  The words of a language reflect the structure of the human mind, allowing us
to transmit thoughts between individuals. However, language can represent only
a subset of our rich and detailed cognitive architecture. Here, we ask what
kinds of common knowledge (semantic memory) are captured by word meanings
(lexical semantics). We examine a prominent computational model that represents
words as vectors in a multidimensional space, such that proximity between
word-vectors approximates semantic relatedness. Because related words appear in
similar contexts, such spaces - called "word embeddings" - can be learned from
patterns of lexical co-occurrences in natural language. Despite their
popularity, a fundamental concern about word embeddings is that they appear to
be semantically "rigid": inter-word proximity captures only overall similarity,
yet human judgments about object similarities are highly context-dependent and
involve multiple, distinct semantic features. For example, dolphins and
alligators appear similar in size, but differ in intelligence and
aggressiveness. Could such context-dependent relationships be recovered from
word embeddings? To address this issue, we introduce a powerful, domain-general
solution: "semantic projection" of word-vectors onto lines that represent
various object features, like size (the line extending from the word "small" to
"big"), intelligence (from "dumb" to "smart"), or danger (from "safe" to
"dangerous"). This method, which is intuitively analogous to placing objects
"on a mental scale" between two extremes, recovers human judgments across a
range of object categories and properties. We thus show that word embeddings
inherit a wealth of common knowledge from word co-occurrence statistics and can
be flexibly manipulated to express context-dependent meanings.
