Do concepts in probability help us understand when an analogical inference is acceptable? I'm a philosophy undergraduate. I've recently read about analogical inferences. When making inferences by analogy, we observe that many of the properties of the analogues are the same, then infer that the rest of the properties are probably the same. 
For example, an analogy between sets of the vital properties of two plants: 


*

*Premise 1: a tree needs roots in the ground, sun, leaves, and water to live; 

*Premise 2: a weed needs roots in the ground, sun, and leaves to live, 

*Conclusion 1: a weed probably needs water to live too.


I also read that the more properties one can predicate of both analogues, the stronger the analogy between them. I don't know enough about probability and defeasible inference to discern whether that claim is accurate. 
To me, it seems as though what warrants inductive inferences (on which statisticians are experts) warrants analogical inference: If we regard the set of vital properties of each plant as a population, and regard each vital property of each plant as members of that population, and regard the set of vital properties mentioned in the premises of the analogy as a sample, then at first blush it seems that we could justify the inference that 'if both plants have all the vital properties in the sample, then both plants probably have the same vital properties.'
But if that's an acceptable inference, what makes it acceptable? Are there concepts in probability that can help explain why that's the case?
Thank you.
 A: Analogical reasoning is a weaker form of argumentation than probabilistic reasoning, in that it is based on plausibility and defeasibility. As such, any inference from analogical reasoning is less secure than a probabilistic argument, which is, in turn, less secure than a deductive argument.
When you make a defeasible argument, you are implicitly assuming that its premises are reasonable. In analogical reasoning, the key assumption is that properties occur in clusters, not independently of one another. The probabilistic version of this (which is a stronger, more data intensive argument) is:


*

*Let $\Omega$ be the set of properties possessed by a "reference object", X.

*Let Y be the "comparison object", which has properties K. 

*Let S be a strict subset of the properties of X, i.e., $S\subset \Omega$

*Then, the probabilistic version of the analogical argument is: $P(\Omega \in K|S \in K) \space \dot\propto \frac{\#S}{\#\Omega} $


Where $\dot \propto$ means "approximately proportional to", to indicate the the relation may not be strictly linear.
With regard to warrant, since probabilistic reasoning is stronger than plausible/defeasible reasoning, then of course anything that warrants probabilistic reasoning also warrants plausible reasoning, but not vice versa, since the latter is more of a prima facie form of reasoning.
