Protein aggregation is associated with many debilitating diseases including Alzheimer's, Parkinson's, and light-chain amyloidosis (AL). Additionally, such aggregation is a major problem in an industrial setting where antibody therapeutics often require high local concentrations of protein domains to be stable for substantial periods of time. However, despite a plethora of research in this field, dating back over 50 years, there is still no consensus on the mechanistic basis for protein aggregation. Here we use experimental data to derive a mechanistic model that well describes the aggregation of Titin I27, an immunoglobulin-like domain. Importantly, we find that models that are suitable for nucleated fibril formation do not fit our aggregation data. Instead, we show that aggregation proceeds via the addition of activated dimers, and that the rate of aggregation is dependent on the surface area of the aggregate. Moreover, we suggest that the "lag time" seen in these studies is not the time needed for a nucleation event to occur, but rather it is the time taken for the concentration of activated dimers to cross a particular solubility limit. These findings are reminiscent of the Finke-Watzky aggregation mechanism, originally based on nanocluster formation and suggest that amorphous aggregation processes may require mechanistic schemes that are substantially different from those of linear fibril formation.