Raven's Progressive Matrices (RPMs) have been widely used for measuring abstract reasoning and intelligence in humans. However for artificial learning systems, abstract reasoning remains a challenging problem. This paper investigates the potential of biologically inspired spiking neural networks in addressing this challenge. We focus on unsupervised learning since in most domains where human-competitive conceptual learning is important, unlabelled data is plentiful and the autonomous discovery and understanding of underlying patterns without explicit guidance is paramount. Our experiments show that the overall accuracy of our unsupervised networks significantly outperform some supervised methods. Our results also demonstrate that, unlike their non-spiking counterparts, spiking neural networks are able to extract and encode relational features without any explicit instruction, do not rely on labelled training data, and are able to simulate the human ability of navigating and deciphering complex data landscapes. Our results exhibit state-of-the-art performance for unsupervised learning on the RAVEN (67.0%) and I-RAVEN (40.3%) datasets, indicating that that spiking neural networks are well suited to unsupervised conceptual learning.