“For my dog has three legs” is a strange construction (and a fragment). It threw me for a second. #9 is similarly odd and punctuated strangely as well. It feels archaic. I could see that confusing someone.
Number nine seemed kind of iffy to me. I’d go with the first sentence but the second one seems like a conclusion, too. I guess putting the “for you see” part makes it less conclusiony?
I agree with what others have said. I had no idea what the quiz was expecting me to do, and had to read through the thread to find out.
I always pick the longest one and I’m right … again.
For those who weren’t sure what the instructions were asking you to do, that’s not the problem in the class because we’ve been running through example after example just like these in class. And on the quiz itself, the answers are presented in multiple choice format.
For those who think “For my dog has three legs” is a sentence fragment its just… not. Nor is it an incomplete sentence. You guys probably also think you should never begin a sentence with “but” or “and”. 
“For you see” indicates that the “author” is about to give you reasons to think that what came before is true. He’s about to give evidence, or to give considerations meant to convince you that the first sentence is true. That makes the first sentence the conclusion.
Number five looks a bit tricky to me.
5. For every dog that has three legs, there are a thousand dogs that have four legs. This is because three-leggedness is very unusual.
I think that the way this is set up, sentence one is the conclusion. But it’s an incorrect conclusion - it’s not actually true that we know that “for every three-legged dog there are a thousand four-legged ones because three-leggedness is unusual”.
I know that question four has primed us for the logic of the conclusion-stater to be bad. But the logic of question five is bad in a different way - the speaker has actually made a mistake about what a conclusion actually is, and how it differs from data. Question four, they’ve just drawn a silly conclusion.
That one rather threw me.
To be clear, I’d typically (but not always) avoid sentences beginning with the word “for.” But in this case I had a few reasons to use it. Chief among them is that I wanted each example to consist of exactly two sentences so that I wouldn’t need to include confusing phraseology about “clauses” and such in the instructions. Yet “for” is an important term to learn to notice when it comes to this exercise, so I couldn’t forego its use altogether. Moreover use of “for” as… whatchamacallit… a sentential coordinator?.. is pretty standard in most forms of writing (less so in Academic writing but you’ll find it even there) so nothing was blocking my use of it.
Yeah, I can see how that one could be tricky in a way. It also has a deceptive keyword. (“For.”)
FWIW I’ve been emphasizing in class the fact that for these kinds of exercises, we’re not evaluating the inference, we’re simply characterizing it.
‘For’ introduces a subordinating clause, and it’s very unusual to see a subordinating clause as a sentence on its own. (‘And’ and ‘but’ are different - they introduce coordinating clauses).
It’s not at all unusual; I see it all the time, in respectable venues. I don’t know how to cite this… Is there a way to search through Google Books for the string “. For”? Just typing in that string doesn’t seem to do the trick…
The “From each of the following inferences” bit throws me, since all the examples don’t seem to include inferences.
But it’s not an inference. Presumably the author has had pizza, and is declaring its awsomeness based on personal experience. Maybe the cheese is why he finds it awesome, but he’s not just saying “Pizza has cheese on it? It must be awesome then.”
In #5, too, is one of those sentences supposed to be an inference? The first sentence would be an awfully specific inference to make based on “three-leggedness is very unusual”.
But he didn`t say he tried pizza and liked the cheese based on personal experience. He is saying it’s awesome because it has cheese on it.
In the sense of “inference” we’re using in the class (admittedly a quasi-technical sense) each pair of sentences on the quiz is an inference. An inference is, so to speak, a single act of reasoning. By this I mean it’s an assertion of a conclusion on the basis of one or more premises. In each of the examples in the quiz, one sentence is most plausibly read as containing a conclusion, the other most plausibly read as containing a premise intended to support that conclusion.
In the pizza/cheese example, the speaker asserts that pizza is awesome based on the fact that it has cheese on it and cheese is alwayz good. Hence it’s an inference.
Same goes for the three-legged/four-legged example. The speaker asserts that there are a thousand 4leg dogs for every 3leg dog, and the evidence he gives for this is the fact that 3leggedness is unusual. The first is asserted on the basis of the second. Hence, an inference. The first is the conclusion, the second the premise.
That may clear it up, but for the sake of my curiosity, can you tell me what you thought an inference was?
Even if it was based on personal experience (and really, almost everything is isn’t it?) it would still be an inference.
An inference is the assertion of one sentence with a rational basis (not necessarily a good rational basis) to be found in another asserted sentence. No, I don’t put it that way to my class. 
The good news is after spending 3 hours on it, having them do practice and real quizzes online over the week, and spending another 3 hours on it today, the students seem to be catching on with some reliability. Visibly improved results are appearing in quizzes and in anonymously administered pop-quizzes. So yay.
You’re inferring the later is true, but it’s not the only interpretation, and not really a reasonable one. If someone said “pizza is awesome” to me, I would interpret it as their opinion. The second sentence is just offering an explanation, as if someone had asked “Why is pizza awesome?”
Are you really interpretting “pizza is awesome” as an inference? That the person saying that doesn’t know or have that opinion, he’s just inferring if from the presence of cheese?
On preview:
I’m going to have to look this up. That’s not what I would have understood “inference” to mean.
I disagree on #5.
It is more natural to read the second sentence as the conclusion, if either sentence must be one.
First note that the second sentence says absolutely nothing about dogs having four legs. And note that in #4 that information was not known. The first sentence would be oddly specific even if the second sentence did mention four legged dogs, but since it doesn’t the first sentence would be outright absurd as a conclusion. Why not five legs? Or two?
Now, it is clearly more natural to read the first sentence as a previously known fact. So how can the second sentence be a conclusion? The second sentence does not mention dogs at all! In other words, the knowledge that most dogs are four legged, rather than three-legged, could be used to conclude that three-leggedness is uncommon in general (not just restricted to dogs).
Like I said, I would like to know what you would have thought it meant. This could help me in future teaching endeavors…
ETA: See definition b here. I’d have added in that it’s intended to be probable, though, not jsut that it is probable given the assumptions.
Didn’t see this on preview:
This I agree with.
This I don’t. If someone were to actually make the statements, I would interpret “Pizza is awesome” as a direct observation of the speaker.
How does the reader know that the speaker doesn’t know the prevalence of three-legged dogs? Perhaps he read of a study where that figure was found. And the statement “This is because three-leggedness is very unusual.” was his (poor) attempt at explaining the one-in-one-thousand figure.
The bolded statement above is basically what I thought.
When you wrote
I didn’t find that sufficient because it seems to include an explanation of a direct observation as a case of inference, with the direct observation an inferance of the explanation.
e.g.
“The walls of my room are blue. For you see, I painted them blue this morning.” That’s not an inference by the bolded definition. But you could argue that “I painted them blue” as a rational basis for them being blue.