Ask Lemmygrad

Not really.

It means there's two opposite sides to an issue. If I destroy one side, the contradiction goes away. E.g. I take the monarchy and lop their heads off -> feudalism gone.

In this context it is a reference to dialectical thinking, specifically dialectical materialism, where we say there are two opposing forces in order to understand a situation. If we are right that these forces are in opposition and struggle against one another, our insights from this framing will be more correct. For example, imagine an ice cube in a freezer. If we open the door of the freezer, the ice cube might stary to melt, but this really depends on the dynamics of opposing forces: those tending to heat the cube, namely the ambient air, and those tending to cool the cube, namely the compressor and how active it is. If the room is nearly at freezing already (tendency to heat is weak) and the compressor fairly strong, the ice cube won't melt. But we can imagine other scenarios where it might start melting. This is the usefulness of dialectical thinking, you can think of situations in terms of how they are changing based on where they are now and how they function.

Socialists are concerned with dialectical situations like class struggle or imperialism.

For primary vs. secondary, this isn't much more thsn just saying one of the dialectical situations is the most important, it has so much more impact tjat if even determines the others. This is not always a useful way of thinking, but you can think of it as thinking of the dialectics between dialectical situations.

Contradictions are "impossible" in combinatorial logic. In combinatorial logic, the output of a logical formula is determined entirely by the inputs. For example

True = (false) OR (true)

In such a formula, the output of a "contradiction" is always false, regardless of the input. The classical example of a contradiction is

(A) and (not A)

Which always outputs false, in combinatorial logic. Combinatorial logic is not the most advanced form of logic available in maths. It is infact the most basic with the least computing power, and virtually every computation ever performed is at the bare minimum a sequential logic.

In sequential logic, we introduce memory, or time. In sequential logic, contradictions are not only "possible", but extensively used. The most famous such contradiction is

0 = 1

Which in sequential logic produces a square wave oscillation. Basically, if you were to create an electrical circuit to compute 0=1, the circuit would oscillate between 1 and 0, thereby creating an oscillator. This is infact how digital clocks are created!

This is very similar to how contradictions are used in dialectics. They act as "motors" which produce a time or progression effect. Basically, a society without contradictions will have no movement. In human societies, class contradictions are the primary contradictions which dominate the progression of the society.

You should note that Marx and Engels were not aware of sequential logic, so they would have explained things differently.

https://en.prolewiki.org/wiki/Contradiction let me know if it helps because if it doesn't it means we need to rewrite it