Here's a simple definition from economics, for instance, that people contest all the time.
Gross Domestic Product (GDP) = Consumption (C) + Government spending (G) + Investment (I) + (Exports (X) - Imports (M)).
This doesn't depend on any theory. It simply states that total economic activity is equal to all the money households spend buying stuff (C), plus all the money the government spends on buying stuff (G), plus all the money people invest (I) plus what we make from selling exports (X) minus the money we spend on imports.
For instance, in 2010, the equation for GDP for the US looked like this:
GDP = C + I + (X-M) + G
(all numbers in trillions)
If we had sold another trillion in exports or invested another trillion or spent another trillion on consumption or government spending, GDP would have been $15.6 trillion.
Now this says nothing about whether you like how the money is spent. A dollar of consumption (C) spent on a strip club adds to the total as much as a dollar of consumption spent on ahip replacement for a 92 year old adds to the total as much as a dollar for new stained glass windows for the church adds as much as a dollar some little kid spends on ice cream. Economic accounting like this doesn't make any judgments on how people spend their money.
In the same way, a dollar of government spending spent on defending the nation against terrorists is treated no differently than a dollar spent on educating the young is treated no different than a dollar spent on building a road for a corporation is treated no differently than a dollar spent on a welfare mother. Again, it's just different ways that the dollar gets spent in order to raises total Government spending (G), which in turn raises GDP.
Now it is true that a dollar spent on developing the Internet or solar power is likely to lead to higher GDP in the future. Investment is more cool than the other elements of GDP. But of course, only up to a point. If we only invested and didn't consume, we'd quickly die out, like people who turned all their corn into seed corn and starved to death. You can - and should -argue about how much to invest and in what. But I is just another component of GDP and the more we invest, the higher GDP that year.
If you lower C or I or G or (X-M), you will lower GDP. This is not theory. This just results from simple definition.
If you lower G (government spending) GDP goes down. This is the same thing that happens if you lower C or (X-M) or I. And yet we hear all the time that if only we lowered G, GDP would go up. I still haven't figured out the math on that.
It is legitimate to argue about what is the best mix of these. The question of how to increase exports and investments seems really important. The choice about what sorts of investments to make seems really important. But the strategies to do that need to recognize that such changes take time and will span business cycles. The right time to talk about lowering G is when C or I or X are rising. To lay off government workers or government contractors when unemployment is high just lowers GDP by lowering G and giving GDP no offsetting rise in any other component.