Why is faulty generalization called an informal fallacy?

According to wikipedia faulty generalization belongs to the class of informal fallacies. Also, a fallacy is called informal if it

originates in a reasoning error other than a flaw in the logical form of the argument.

But I'm wondering why is it assumed it cannot be formalized. Isn't the following proposition in FOL a formalization of faulty generalization?

∃x: F(x) ∴ ∀x: F(x)

Here F(x) is an arbitrary function where a variable x is involved, but other variables can be used as well. An informal example would be: "There are sighted people. Therefore, all people are sighted." In formal way this is ∃x: Px → Sx ∴ ∀x: Px → Sx. Px means "x belongs to people" and Sx means "x is sighted".

The replacement of a quantifier is a formal fallacy, isn't it? So, why is faulty generalization assumed to be an informal fallacy?

• The FOL sequent is not well-formed. Did you maybe mean: ∃x(Px→Qx) .: ∀x(Px→Qx)? Or even more simply ∃xPx .: ∀xPx? Both are invalid, of course, but I’m not sure either is a good formalisation of Faulty Generalisation. Usually, when such a generalisation is made, it starts from specific instances and not just an existential quantification, no? So, perhaps we could try: Pa, Pb, Pc .: ∀xPx - which is still invalid. Jul 28, 2018 at 9:07
• The formalisation of ‘There are sighted people’ is ∃x(Px ∧ Sx), with ∧ instead of →. ∃x(Px → Sx) says that there is something that is S if it is P. This sentence is true in all structures where nothing is P. Jul 28, 2018 at 12:27
• @MarxOxford, at first I thought so, but then it would mean "Any x is a sighted human", not the one I want to have. I want to have "Every x who is human is sighted". The truth table of the implication is appropriate one. Jul 28, 2018 at 12:51
• I was talking about the premise, “There are sighted people”. The conclusion, “All people are sighted”, must be formalised with → (and ∀), as you did. Jul 28, 2018 at 12:56
• @MarkOxford, I'm not sure why we can't use implication. "Some x who are humans are sighted" which cannot be reversed. If we put ∧ we get "Some x who are humans are sighted and some x who are sighted are humans", which is irrelevant. Jul 28, 2018 at 13:05