all premises to be true and the conclusion false all at the same time. • Showing a scenario in which all premises are true, and in which the conclusion is true as well, does not demonstrate validity, b/c there may still be a different scenario in which all premises are true and the ...
PHIL 160: Introduction to Philosophy of Science
... PHIL 160 What is the kind of evidence that supports scientific hypotheses and/or theories? How strong is that evidence? Suppose a theory includes objects (such as quarks) or historical events/processes (such as geological or evolutionary events/processes) that are not directly observable? What kind ...
... PHIL 160 What is the kind of evidence that supports scientific hypotheses and/or theories? How strong is that evidence? Suppose a theory includes objects (such as quarks) or historical events/processes (such as geological or evolutionary events/processes) that are not directly observable? What kind ...
Chapter 5: Methods of Proof for Boolean Logic
... The general proof strategy looks like this: if you have a disjunction, then you know that at least one of the disjuncts is true—you just don’t know which one. So you consider the individual “cases” (i.e., disjuncts), one at a time. You assume the first disjunct, and then derive your conclusion from ...
... The general proof strategy looks like this: if you have a disjunction, then you know that at least one of the disjuncts is true—you just don’t know which one. So you consider the individual “cases” (i.e., disjuncts), one at a time. You assume the first disjunct, and then derive your conclusion from ...
Propositional Logic
... The validity of an argument do not depend on the truth of the premises but with the fact that if someone accepts the truth of the premises he/she must accept the conclusion. If someone does not accept the premises, he/she wont accept the conclusions but this does not invalidate the argument. ...
... The validity of an argument do not depend on the truth of the premises but with the fact that if someone accepts the truth of the premises he/she must accept the conclusion. If someone does not accept the premises, he/she wont accept the conclusions but this does not invalidate the argument. ...
Abstract for ‘Consequentialism’ 1 Inferentialism vs referentialism David Ripley
... validities suffice for others, that grounds the meaning of the conditional, on such a view; which inferences are legitimate, and what the truth conditions are, are both downstream. While the label is new, views of this sort are not. Consequentialism, in this sense, is adopted by [Restall, 2009] and ...
... validities suffice for others, that grounds the meaning of the conditional, on such a view; which inferences are legitimate, and what the truth conditions are, are both downstream. While the label is new, views of this sort are not. Consequentialism, in this sense, is adopted by [Restall, 2009] and ...
Chapter 12 Reasoning, Logic, and Fallacies
... then show that the sample size is too small. Note: a formal proof would require a mathematical calculation. This is the subject of probability theory. For now, you must rely on common sense. • References: Barker: 189, Cedarblom and Paulsen: 372, Davis: 103 26 May 1995 ...
... then show that the sample size is too small. Note: a formal proof would require a mathematical calculation. This is the subject of probability theory. For now, you must rely on common sense. • References: Barker: 189, Cedarblom and Paulsen: 372, Davis: 103 26 May 1995 ...
Basic Concepts of Formal Logic
... linguistic properties. Logic is not concerned with the mental processes that take place in our mind when we are actually thinking. Nor is logic concerned with the linguistic properties of different languages and the ways in which words come to acquire their significance in particular linguistic comm ...
... linguistic properties. Logic is not concerned with the mental processes that take place in our mind when we are actually thinking. Nor is logic concerned with the linguistic properties of different languages and the ways in which words come to acquire their significance in particular linguistic comm ...
Methods of Proof for Boolean Logic
... Proof of Q by contradiction: assume Q and derive a contradiction. ...
... Proof of Q by contradiction: assume Q and derive a contradiction. ...
Methods of Proof for Boolean Logic
... Proof of Q by contradiction: assume Q and derive a contradiction. ...
... Proof of Q by contradiction: assume Q and derive a contradiction. ...
Propositional Logic Proof
... By the end of this unit, you should be able to: – Explore the consequences of a set of propositional logic statements by application of equivalence and inference rules, especially in order to massage statements into a desired form. Note: in this learning goal, we are not asking you to memorize the i ...
... By the end of this unit, you should be able to: – Explore the consequences of a set of propositional logic statements by application of equivalence and inference rules, especially in order to massage statements into a desired form. Note: in this learning goal, we are not asking you to memorize the i ...
Lecture slides
... To say that an argument form is valid means that if the substituted statements result in valid premises, then the conclusion is also true. Here the two premises are: If p then q p The truth of the conclusion is said to be inferred from or deduced from the truth of the premises. If statements substit ...
... To say that an argument form is valid means that if the substituted statements result in valid premises, then the conclusion is also true. Here the two premises are: If p then q p The truth of the conclusion is said to be inferred from or deduced from the truth of the premises. If statements substit ...
PPTX
... • By the end of this module, you should be able to • Determine whether or not a propositional logic proof is valid, and explain why it is valid or invalid. • Explore the consequences of a set of propositional logic statements by application of equivalence and inference rules, especially in order to ...
... • By the end of this module, you should be able to • Determine whether or not a propositional logic proof is valid, and explain why it is valid or invalid. • Explore the consequences of a set of propositional logic statements by application of equivalence and inference rules, especially in order to ...
Module 4: Propositional Logic Proofs
... that I can transform this premise using rules of inference or logical equivalence laws? • If p ^ q is true, what do I know about p and q? • If p v q is true and q is false, what do I know about ...
... that I can transform this premise using rules of inference or logical equivalence laws? • If p ^ q is true, what do I know about p and q? • If p v q is true and q is false, what do I know about ...
Logic Review
... Premise: Either Fred took the train or he took the ferry. Premise 2: Fred did not take the ferry. Conclusion: Fred took the train. Premise: Either A or B. Premise: not B Conclusion: A ...
... Premise: Either Fred took the train or he took the ferry. Premise 2: Fred did not take the ferry. Conclusion: Fred took the train. Premise: Either A or B. Premise: not B Conclusion: A ...
Philosophy 120 Symbolic Logic I H. Hamner Hill
... • Gödel showed that a formal system must be either incomplete—there are true claims for which you can’t construct a proof—or inconsistent—you can prove both a claim and its negation! • Since we know that anything follows from a contradiction (if you don’t believe it, test the claim with a truth tabl ...
... • Gödel showed that a formal system must be either incomplete—there are true claims for which you can’t construct a proof—or inconsistent—you can prove both a claim and its negation! • Since we know that anything follows from a contradiction (if you don’t believe it, test the claim with a truth tabl ...
coppin chapter 07e
... A is possibly true, which is written: ◊A If A is non-contingent, then it is necessarily true, which is written: A ...
... A is possibly true, which is written: ◊A If A is non-contingent, then it is necessarily true, which is written: A ...