Premise 1 (P1): Consciousness and Intentionality

Variables:
A: Consciousness
B: Intentionality
If: A ➔ B

Example: When you perceive a table, your consciousness (ego) is directed towards the table (cogito), and you experience its properties such as solidity and spatial dimensions (cogitatum).

Premise: Matter has the essential attribute of extension as an intrinsic property.

Phenomenological Justification: Eidetic reduction of physical properties involves stripping away contingent aspects to uncover their invariant features. This method reveals that matter is characterized by measurable dimensions such as length, breadth, and depth, which are essential and intrinsic to physical objects.

Premise 3 (P3): Absence of Intentionality in Extension

Premise: The intrinsic properties of extension (length, breadth, and depth) do not manifest any aspects of intentionality.

Variables:
D: Extension (length, breadth, and depth)
¬B: Lack of intentionality
If: D ➔ ¬B

Phenomenological Justification: Through phenomenological reduction, it is clear that the spatial dimensions of physical objects lack directedness, subjectivity, and qualitative content. These dimensions are purely spatial measurements devoid of intentionality. Even though the cogitatum (the content of consciousness) includes properties like length, breadth, and depth, these properties themselves do not exhibit intentionality. Intentionality is a feature of the act of consciousness (cogito) directed by the ego, not an attribute of the spatial dimensions.

Example: The length, width, and height of a table do not exhibit any qualities of being directed towards something, nor do they contain subjective experiences. While you can perceive the dimensions as part of your intentional act, the dimensions themselves lack any intentional structure.

Conclusion (C1): Non-Derivability of Intentionality from Physical Properties

Conclusion: Intentionality is an intrinsic feature of consciousness and cannot be derived from the physical properties of matter.

Variables:
A: Consciousness
¬C: Non-reducibility to matter
If: A ➔ ¬C

Phenomenological Justification: Given that intentionality, comprising the subject (ego), the act of consciousness (cogito), and its qualitative content (cogitatum), is an essential feature of consciousness and not present in the intrinsic properties of matter, consciousness cannot be reduced to or derived from matter.

Example: The subjective experience of seeing a red apple (including the ego, cogito, and cogitatum) cannot be explained merely by the physical properties of the apple.

Inference Rule (Hypothetical Syllogism):
If A (Consciousness exists) leads to B (Intentionality exists) (P1),
And if C (Matter exists) leads to D (Extension exists as an intrinsic property) (P2),
And if D (Extension exists as an intrinsic property) leads to ¬B (Intentionality does not exist) (P3),
Then if C (Matter exists) leads to ¬B (Intentionality does not exist) (Hypothetical Syllogism on P2 and P3),
And if ¬B (Intentionality does not exist) leads to ¬A (Consciousness does not exist) (Contraposition of P1),
Then C (Matter exists) leads to ¬A (Consciousness does not exist) (Hypothetical Syllogism on Step 4 and Contraposition of P1).

Conclusion

Therefore: If A (Consciousness exists), then it cannot be reduced to matter (neg C). A ➔ ¬C

Consciousness: The state of being aware of and able to think about one's own existence, thoughts, and surroundings.
Example: When you are aware of reading this text, you are in a state of consciousness.

Intentionality: The characteristic of consciousness by which it is always directed towards or about something.
Example: When you think about a tree, your thought is directed towards the tree.

Matter: The substance of which physical objects are made, characterized by extension as an intrinsic property.
Example: A table is made of wood, which is matter.

Extension: The spatial dimensions that characterize physical objects, referring to measurable properties such as length, breadth, and depth.
Example: The dimensions of a physical table, such as its length, width, and height, are its extension.

Ego: The subject of consciousness; the "I" or self that experiences, thinks, and acts.
Example: When you see a red apple, it is your "I" that perceives the apple, experiences its redness, and recognizes its roundness.

Cogito: The act of consciousness, which is always directed towards an object or content.
Example: The act of perceiving a red apple is the cogito.

Phenomenological Reduction: A method in Husserlian philosophy that involves "bracketing" or setting aside preconceptions and judgments about the external world to focus purely on the structure of consciousness and the phenomena as they appear.
Example: When experiencing the color red, phenomenological reduction would involve setting aside any scientific or cultural knowledge about the color and focusing solely on the experience of "redness."

Eidetic Reduction: A method in Husserlian philosophy aimed at uncovering the essential structures of experiences by stripping away the contingent and variable aspects to reveal the invariant features of phenomena.
Example: By examining multiple instances of experiencing a red object, eidetic reduction seeks to determine the essential characteristics that define the experience of "redness" across all instances.