Deep learning has been increasingly incorporated into various computational pathology applications to improve its efficiency, accuracy, and robustness. Although successful, most previous approaches for image classification have crucial drawbacks. There exist numerous tasks in pathology, but one needs to build a model per task, i.e., a task-specific model, thereby increasing the number of models, training resources, and cost. Moreover, transferring arbitrary task-specific model to another task is still a challenging problem. Herein, we propose a task-agnostic generative and general pathology image classifier, so called GPC, that aims at learning from diverse kinds of pathology images and conducting numerous classification tasks in a unified model. GPC, equipped with a convolutional neural network and a Transformer-based language model, maps pathology images into a high-dimensional feature space and generates pertinent class labels as texts via the image-to-text classification mechanism. We evaluate GPC on six datasets for four different pathology image classification tasks. Experimental results show that GPC holds considerable potential for developing an effective and efficient universal model for pathology image analysis.