"Pressure Yourself." The broad meaning of the word here is "put to the test." It can be a negative exercise, where one tries to put God to the test from hostile motives. It is the word translated "tempted" in Galatians 6:1. But, it can also be used in a positive way, as in 2 Corinthians 13:5. Paul is saying, "Put yourself to the test." Louw and Nida put, "Determine the nature of something by submitting it to the test" (Gk.-Eng. Lex., 27.46). What thing is Paul telling them to put to the test to find out its nature? Their lives as measured by God's Word. The concept of pressure-testing it is to look deeply and closely and find out, truly, if they each were continuing in the faith. That is an exercise which will require a lifetime of persistent effort, and it certainly leaves little time for pulling out the magnifying glass and the microscope on our brethren.
"Prove Yourself." The meaning of "prove" is similar to the word translated "test" or "pressure." Trench says it means "to approve after examination" (Synonyms, 278). The need was to keep themselves on the hook until they had been thoroughly, honestly examined by self. There is always plenty to see and evaluate in ourselves, enough to keep us busy every day.
"Perceive Yourself." What was it Paul wanted them to see in themselves? It was whether or not Christ was in them. If He was not, they had failed the test. When we look into the Bible and put yourself to the test, do you see from that examination that Christ is in you? We might be able to fool others, but we cannot fool ourselves. He cannot get in our hearts by wishing, feeling, hoping, or intending. Paul emphasizes "the faith" as crucial to this process.
Look closely at self. What do you see inside yourself? So pursue and live so that Christ is in you. When He is, He will shine forth through you!