You didn't say what type of syrup, so I'll assume a typical syrup like maple. According to stilltasty.com, it's good for one year if refrigerated and indefinitely if frozen.
Stilltasty uses government food safety guidelines as its criteria, so it tends to be very conservative. I have a bottle of maple syrup that was opened over a year ago and I intend to keep it and finish the bottle even if it takes another year, and it is not refrigerated. It's kept in a pantry at room temperature. Since bacteria don't grow readily in heavy sugar solutions, bacterial contamination is almost never an issue with syrups, jellies, etc. Sometimes the sugars will separate out, but you can fix that by simply warming the syrup in a microwave or hot water. The sugar crystals will re-dissolve. Mold can sometimes get established, but that's plainly visible and you should toss anything with mold in it.
So, basically, government guidelines say throw that 2014 syrup away immediately. I, however, would eat it without worry.
EDIT: In response to a question in comments, I've added this link: