It is relatively straightforward to prove an argument to be invalid. It ishard to prove one valid,and that will certainly be the thrust of a lot of of the rest of the course.But, that comes later on. For now, luckily, we"re finding out a simplemeans to demonstrate invalidity--the counterexample approach.This is advantageous bereason if you deserve to prove a particular argument tobe invalid you can overlook it and also do not need to issue aboutchecking whether it"s premises are true or not, which deserve to be difficult.
To usage the counterexample strategy it is vital to be able toabstract the formfrom the content of a offered dispute. That done, you thensubstitute back into the argument a different, basic, familiarcontent. Your goal in doing this will certainly be to try to pressure thedebate right into having all clearly true premises, however a falseconclusion. If it is feasible to execute this to an discussion, thedispute is obviously invalid. (If the "obviously" inthe former sentence appears misinserted to you, testimonial the definitionof validity in lesboy # 4) If you cannot substitute words thatgive true premises and false conclusion it does not necessarilymean that the debate is valid. The debate may be validor you may simply have actually fairesulted in prove it invalid.
We extract the create by making use of funding letters to symbolizeterms in the statements. (Capital letters are nothing more than aconvenient convention. Any symbol would certainly perform too.) One letterstands for each term.
You are watching: The counterexample method shows that an argument is invalid by _______
A term is a simple component of a statement.
e.g. All hamsters are furry pets.
Tright here are two terms in this statement, hamsters and also furry animals. Terms deserve to be much longer phrases such as "people who like to eat pasta"
Each term can be reinserted by a solitary capital letter. Once again, widespread sense will assist you out here.
e.g. All H are
Be regular. If a particular letter stands for a details term in one part of an debate, it have to stand for that exact same term throughout the debate.
To prove invalidity of a deductive dispute you can firstabstract the form from the content of a provided debate
1. Abstract the form from the content, listing the premises first and the conclusion last.
2. Beside the abstracted discussion, erected the skeleton of the argument, noting that premises need to be true and also the conclusion false.
3. With a pencil, attempt substituting terms into the skeleton that cause all true premises and a false conclusion.
4. Be certain your substitution instances are continual in between the 2 disagreements, i.e. if the letter "C" is replaced by the new term "mammals" in one component of the discussion, it should carry out so all over.
All hamsters are furry pets.
All hamsters are creatures who favor to eat carrots.
All furry pets are creatures who like to eat carrots.
All H are F. TAll dogs are animals.
All H are C. TAll dogs are mammals.
All F are C. FAll animals are mammals.
Also note that "some" indicates "at leastone" so "some dogs are animals" is true. It islikewise true that "all dogs are animals" and if allare then definitely some are also. Tbelow is a tendencyto think that "some dogs are animals" suggests that"some dogs are not animals" and also then assume that bothstatements are false. This is not the instance. In logic, as abasic ascendancy, do not infer any even more than what is provided.
****You will certainly just be asked to have the ability to offer counterexamplesto categoricalsyllogisms (made up of "all," "some,""no" statements) so you deserve to disregard the parts of yourreading wright here Hurley explains around substituting right into conditional statements.******
LOGIC COACH ASSIGNMENT: 1.5 I 1-6. Keep in mind that the program takes youwith a number of steps, one display screen at a time, and also you have to perform each action correctlyto relocate on. It likewise constantly assigns the letters S, P, M, in the create phase ratherthan letters that correspond to the terms, as the message tells you to. Tright here is amethod to this madness that you"ll learn later. Just bear via the routine forcurrently.
ASSIGNMENT: (20 points each)
Construct counterexamples to each of the following disagreements to prove that they areinvalid. I suggestthat you use terms from the adhering to list: cats, dogs, fish,mammals, pets, bereason everyone agrees about them. (Understandthat a fish is not a mammal, but it is an animal; cats and dogsare both mammals and pets.) But, if you want to be creativeand also usage your own words store in mind the sentences you constructshould be clearly true or false, otherwise you haven"tcompleted anything. Be consistent through your terms. Sjust how yourintermediate steps.*Be mindful in determining which statement isthe conclusion. Use indicator words as aguide (Hurley p. 3). Picking the wrong statement as a conclusionwill certainly cause the entire problem to be wrong!
1. No Coptics are Shinto. No Shinto are Hasidic. It complies with that no Hasidim are Coptics.
2. No corporate directors are investigators because all auditors are investigators and no auditors are corpoprice directors.
3. No airline flights that enable cigarette smoking are flights that are safe for nonsmokers. Because of this, some airline fights that allow smoking cigarettes are not international flights, considering that some flights that are safe for nonsmokers are not global flights.
4. All college professors are teachers, so all teachers are educators, given that all college professors are educators.
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5. Some persons that regret their crimes are convicted murderers. So some convicted murders are persons capable of being reformed, considering that all persons capable of being recreated are persons that regret their crimes.