In Lakatos’s description, the theory cannot be refuted by one attempt, there is a protective belt for it. It seems to make the theory more stable but leave other questions unanswered. For example, how to define the hard core from the protection belt? Would people in the same research discipline acknowledge the same hard core? Why hard core cannot be challenged?

What is the hard core of democratic theory? People may have different arguments. Some people claim the hard core is representative of the institutions, like Schumpeter. For others, the democracy is about the protection of freedom, like Miller. For the protection belt, the first group may work on the election system to make a number of votes received equal to the number of seats gained, while the other group would try to refine the judicial system to avoid human rights being violated. The election system and judicial system could also serve as a protection belt for each other’s hard core. It seems like Lakatos’s methodology is not very clear on an operational basis. Like the example, he gave in the book, why Prout’s studies could remain a hard core with so many refutations?

Hard core is different from the paradigm, but they are very similar in practices. To Kuhn, a paradigm is a religious belief, but for Lakatos, hard core is the key element of a research program. The problem is how do we use Lakatos’ idea to determine if the science is in progress or degenerate, which sounds simple in Kuhn’s world since we only talk about whether or not to find a replacement. For Lakatos, every hard core could still survive even if it lost its protective belt. If we want to determine whether or not there is progress in this research domain, we need to pinpoint what the hard core is. Defining hard core is much more difficult than defining paradigm. Though paradigm isn’t clearly defined in Kuhn’s literature, it could be understood as a vague idea by the scholars in their own field. Instead, how do we define the shift of hard core if we couldn’t define the hard core? And if all auxiliary hypotheses are rejected, should we abandon this hard core? Or is it a real hard core?

Take game theory, for example, the hard core may be the expected utility: the von Neumann–Morgenstern axioms, including completeness, transitivity, independence of irrelevant alternatives, and continuity. Problems are what is the protective belt? Nash equilibrium? Cooperation Game? The game which we are familiar with is elaborations based on these axioms to describe how actor reacts to the lack of information. Is any protective belt existing once we accept the expected utility as a true principle?

From the book, we have little idea about if Lakatos consider demarcation an important issue. For instance, Christian claims that God exists, and God loves everyone as long as you believe him. If this statement being qualified as a hard core, and the protective belt is all the theory and evidence that prove this world functions perfectly under the guideline of God. It seems like there are no demarcation criteria in Lakatos’ pieces. But is this problem matter? Why don’t we just define scientific theory as “How prior scholars see this world, and how do they solve puzzles?” to avoid the demarcation. As Lakatos said, we could always use auxiliary hypotheses to solve refutations, and science is fallible. There is not a constant demarcation, but what we need to bear in mind is that we have to discard the thought or belief of certain theory is absolutely right.

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