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Our direct notions of these realities are noumenalpercepts. Because these ideas underlie and condition all other ideas, they are called necessary ideas.

Acts of Noumenal-Perception analyzed.-I turn my hour-glass. My little girl patiently watches till the last grain of sand has fallen, and says, "Papa, it took a long time." Intuitively the child perceives concrete time. The capability to know noumena immediately is called noumenal-perception. In the same way you may examine space, cause, etc., and discover for yourself the nature of this marvelous power. You find that you perceive noumena as well as phenomena. Your analysis gives the

Conditions of knowing Necessary Ideas.-The apple falls. "What made it fall?" asks the three-year-old Newton. The question involves the three conditions of knowing necessary truths:

1. Objective reality. Space exists, though you may not perceive it. Space is an objective reality. The notion, cause, would be impossible but for the objective reality of causes. Gravity is an objective reality. Time is a reality independent of self. Matter and mind are objective realities. We perceive necessary realities.

2. Phenomena involving necessary realities. The falling apple involves cause. Phenomenal experience does not give the idea, this cause, but is necessary to the perception of it. Seeing the falling apple was necessary in order that Newton might perceive gravity. No one gains the idea, right, until he perceives right acts. Phenomena condition the perception of noumena. Without phenomena we can not know noumena.

3. A capability to perceive necessary realities. A being not endowed with noumenal-perception might know phenomena but could never cognize noumena. Even the little child knows at once concrete space and concrete cause, just as it knows color and sound and odor. Self, as noumenal-perception, directly beholds concrete necessary realities. Your analysis gives you also the

Tests of Necessary Ideas.-How do we know a necessary idea? There are four safe tests:

1. Self-evidence. Self stands face to face with ne cessary realities. Mediate proofs are not only not needed—they are an insult to the mind. Think of attempting to prove that something made the apple fall! We know that we perceive these noumena. We do not and can not define our necessary ideas nor prove them. They are self-evident. Axioms are abstract necessary truths, elaborated from necessary ideas, and, like these ideas, are self-evident.

2. Necessity. The mind must start with something. There must be primary ideas before there can be secondary ones. Noumenal ideas must be, in order that phenomenal ideas may be, just as noumena must be that phenomena may be. Space must be, in order that extended objects may be. Mind must be, that thought may be. I must perceive the necessary reality, concrete being, before I can say, "He is." We perceive these foundation ideas to be ultimate and final. We discern their necessity in all knowing. They are necessary ideas.

3. Universality. Necessary ideas are accepted by all. One or more necessary ideas are present in each

act of the mind. Necessary ideas are the universal ideas that underlie and condition all other ideas.

4. Independence. Like a chemical element, a necessary idea is ultimate. A necessary idea can not be derived from other ideas. Each necessary idea is absolutely independent of other necessary ideas. An idea that is self-evident, necessary, universal, and independent, is a necessary idea.

Noumenal-Percepts are singular, concrete, necessary notions. Keep in mind that only our concrete notions are called percepts. I perceive this large tiger, but I do not perceive vertebrate. The notion, this tiger, is a sense-percept. I perceive self remembering the story of Tell, but I do not perceive abstract memory. The idea, this memory, is a conscious-percept. I perceive that heat causes this water to boil, but I do not perceive that every effect must have a cause. The idea, this cause, is a noumenal-percept. Sense-percepts, conscious-percepts, and noumenal-percepts, are individual concrete notions. We perceive the concrete, not the abstract; the individual, not the general. Noumenal-percepts are concrete notions of necessary realities.

We perceive the individual, not the general. I perceive this space, not infinite space; this cause, not universal cause; this time, not eternity; this infinity, not the unlimited. What a world of confusion would be avoided by heeding this plain psychological fact! Noumenal-percepts are concrete notions of necessary entities and necessary relations. Most of the designations of these ideas are now merely historic. The following are some of the

Names.

Noumenal-Percepts, or Noumenal-Intuitions.
Necessary Ideas, or a priori Ideas.

First Truths, or Necessary Truths, or Intuitions.
Categorical Ideas, or Regulative Ideas.

Innate Ideas, or Connate Ideas.

Through the centuries these expressions have confused philosophers, but need not now confuse you. You find that you are endowed with the capability to know intuitively substances and necessary relations. You call the concrete ideas thus gained noumenal-percepts, or noumenal-intuitions, or necessary ideas. Perhaps, for the present, it will be well to disregard the other names. Later you will be interested in tracing their history. Necessary judgments, elaborated from necessary ideas, are called axioms, first truths, and necessary truths.

Necessary Realities, Necessary Ideas, Necessary Judgments.-You need to clearly distinguish these expressions. To help you to do so, this connected view is given:

1. Necessary realities are the realities that make phenomena possible. Mind, matter, cause, space, time, infinity, truth, beauty, right, and a few other realities, are classed as necessary realities because they must be in order that phenomena may be.

2. Necessary ideas are our immediate notions of necessary realities. My notion, this space, is necessary to my knowing that the table is here and the stove there. My idea, this space, is a necessary idea. Our elementary notions of necessary realities are termed necessary ideas because they underlie and condition all other ideas.

3. Necessary judgments are truths elaborated from necessary ideas. Cold causes this water to congeal. My idea, this cause, is a necessary idea; but, that every effect must have a cause, is a necessary judgment, a necessary truth. Axioms are necessary truths elaborated from necessary ideas.

Tree of Necessary Ideas.*-As the tree of life bore twelve kinds of fruit, so this tree bears twelve kinds of necessary ideas. These ideas are involved in all knowing. Self, as noumenal-perception, immediately knows these ideas in individual and concrete cases. Self, as reason, infers general truths from particular truths.

*Bascom's enumeration of necessary ideas is adopted.

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