The semantic variant of primary progressive aphasia (sv-PPA) is a degenerative condition which causes surface dyslexia/dysgraphia, resulting in reading/writing errors of irregular words with non-transparent grapheme-to-phoneme correspondences (e.g., 'plaid') as opposed to regular words (e.g., 'cat'). According to connectionist models, most authors have attributed this deficit to semantic impairments, but this assumption is at odds with symbolic models, such as the DRC account, stating that the reading/writing of irregulars relies on the mental lexicon. Our study investigated whether sv-PPA affects the lexicon in addition to the semantic system, and whether semantic or lexical deficits cause surface dyslexia/dysgraphia, while challenging the two major models of written language. We explored a cohort of 12 sv-PPA patients and 25 matched healthy controls using a reading and writing task, a semantic task (category decision: living vs. non-living), and a lexical task (lexical decision: word vs. no-neighbor non-word). Correlation analyses were conducted to assess the relationship between reading/writing scores of irregulars and semantic vs. lexical performance. Furthermore, item-by-item analyses explored the consistency of reading/writing errors with item-specific semantic and lexical errors. Results showed that sv-PPA patients are impaired at reading and writing irregular words, and that they have impaired performance in both the semantic and the lexical task. Reading/writing scores with irregulars correlated significantly with performance in the lexical but not the semantic task. Item-by-item analyses revealed that failure in the lexical task on a given irregular word is a good predictor of reading/writing errors with that item (positive predictive value: 77.5%), which was not the case for the semantic task (positive predictive value: 42.5%). Our findings show that sv-PPA is not restricted to semantic damage but that it also comprises damage to the mental lexicon, which appears to be the major factor for surface dyslexia/dysgraphia. Our data support symbolic models whereas they challenge connectionist accounts.