Is this a proper argument by reductio ad absurdum?

Question

For a logic paper, I have to evaluate two letters that deal with a Senate Bill allowing the regulation of dogs. The first letter provides an argument by analogy to the conclusion that dogs should be restricted to their owners' homes, so I tried to come up with a reductio ad absurdum argument against it. Furthermore, I attempted to capture the results of the reductio argument in the form of a dilemma. So my question is, Does my reductio and dilemma work?

Here are the arguments:

The detractor accepts the proposition that dogs and smokers are analogous, but assume for the sake of argument the contradiction of this proposition.

(1) Dogs and smokers are analogous.

(2) If dogs and smokers are analogous, then dogs ought to be restricted to their homes.

So

(4) Dogs ought to be restricted to their owners’ homes.

(5) If dogs ought to be restricted to their homes, then smokers ought to be restricted to their homes.

So

(6) Smokers ought to be restricted to their homes.

However

(7) Smokers ought not to be restricted to their homes.

So

(8) Dogs and smokers are not analogous.

From this follows the dilemma:

(1) Either dogs and smokers are analogous or dogs and smokers are not analogous.

(2) If dogs and smokers are analogous, then smokers ought to be restrained to their homes.

(3) If dogs and smokers are not analogous, then letter one’s argument by analogy fails.

So

(4) Either smokers ought to be restrained to their homes or letter one’s argument by analogy fails.

Answer 1

Step two of your argument is nonsensical. Your error is that you--or the detractor--never specify how dogs and smokers are similar at all.



Your argument does not follow. This one is somewhat better, but has flaws as well. I don't know enough information about the proposed law to make a sound argument.



1. Dogs must be kept to their homes by law.



2. Dogs must receive veterinary treatment by law.



3. It is impractical/impossible for veterinarians to do house calls for all dogs .



4. Dogs must therefore leave their homes to receive veterinary treatment required by law.



5. Dogs cannot legally leave their homes to receive veterinary treatment required by law.



6. Reductio ad absurdum.

Answer 2

Nice. You've made progress. You've shown that you understand both a dilemma and reducio.



Now for some fine tuning. If the original analogy equates dogs and smokers (not smoking) then your reducio does succeed in raising the dilemma, since you must accept the premise of the original argument, warts and all, in order to demonstrate the contradiction.. You can safely ignore the equivocation.



If the original analogy equated dogs with smokING then your argument has equivocated the activity of smoking with the person who engages in the activity.



for example, we restrict many activities to different locations, but the people who participate in the activity are free to leave when not engaged in the activity.



good job!



BTW, if the other two answerers would look up what a reducio argument is they would see how silly their answers are. the asker understands what he is doing here.



Formally the above argument is this:



(1) & (4) are assumed to be true. this is what the original argument holds



if (1) then (4)

(1) therefore (4) Modes Ponens



if (4) then (6)

(4) therefore (6) Modes Ponens



By normal social agreement (not 6)



Therefore (6 & not 6) the argument has been reduced to a contradiction (absurdity)

Hence the argument is false.

This is a reducio argument. Assume the conclusion and draw out a contradiction to prove the opposite of that which is assumed

Answer 3

You didn't specifically give us the provisions of the second letter, only those of the first letter.



The line of reasoning you have just given us is not so much an example of "reductio ad absurdum," (reduced to an absurd level) as it is an example of sylllogistic reasoning. That is a type of reasoning that presents a thesis, an antithesis, then a synthesis; (A conclusion based on the two prior parts.)



There is little that is analogous in your two scenarios, because putting house restriction on a dog and a human are two entirely different things. The average human smoker has to go to work, go shopping, go to medical appointments, etc. So, putting all smokers on house restriction would have a disastrous affect on the lives of most of them. A dog has to do none of those things, so most of them could easily endure a house restriction. I once had a boss with a very narrow, closed mind who took everything said quite literally. One day as I came into the office with some fellow employees, I was lighting a cigarette as the boss was approaching. (That was legal back then.) There was a fire alarm on the wall between us that said "In case of fire, break glass." He didn't say anything to me as we passed. Later on, talking with my friends, I said "I'm surprised he didn't break the glass in the fire alarm; after all, I did have fire in my hand." That is an example of reductio.ad absurdum.