What Does Logic Study? What Is The Difference Between An Arg

What Does Logic Study2 What Is The Difference Between An Argumen

1. What does Logic study? 2. What is the difference between an argument and a non-argument? 3. What is so special about statements, in contrast to other kinds of expressions? 4. Describe the standard of truth on which both categorical and propositional logic rest. 5. What is a category? 6. Name the two main branches of logic. 7. Describe the fundamental principle of each branch of logic. 8. Give an example of an argument that is deductive, and one that is inductive. 9. Define the concept of 'validity.' What kinds of arguments are valid or invalid? 10. Define the concept of 'strength.' What kinds of arguments are either strong or weak? 11. Define 'Soundness' and 'Cogency.' 12. Why is it possible to have a valid argument with false premises? 13. List the four standard form categorical propositions. 14. Draw the Venn Diagrams for each of the four standard form categorical propositions. 15. Here are two categorical propositions. A: No A are B O: Some A are not B. On the Aristotelian standpoint, are these two propositions consistent? On the Boolean standpoint, are these two propositions consistent? 16. Here is a statement in Propositional Logic. Construct a truth table to show all the possible truth values this statement can have. If (A or not B) then B. (Remember to write this out using the symbolism for the logical connectors because I am unable to do it here.) 17. Here is an argument in Propositional Logic. Construct a truth table to test for validity. If juvenile killers are as responsible for their crimes as adults, then execution is a justifiable punishment. Juvenile killers are not as responsible for their crimes as adults. Therefore execution is not a justifiable punishment. Symbolize the argument on a single line, and construct the truth table. (Note, it should be symbolized like this, but with the connector symbols: If J then E/ not J // not E. 18. Suppose you have a statement in Propositional Logic where all of the truth values under the main operator are true, what kind of statement is it? 19. Suppose you have a statement in Propositional Logic where all the truth values under the main operator are false, then what kind of statement is it? 20. Suppose you have a statement where all the truth values under the main operator are a mix of Ts and Fs, what kind of statement is it? 21. Suppose you have two statements to compare, and they have the same truth value on every line, then what is their relation? 22. Suppose you have two statements and they have opposite truth values on every line. What is their relation? 23. Here is an argument in Propositional Logic. Use the Indirect Proof method of truth table to test for validity. Remember to make an initial assumption. If not A then (B or C) / not B // If C then A. (Again, remember to write this argument out using the symbols for the logical connectors.)

Paper For Above instruction

Logic is a fundamental branch of philosophy that investigates the nature of reasoning, the principles governing valid inference, and the structure of propositions. It plays a pivotal role in disciplines ranging from mathematics and computer science to linguistics and cognitive science. At its core, logic seeks to understand how conclusions can be derived from premises, ensuring that reasoning processes are coherent and reliable.

Understanding what logic studies involves examining its primary focus on the principles of valid reasoning. Logic is concerned with the structure of arguments and the criteria that distinguish sound reasoning from fallacious thought. Its central aim is to develop formal systems that accurately represent reasoning patterns, allowing for systematic analysis and evaluation of arguments.

The distinction between an argument and a non-argument is fundamental in logical analysis. An argument consists of a set of premises intended to support or imply a conclusion, whereas a non-argument lacks this inferential structure and does not aim to establish a conclusion. Recognizing this difference is crucial for analyzing everyday reasoning and formal proofs alike.

Statements are unique in logic because they assert or deny something that can be true or false. Unlike other expressions such as commands or questions, statements have a truth value, providing a basis for logical evaluation. This characteristic of statements allows logicians to analyze their truth values systematically and form the foundation for various logical systems.

Both categorical and propositional logic rest on a standard of truth grounded in classical bivalence, where every statement is either true or false, with no third option. This standard enables the formal analysis of argument validity and logical consequence, ensuring that logical systems are consistent and reliable.

A category, in logic, refers to a class or set of objects sharing specific properties. Categories serve as the fundamental building blocks of categorical propositions and facilitate the organization of concepts and their relationships in logical analyses.

The two main branches of logic are categorical logic and propositional logic. Categorical logic studies relationships between categories or classes, focusing on the nature of inclusion, exclusion, and intersection among sets. Its fundamental principle is that categorical propositions express the relationships between classes. Propositional logic, on the other hand, deals with the logical relationships among entire propositions, emphasizing connectives and logical operators to form complex statements based on simpler ones.

An example of a deductive argument is the syllogism: All humans are mortal. Socrates is a human. Therefore, Socrates is mortal. An inductive argument might be: The sun has risen every morning in recorded history, so it will likely rise tomorrow. Deductive arguments aim for certainty, while inductive arguments rely on probability and evidence.

Validity in logic refers to an argument where, if the premises are true, the conclusion must necessarily be true. Valid arguments cannot have true premises and a false conclusion simultaneously. Invalid arguments are those where the truth of the premises does not guarantee the truth of the conclusion.

Strength pertains to inductive reasoning, indicating how convincing an argument is based on evidence. A strong argument makes the conclusion highly probable given the premises, whereas a weak argument leaves the conclusion uncertain or unlikely.

Soundness combines validity with the truth of premises, meaning a sound argument is both valid and has all true premises. Cogency applies to inductive arguments, meaning an argument is cogent if it is strong and its premises are true, making the conclusion highly probable.

It is possible to have a valid argument with false premises because validity concerns the structure of the argument, not the truth of its premises. An argument can follow a correct logical form but still be invalid if its premises are false and the form is not logically sound.

The four standard form categorical propositions are: All A are B, No A are B, Some A are B, and Some A are not B. These propositions form the basis of classical categorical logic and are used to analyze relationships among classes.

Venn diagrams visually represent categorical propositions, illustrating the inclusion, exclusion, or intersection of classes. For "All A are B," the diagram shows A completely within B. For "No A are B," the classes A and B are disjoint. For "Some A are B," there is an overlapping region, indicating some members share properties. For "Some A are not B," part of A lies outside B.

Regarding consistency, the propositions "No A are B" and "Some A are not B" are inconsistent under Aristotle's logic because one asserts total exclusion while the other asserts at least some members are outside B. Under Boolean logic, their consistency depends on whether we interpret the propositions as compatible, but generally, they are considered inconsistent in classical logic as well owing to their conflicting claims about class relationships.

The propositional logic statement "If (A or not B) then B" can be analyzed using truth tables by listing all possible truth values for A and B, calculating the truth values of the subformulas, and determining the overall truth value of the conditional statement under each scenario. This analysis aids in understanding the logical validity of such implications.

To evaluate the argument about juvenile killers and justice, the argument's validity can be tested by symbolizing it, for example: If J then E / not J // not E, and constructing a truth table. If, in all cases where the premises are true, the conclusion is also true, the argument is valid. Otherwise, it is invalid.

When all truth values under the main operator of a statement are true across all valuations, the statement is considered a tautology, demonstrating logical necessity. Conversely, if all are false, the statement is a contradiction, demonstrating logical impossibility. A statement with a mixture of truth values is a contingency, not necessarily true or false under all interpretations.

Two statements with identical truth values on every line are logical equivalents. There is a perfect correlation between their truth values, making them interchangeable in logical arguments. Conversely, statements with opposite truth values on every line are called logical negations, indicating they are mutually exclusive and cannot be true simultaneously.

The indirect proof method involves assuming the negation of the conclusion and demonstrating that this leads to a contradiction with the premises using truth tables. For example, for the argument "If not A then (B or C) / not B // If C then A," symbolizing with logical connectors and systematically testing the assumptions helps identify whether the argument is valid or invalid.

References

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