Your syllogisms are a bit funny, if I might say so. You need to construct them differently if you’re going to use the word “therefore” or properly call them syllogisms.
That can be easily explained. They are not syllogisms. None of them were supposed to be. I was just informally writing out my argument to make it easier to understand.
I could have said:
Premise: I have a brother.
Premise: My brother’s name is Tom.
Conclusion: My brother’s name is Tom.
It is okay for the conclusion to be the same as one of the premises. This is called the argument from reiteration.
Premise: I have a blue nose.
Therefore: I have a blue nose.
This is a valid argument because it is impossible to go from a true premise to a false conclusion. If the premise is true, the conclusion is also true be because it is the same as the premise.
Premise: I have blue ears.
Conclusion: All animals are dogs or they aren’t.
This is also a valid argument because it is impossible for the conclusion to be false if the premises are true. In this case it is valid because the conclusion is logically true. A or not-A is logically true, no matter what the premise.
The following argument is* also* valid:
Premise: My dog Spot is not a dog, and my dog Spot is a dog.
Conclusion: I am the smartest man ever.
This argument doesn’t look valid but it is. It is impossible for this argument to lead to a false conclusion from a true premise because it is impossible for the premise to be true.
In the case of the blue nose, the conclusion is true if and only if I have a blue nose (happens to be false in this case, but I could easily grab some paint and make it true). In the case that all animals or dogs or they are not, it must be true because it can not be otherwise. In the case of my being the smartest person ever, it happens to be false. The truth value of the conclusion isn’t based on the validity of an argument.
None of my arguments are syllogisms, they have just all happened to have two premises and a conclusion.
As for the rest of your response, it seemed to focus on our subjective judgment of the cases rather than the objective reality of them. Whether or not it is difficult for us to judge, it does not follow that it cannot be true. Whether or not we subjectively agree with the analysis, it does not follow that the analysis is wrong.
My argument is based on the fact that you are using the word “objectively” incorrectly. It isn’t that what we are discussing is difficult to judge, it is that there is no right answer.
Which is more beautiful?
It is subjective, it depends on what qualities of beautiful you value more. There is no right answer.
Which is longer? It depends on which is longer. Whether we know it is longer is immaterial.
Let us say you are right though. That all qualities are objectively definable. Your argument would follow that there is an ideal lenght that all other lengths are mearly degrees of. God decreed the ideal length and all other lengths fall short of this. The argument is patently absurd.