The fruit of the Bradford pear tree is thought to be poisonous to dogs. The American Dog Trainer Network lists pear seeds on their Poisonous Substances list. The pear from the Bradford pear tree contains seeds; each have a small amount of cyanide inside of them.
To prevent your dog from eating the pear seeds clean up every pear you can find and consider replacing your tree with another ornamental that doesn't bear fruit.
If you think your dog has been poisoned call the ASPCA Animal Poison Control Center hotline at 888-426-4435. Be ready to report the species, breed, age, sex, weight, symptoms, the amount of pear seeds eaten, and the time elapsed since the time of exposure.
Other trees and shrubs known to be poisonous to dogs include the Black Locust, the Elderberry, Oak trees, and wild and cultivated cherries.
The ASPCA offers Tips On Keeping Your Pet Safe Over The Holidays and Growing the Home Garden suggests Reasons Why Your Shouldn't Plant a Bradford Pear Tree.