Why is my React/JSX if statement still executing?

I have a contact form that I'm looking to prevent submittal on if there is no entry in any of the following form inputs: name, email, and/or message. The form continues to fire, though, under the current syntax even with one of the refs coming up blank. Having trouble determining why?

submit = (event) => {
event.preventDefault();
    (this.refs.name.value  === "" || this.refs.email.value === "" || 
    this.refs.message.value === "")  
?
    alert("Sorry.  Message not submitted.  Form requires Name, Email, 
    & Message.")
:
    this.setState({
    modalIsOpen: true,
    }) 
    axios({
     method: "POST", 
     url:"/submit", 
     data: {
      name: this.refs.name.value,   
      email: this.refs.email.value,  
      message: this.refs.message.value
     }
   })};