Are seedless fruits considered life?
Definition of life

The definition of what is alive and what is not is not a matter of biology but a matter of philosophy. Most definitions are based on:


Physiology


Existence of a metabolism

Evolution


Ability to reproduce and have heritable traits

Ecology


Ability to respond to the environment



There are plenty of possible definitions of "life". Note also that behind the complexity of defining what is alive there is the issue of defining the unit (the individuality if you want) on which the concept of life applies.

Your definition of life

You suggest a quick and simple definition so let's consider it.


  to be considered life, it must be able to reproduce


If you talk about the watermelon tree

If this is your definition, then Citrullus lanatus is definitely alive as it is able to reproduce (otherwise we would not be able to cultivate them).

If you talk about the watermelon fruit

Now you may ask is the fruit itself alive. Then, using your definition again, I suppose the answer is no because a given seedless watermelon will not be able to give birth to other seedless watermelons (even via the make-up of a watermelon tree). 

Note that following the same logic one could argue that one's head is not alive either as one's head does not reproduce. Only your gonads do. Your dog might not be considered alive either. A castrato (singer) would not be alive either. A woman, after menopause, cannot reproduce either! Arguably, a cloud replicates or a fire replicates and could eventually be considered alive following your definition. So really, as you can see your simple definition hardly fit your intuition of what should be called alive.

My opinion on your definition

Personally, I am not a big fan of your definition but again it is nothing but a matter of preferences. I don't like that your definition is unclear because there are plenty of limit cases and because there are plenty of cases we would want to call alive that we can't anymore (like a woman after menopause for example!) Every definition of life would eave limit cases but with your definition, it really easy to find these limit cases. 

Is this question about Biology?

No, it is not. It is a question of philosophy.

Other interesting post on Biology.Stack

You might want to have a look at why isn't a virus alive.