An induction can't be valid? Generalization is a type of induction, and I can imagine some valid generalizations:
1. I have DNA.
2. You have DNA.
3. Therefore, any person has DNA.
Though wikipedia says this:
Adamoriens wrote:The term validity in logic (also logical validity) is largely synonymous with logical truth. However, the term is used in different contexts. Validity is a property of formulae, statements and arguments. A logically valid argument is one where the conclusion follows from the premises.
I can understand where you're coming from because the conclusion doesn't
directly "follow", but even if
logical validity doesn't apply, there must be a distinction between the condition of the argument applying an induction and it applying a fallacy.
Also, that an induction is valid doesn't necessarily make it sound; but this doesn't need to mean it's always valid. If it's not valid, it can't in
any case be sound.
Adamoriens wrote:- All squares have four vortices.
- All tetrahedrons have four vortices.
- All tetrahedrons are squares.
Properly construed, the argument you give as an example is deductive rather than inductive, so the presence of a formal fallacy is not troublesome. However, I concede that formal fallacies may occur in an inductive argument, but only as flaws in a deductive step. My understanding is that a formal fallacy can only be detected by examining an argument's relations rather than its content, and if the relations between the premises and the conclusion are not logically necessary, this is said to be invalid. Of course, only deductive arguments demand this sort of relation, so formal fallacies are most often found there. In short, you could call an inductive argument invalid if there were a flawed deductive step somewhere in it and be somewhat correct, but it would be imprecise.
You have changed my example, since the child didn't even know what a tetrahedron is, so he/she can much less have a definition for it. The induction (from particular to general) was devised with the underlying logic that:
1) The child knows that squares have four vertices.
2) The child only knows squares to have this characteristic.
Therefore, in the sight of an unknown shape (a tetrahedron), he mistakenly generalized (generalization is a type of induction) a (deficient) definition of square to cover the tetrahedron, and herein lies the categorical fallacy which renders his logic invalid and therefore his conclusion false.
Induction and deduction, as far as I know, are kinds of reasonings for arguments, not kinds of structures for arguments, so I don't know how correct is it to apply a valid/sound difference here. I'm not any expert in logic, though, and might very well be wrong.
But as far as I understand "validity" deals with how logically the conclusion of an argument is derived from its premises, while "soundness" deals with the truth value of the conclusion. If an argument which attempts to apply an inductive reasoning fails to do so making a formal or informal fallacy, then the inductive reasoning is not so and the conclusion is derived invalidly (for applying an invalid reasoning), making the argument, as well, unsound.
Adamoriens wrote:Any simple inductive argument (ie. empty of deductive steps) by definition cannot have formal fallacies, since no one demands that that it follow with logical consequence. Otherwise it would be deductive.
I don't follow you here. An inductive reasoning has to derive something general from something particular; if it fails to do this appropriately, isn't it invalid logic? What we demand from an induction is it to derive something general from something particular, but these both "something"s have to be meaningful and equally true. E.g.:
1. I have two parents.
2. You have two parents.
3. Therefore, a rock has two parents.
Is this a valid induction through
generalization? Since both premises are true, and the conclusion is false, it must be invalid. We have attempted to infer the status of a rock through the statuses of two people, but rocks are not people, and herein lies the categorical fallacy which makes the reasoning
invalid.
Adamoriens wrote:That will not be necessary, I think, since your purpose would be to show that such an example is inductively weak. But nowhere have I claimed that religious beliefs are formed on the basis of strong induction, merely that all religious beliefs can be construed as inductions of some sort.
You're missing my point. I'm arguing altogether that I haven't seen any argument for faith through induction which properly resembled any weak or strong induction I can accept, that's why I ask you to provide one. I've only seen errors in category like the one I put above, and there's a huge gap between these three types. If you present an argument that resembles a weak induction, I'll have to change my statement that "faith is not based in a valid induction" (weak induction is, for example: "my hair is black therefore the hair of all people is black"). Do something close to this, for example, for any doctrine.
Adamoriens wrote:And, if my understanding is correct, an inductive argument (such as that underpinning a religious belief) remains an inductive argument, no matter how perforated with fallacies etc.
Please name one of these which underpines a religious belief.
Of course it will remain being an induction, but an invalid (fallacious? fake?) one. That is, something that attempts to apply an inductive reasoning but fails to do so appropriately, like my example in the half of the post.