Humans judge the similarity of two objects not just based on their visual appearance but also based on their semantic relatedness. However, it remains unclear how humans learn about semantic relationships between objects and categories. One important source of semantic knowledge is that semantically related objects frequently co-occur in the same context. For instance, forks and plates are perceived as similar, at least in part, because they are often experienced together in a ``kitchen" or ``eating'' context. Here, we investigate whether a bio-inspired learning principle exploiting such co-occurrence statistics suffices to learn a semantically structured object representation {\em de novo} from raw visual or combined visual and linguistic input. To this end, we simulate temporal sequences of visual experience by binding together short video clips of real-world scenes showing objects in different contexts. A bio-inspired neural network model aligns close-in-time visual representations while also aligning visual and category label representations to simulate visuo-language alignment. Our results show that our model clusters object representations based on their context, e.g. kitchen or bedroom, in particular in high-level layers of the network, akin to humans. In contrast, lower-level layers tend to better reflect object identity or category. To achieve this, the model exploits two distinct strategies: the visuo-language alignment ensures that different objects of the same category are represented similarly, whereas the temporal alignment leverages that objects from the same context are frequently seen in succession to make their representations more similar. Overall, our work suggests temporal and visuo-language alignment as plausible computational principles for explaining the origins of certain forms of semantic knowledge in humans.