# Is this an inductive or a deductive argument?

Two flowers of the same cultivar were planted in adjacent plots .
The first was fertilized with Miracle-Gro and it flourished (2); The second was not and it din't(3) .

Therefore , Miracle-Gro stimulates plant growth .
I think it's deductive but invalid
Because (2)& (3)
But the book say it's inductive why ?

• and what is the difference between invalid deductive argument and inductive argument ? – Abdelrhman Fawzy Jun 24 '17 at 14:26
• Induction concerns itself with making general or universal assertions based on specific facts. In other words, Miracle-Gro did such and such; therefore Miracle-Gro always does such and such. – user3017 Jun 24 '17 at 15:12
• why do you think it's invalid deduction? – user20153 Jun 24 '17 at 19:33
• there's a big difference between "miracle gro stimulated growth in this case" and "miracle gro stimulates growth in all cases". the former is deductive, the latter inductive. – user20153 Jun 24 '17 at 19:36
• i have no idea what you're talking about, sorry. inductive reasoning is not useful? huh? – user20153 Jun 24 '17 at 20:59

Especially in introductory logic textbooks, deductive arguments are usually defined something like this: "the conclusion must be true given the premises" or "it's impossible for the premises to be true and the conclusion false." Then inductive arguments are defined as arguments that aren't deductive. Using this definition, the Miracle-Gro argument counts as inductive, because it's possible for the premises to be true (plant A was fertilized, plant B wasn't, plant A flourished, plant B didn't) and the conclusion false (Miracle-Gro doesn't stimulate plant growth).

If you're asking in the context of an introductory logic course, that answer is probably good enough. In the rest of this answer, I'll introduce some limitations for the standard definition of inductive and deductive.

The first limitation is that it doesn't distinguish different kinds of inductive arguments. Both enumerative induction (the sun rose yesterday, the sun rose 2 days ago, the sun rose 3 days ago, ..., therefore the sun will rise every day) and argument from analogy (Hypatia was a woman, Hypatia was mortal, Hillary Clinton is a woman, therefore Hillary Clinton is mortal) are not-deductive, and are grouped together as "inductive" by the definition. But there are important and interesting differences between enumerative induction and argument from analogy.

A second limitation is that the definition places all bad arguments in the inductive category. Consider a complete non sequitur: Hillary Clinton lost the election, therefore some cats like to eat fish. This doesn't pass the test for deduction, so the definition places it in the inductive category. But it's not even remotely plausible as an argument, which makes it very different from enumerative induction and argument from analogy.

A third and related limitation has to do with enthymemes, or arguments with an "implicit premise." Consider this argument: Hillary Clinton received fewer electoral votes than Donald Trump, therefore Hillary Clinton lost the election. Taken on its face, the argument is not deductive, because the premise could be true and the conclusion false (if the US had a different electoral system). But many readers would recognize an implicit premise (roughly, that any candidate who received fewer electoral votes lost the election). Once that premise is stated explicitly, the argument becomes deductive.

The problem is that, if implicit premises are allowed, every argument counts as deductive. Take the argument Hillary Clinton lost the election; if Hillary Clinton lost the election then some cats like to eat fish; therefore some cats like to eat fish. This is now a deductive argument (and it's even sound!).

A fourth limitation is that the definition depends on modal assumptions; that is, assumptions about what must be the case or what's impossible. Consider the argument that this table has mass, therefore this table cannot travel at the speed of light. Is the argument deductive? It is if general relativity sets the boundaries on what's possible and impossible. But that means general relativity is necessarily true, and we typically think that's not the case (in other words, we typically think general relativity is contingently true). Next consider the argument that I am a bachelor, therefore I am unmarried (a version of one of the standard examples of an "analytic truth"). Whether this argument is deductive depends on whether a certain definition of the term "bachelor" sets boundaries on what must be the case or what's impossible. But it seems like that definition could be contingent — we might have used the term "bachelor" differently.

(This limitation also applies to formal logic. $p \& (p \to q) \to q$ is a tautology only because of the definitions of the operators $\&$ and $\to$, and we could have adopted different standard definitions. See Etchemendy, The Concept of Logical Consequence.)

Given these limitations of the standard definition, I usually suggest a different approach to my introductory logic students. Good arguments are ones in which the premises provide good reasons to accept the conclusion. Then we can talk about different kinds of arguments (modus tollens, enumerative induction, analogy, and so on) and the supporting and undermining conditions for each kind of argument. So, instead of asking whether the Miracle-Gro argument is inductive or deductive, we focus on asking what makes for a good or bad experimental test of Miracle-Gro.