The purpose of this study is to deploy a novel methodology for classifying different argumentative support (supporting evidences) in arguments, without considering the context. The proposed methodology is based on the idea that the use of Tree Kernel algorithms can be a good way to discriminate between different types of argumentative stances without the need of highly engineered features. This can be useful in different Argumentation Mining sub-tasks. This work provides an example of classifier built using a Tree Kernel method, which can discriminate between different kinds of argumentative support with a high accuracy. The ability to distinguish different kinds of support is, in fact, a key step toward Argument Scheme classification.