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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.


Axioms are necessary truths generalized. You will critically apply the four tests given above, and remove from the tree spurious fruit.

Build on the Rock.-Truth must be seen with sunlight clearness. You can afford to linger here. A few hours of penetrating thought may save you from a life of groping.

1. Space. I walk a mile. What is this through which I walk and in which all things are? The child perceives the idea, where things are, and learns to call this reality space. As space is not a phenomenon, we can not gain the idea through outer or inner-perception. As space is elementary, we can not infer this idea from other ideas. Self, as noumenal-perception, knows immediately this space, and this, and this. Let us try the four tests: (1) I stand face to face with this space. I know that I perceive this space; this is self-evidence. (2) That things may be, space must be. Space is a necessary reality. (3) I think of things as in space. Everything is somewhere. The space-idea pervades all thinking—is universal. (4) I find it impossible to derive this idea from other ideas, just as it is impossible to derive gold from the baser metals. Space is a necessary reality, and the space-idea is a necessary idea. Most of the axioms of geometry are intuitive truths generalized from space-percepts.


2. Time. I take the train at Philadelphia and go to New York. I spend from breakfast to dinner with friend. What passes? Mamma, you stayed a long time." The child has the idea-time. How did it gain this idea? You answer that the child intuitively perceives this time, and this, when its experiences involve

time. You reason as follows: The idea, this time, must be a phenomenal-percept, a specific truth under some general truth, or a noumenal-percept. It is not a phenomenal truth. No one claims that it is a specific idea under some general idea. We can not avoid the conclusion: the idea, this time, is a noumenal-percept. Apply the four tests of necessary ideas. What kind of truths are the axioms of algebra? Is an axiom a necessary idea or a necessary truth?

3. Existence. The mountain is-exists. It is is the only affirmation applicable to everything. That existence is a necessary idea will be readily seen. Indeed, this idea seems to underlie all other ideas. Self, as noumenal-perception, intuitively knows things as existing. Prove that the notion "concrete existence" is a necessary idea.

4. Right. The bad boy strikes his mother. His little sister says to him, "You ought not-wrong; naughty." The child reads the story of the good Samaritan: its "bad Pharisee" and "good Samaritan" show that the child has the idea of right and wrong. In fact, whenever the child observes acts involving right, it at once perceives the idea of right. From experience and education it finds out what is right, and soon learns to say, "That is right." Show that the notion "concrete right" is a necessary idea.

5. Beauty. "The babe is beautiful." The child perceives something pleasing in things. Before it learns to say "Beautiful bird!" it knows concrete beauty. Self, as sense-perception, sees the yellow primrose, and, as noumenal-perception, knows it as beautiful. Apply to beauty the tests of necessary ideas.

6. Truth. The blood circulates. The earth is spherical. These are statements of truths, for they assert realities. Arnold was a traitor. This is true-it asserts a fact. Washington was a traitor. This is not true—it asserts a falsehood. The child intuitively beholds the truth-idea in individual truths.

I see

7. Matter. I press the table; it resists me. that it has extension. I find that I can move it. I place it on the scales; it has weight. The enduring thing having these attributes I learn to call matter. Self, as sense-perception, knows immediately physical phenomena. Self, as noumenal-perception, knows immediately matter-things having properties. It is selfevident that the substance sugar must be, in order that the property sweet may be. We know things as having attributes. I see the tree. This mental act involves sense-perception, for I intuitively cognize the tree as tall and green. It involves self-consciousness, for I cognize self perceiving the tall, green tree. It also involves noumenal-perception, for I intuitively cognize the entity, which is tall and green, as a material substance.

8. Mind. I think, I admire, I decide. I am conscious of thinking, feeling, willing. That mental acts may be, a mental entity must be.

"I think we are not wholly brain,

Magnetic mockeries; casts in clay;
Let science prove we are, and then

What matters science unto men?"

I know by direct insight that the noumenon underlies the phenomenon. The spirit entity that thinks, I intuitively know as self. I perceive self thinking, feeling, and willing. I am conscious of noumenal-intuition

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