When a neuron fires and the resulting action potential travels down its axon toward other neurons' dendrites, the effect on each of those neurons is mediated by the strength of the synapse that separates it from the firing neuron. This strength, in turn, is affected by the postsynaptic neuron's response through a mechanism that is thought to underlie important processes such as learning and memory. Although of difficult quantification, cortical synaptic strengths have been found to obey a long-tailed unimodal distribution peaking near the lowest values (approximately lognormal), thus confirming some of the predictive models built previously. Most of these models are causally local, in the sense that they refer to the situation in which a number of neurons all fire directly at the same postsynaptic neuron. Consequently, they necessarily embody assumptions regarding the generation of action potentials by the presynaptic neurons that have little biological interpretability. We introduce a network model of large groups of interconnected neurons and demonstrate, making none of the assumptions that characterize the causally local models, that its long-term behavior gives rise to a distribution of synaptic weights (the mathematical surrogates of synaptic strengths) with the same properties that were experimentally observed. In our model, the action potentials that create a neuron's input are, ultimately, the product of network-wide causal chains relating what happens at a neuron to the firings of others. Our model is then of a causally global nature and predicates the emergence of the synaptic-weight distribution on network structure and function. As such, it has the potential to become instrumental also in the study of other emergent cortical phenomena.