For those readers who are concerned that I have tried to reach substantial conclusions concerning truth and responsible action without giving philosophically sound definitions of those concepts, I offer the following.
THE PARADOX OF ANALYSIS
Much of philosophy is an attempt to define concepts: evidence, truth, knowledge, justice, the good, causation, etc. There is a problem in understanding this project of finding definitions. The problem is called "The Paradox of Analysis." The "paradox" is this:
Either we understand the concept we are trying to define, or we do not. If we do understand it, why do we need the definition? If we do not understand it, how can we evaluate proposed definitions? How can we decide whether or not a proposed definition is correct?
It seems that either the project of finding the right definition is either unnecessary or impossible. Now the solution to the "paradox" is this: we have partial understanding. Some aspects of the concept are understood and some are not. We use the part we understand to evaluate proposed definitions. Then we use the definition to clarify that part we do not as yet understand.
In a little more detail: A concept has many uses and applications. Take the concept "life" for example. "Life" applies to certain items in the world and not to others: trees, spiders, birds, beavers and people are alive; stones, pure water, the sun and dead animals are not alive. Living things are physical objects, they move, they use energy from the environment, etc. These aspects of "life" are understood.
But there are uses and applications of "life" which are not well-understood. Are viruses alive? (They reproduce only by using the machinery of a cell.) Are self-copying molecules alive? (They reproduce, but that is all they do.) Could a man-made computer or robot be alive?
These questions show that the concept "life" is not completely understood. The project of finding a definition proceeds as follows. A proposed definition is tested against what we do understand. It must apply to trees, spiders, etc., and not to stones, pure water, etc. And it must imply being physical, motion, using energy, etc. If it passes these tests [and is "integrated," "simple," "explanatory," and possesses a host of other ill-defined but crucial theoretical virtues] then we may rely upon it to answer the questions of the previous paragraph (if it can).
At present we do not possess a definition of "life" which passes these tests. Therefore we cannot answer the outstanding questions.
Now consider the following proposition: It is wrong to conduct a discussion using a concept for which we do not have a definition.
This is the philosopher's battle cry: DEFINE YOUR TERMS! Is this demand legitimate? Is there some intellectual fault in conducting a discussion using terms which are not defined?
It depends. If you are using the term in one of the areas is which it is not well-understood, then there is a real risk of being misunderstood. You risk failing to really resolve the issue, since the concept may be used differently in the future when a definition is provided. But if you are using the concept in one of the areas in which it is well-understood, these risks are minimal [but not zero - see below]. In this case the response to the philosopher should be: "Explain WHY I should define my terms! Show me the risk I am running. Show me how the argument I am making is compromised by my use of this concept." If he cannot do this, then we may proceed with the discussion without the definition.
For example, suppose we say that dogs are alive, or that smoke is not alive. We should not be stopped by the fact that we have no definition of "life." These are clear cases of the concept. Any proposed definition will be tested by agreeing with these statements. They are not risky even in the absence of a definition of "life."
On the other hand, if we say that viruses are alive (e.g. in a campaign for "the rights of all living things"), we are taking a risk. Whether or not viruses are alive is controversial. Without a definition it is impossible to be confident that the statement is correct. In this case we should wait for a definition.
Consider "truth" as another example. Many uses and applications are clear: "3+2=5," "yellow is lighter than purple," The United States is bigger than Puerto Rico," are known to be true; "7+5=11," "the south pole has a tropical climate," and "Rwanda is a first-world country" are known to be false. Others are not clear: "there is an infinity of twin primes [prime numbers differing by 2]," "the Japanese could have been defeated without the use of the atomic bomb," "the universe will end in cosmic heat death," are at present not known to be true and not known to be false.
Statements, beliefs, theories, guesses, propositions etc. can be true; numbers, rivers, stars, football teams etc. cannot. But it is unclear whether propositions of ethics or esthetics, propositions about the future, or propositions beyond the capacity of all mankind to ever know, can be true.
Use of the concept "truth" follows the same patterns as the use of "life." If we remain within the well-understood areas there is no reason to worry about using the concept even though we do not possess a definition.
Suppose that during a trial a witness is accused of lying under oath. Suppose he tries to defend himself by saying: "Lies are untrue statements. Since there is no accepted definition of "truth" you cannot sensibly discuss whether my statement is untrue." The success of his defense will depend upon the statement he made. If he said that taxation without representation is wrong, or that Berlioz was a greater composer than Brahms, or that it will rain tomorrow, or that the first cell evolved in the northern hemisphere, then his defense is sound. These are all controversial cases for the application of "truth." It will be difficult to establish that what he said is false.
But if he said that the United States spends 5% of its budget on foreign aid, or that it rained yesterday, or that there is a greatest prime number, then his defense is worthless. In these cases the concept of "truth" is well-understood. Any proposed definition will have to respect these cases. Therefore we can conduct the discussion even without the definition.
[Even when using a concept within its well-understood areas the risk is not zero. Sometimes a definition will agree with almost all of the well-understood applications and connections, and will possess the virtues of integration, simplicity, explanatory power etc. to such a degree that it will be used to overrule a few of the well-understood uses. For example, 300 years ago whales were unhesitatingly classified as fish. With the discovery that whales are mammals and that the vast majority of fish are not mammals, whales were reclassified as non-fish.
But this cannot happen too often. For example, if it were discovered that sharks, barracudas, goldfish, tuna, swordfish and flounder were all mammals, then we would simply admit that some fish are mammals, and retain whales as fish. (Or we might stop using the concept "fish" altogether in favor of some better concept(s).)]
Our conclusion is this: Using a concept without a definition is appropriate if it is used within the areas in which it is well-understood. When so used, there is only minimal risk of having to revise the conclusion of the argument due to the discovery of a definition.