The Nature of Language and Thought in an Argument Against Reductionism
More rough notes.
The whole is greater than the sum of the parts: if you lay two planks of wood on top of each other, and they can hold more weight than the combination of what they could individually hold. Together you get more than you had separately, therefore reductionism is wrong.
That argument is flawed, because it is confusing petty reductionism for reductionism. Are any laws of physics violated by the result of putting two planks of wood together? Obviously not. The result of putting the two planks of wood together is fully explainable at a lower-level of the laws of physics.
While that might be the reason why the argument is flawed, I don't think it'll always convince people. We arrive at conclusions through chains of reasoning, and even if our conclusion is shown to be wrong, if we still think our chain of reasoning is valid there's a good chance we'll still think the conclusion is right, too. I think there is one such chain of reasoning for this matter, and that this flawed reasoning comes about because of the nature of language and thought. I'll talk about it now.
It really can seem that we have something here that is 'greater than the sum of the parts' because we have something, the 'strength' of the pieces of wood, that is some amount when the pieces are wood are separate, and yet is more than twice this amount when they are combined. Doesn't it seem that we have in fact gained something here which wasn't there before?
The problem is that in thinking this we are reifying the 'strength'. But wait a moment, doesn't reifying mean "to regard (something abstract) as a material or concrete thing", and isn't the strength of the planks a real thing? It is a real thing, but we must be careful with what we mean by 'real'.
The strength is real, but it is not a substance, such that we have created some new amount of this substance when we put the planks together. Strength is a real property, but it is not a "thing" in itself, and you might describe it as being both "real" and "abstract". It is the product of a number of factors, such as the type of material, the structural arrangement of the item, etc. Quantity of the property (strength) is not simply a function of the quantity of the things making it up.
So what exactly is causing the problem here? Seeing 'strength' as a "real" thing, and thus that we have more of a "real" thing when the planks are combined, and thus that reductionism is violated. The root problem here is in considering that "real" can only mean a real "thing".
The "strength" of something is simply a consequence of the brute physical details of that thing -- there is no thing that is "strength" over and above those details. Those details have real consequences - such as how much weight it can carry before it breaks, but to say there is some actual extra thing called 'strength' responsible for those properties is a mistake. It is confusing a label in our heads for a thing in reality -- whereas that thing in our heads is really a description of reality.