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All Reality Is Made Up Of Multiple Substances.

By: Iustum Date created: April 5, 2025 Date revised: April 10, 2025

The domain of discourse is reality.

1 Definitions

  1. Every substance is the most enduring and underlying reality of a thing.[i]
  2. Every attribute is an essential property of substance.[ii]
  3. Every modification is an accidental property of substance.[iii]

2 Axioms

  1. All reality is a reality made up of multiple modifications.
  2. All reality is a reality made up of one substance, all reality is a reality made up of multiple substances, or all reality is a reality made up of zero substances.
  3. All reality is a reality made up of unique things through unique things
  4. All reality made up of multiple modifications is a reality.
  5. All reality made up of one substance is a reality made up of multiple modification through one substance.
  6. No reality is a reality made up of zero somewhat enduring and underlying atoms.[iv]
  7. No reality made up of only unique modifications through unique substances is a reality made up of multiple modification through one substance.

Explanation. Axiom 2 is an exclusive or. For Axiom 3, unique things have come through unique things or causes to explain that uniqueness; two things cannot come from one thing without changes in essential or accidental properties.

3 Propositions 1-6

Proposition 1. NO REALITY IS A REALITY MADE UP OF ZERO SUBSTANCES.

Proof. If all reality is a reality made up of zero substances, then all reality is a reality made up of zero somewhat enduring and underlying atoms of it [Def. 1]. No reality is a reality made up of zero somewhat enduring and underlying atoms [Axiom 6].

Remark. In the original definition, "most" is a relative term. If atoms are the only thing underlying reality, they become the "most" enduring while underlying reality-atoms becoming substance.

Proposition 2. EVERY REALITY MADE UP OF MULTIPLE MODIFICATIONS IS REALITY MADE UP OF ONLY UNIQUE MODIFICATION THROUGH UNIQUE THINGS.

Proof. All reality is a reality made up of unique things through unique things [Axiom 3]. All reality made up of multiple modifications is a reality [Axiom 4].

Proposition 3. NO REALITY MADE UP OF MULTIPLE MODIFICATIONS IS A REALITY MADE UP OF MULTIPLE MODIFICATION THROUGH ONE SUBSTANCE.

Proof. No reality made up of only unique modifications through unique substances is a reality made up of multiple modification through one substance [Axiom 7]. All reality made up of multiple modifications is reality made up of unique things through unique things [2].

Proposition 4. NO REALITY MADE UP OF MULTIPLE MODIFICATIONS IS A REALITY MADE UP OF ONE SUBSTANCE.

Proof. All reality made up of one substance is a reality made up of multiple modification through one substance [Axiom 5]. No reality made up of multiple modifications is a reality made up of multiple modification through one substance [3].

Proposition 5. NO REALITY IS A REALITY MADE UP OF ONE SUBSTANCE.

Proof. No reality made up of multiple modifications is a reality made up of one substance [4]. All reality is a reality made up of multiple modifications [Axiom 1].

Proposition 6. ALL REALITY IS A REALITY MADE UP OF MULTIPLE SUBSTANCES

Proof. All reality is a reality made up of one substance, all reality is a reality made up of multiple substances, or all reality is a reality made up of zero substances [Axiom 2]. No reality is a reality made up of one substance [5]. No reality is a reality made up of zero substances [1].


Notes

  1. ^ Smith, N. D. (2022). Introduction to Philosophy. https://openstax.org/details/books/introduction-philosophy
    "The Latin term substantia, translated as 'substance,' describes the basic reality or essence of a thing that supports or stands under features that are incidental to the substance itself."
  2. ^ Spinoza, B. (1677). Ethics (R. H. M. Elwes, Trans.). https://en.wikisource.org/wiki/Ethics_(Spinoza)
    "By attribute, I mean that which the intellect perceives as constituting the essence of substance."
  3. ^ Spinoza, B. (1677). Ethics (R. H. M. Elwes, Trans.). https://en.wikisource.org/wiki/Ethics_(Spinoza)
    "By mode, I mean the modifications of substance, or that which exists in, and is conceived through, something other than itself."
  4. ^ Sutter, P. (2022, October 31). How did we figure out atoms exist? Space.com. https://www.space.com/how-did-we-discover-atoms.html
    "Thus, almost a hundred years after Dalton conclusively argued for the existence of the indivisible atom, and at the same time as Einstein was providing a way to directly measure those atoms, Thomson and Rutherford discovered that the atom wasn't indivisible at all."