My Method for Reduction

Metaphysics and Epistemology
1

I will show my method of reducing concepts and my method of reducing principles. The processes are related, so I’ve included both. Since concepts are easier to reduce than principles, I’ll show the one for concepts first.

Concept: fragility.

Chain leading to perceptual level:

  • Fragility refers to a potential of materials. That can serve as the genus.
  • Objects fracture when sufficient force separates constituents.
  • This object fractured when it fell off the shelf.

Examples of fragility:

  • fragility of a ceramic mug,
  • fragility of glass,
  • fragility of concrete,
  • etc.

Non-examples:

  • ceramic mug survives hammer,
  • glass survives fall to carpet,
  • normal stability of concrete,
  • etc.

This gives us the differentia, so now we have:

potential of constituents to separate from each other along a course subjected to sufficient stress

Principle: Styrofoam is brittle.

Chain leading to the perceptual level:

  • lower-level principle: Subjecting a sample of styrofoam to bending or compressive forces causes it to break.
  • test results: When styrofoam is subjected to forces of certain quantities, the results are so and so.
  • tentative principle: Pushing something through styrofoam causes cracks. etc.
  • observation: When I pulled out a new gadget hastily from a box, part of the styrofoam caught on the edge, bent, and broke off.

Although this chain helps us get to the perceptual level, they don’t firmly connect the PROPERTY of brittleness to the perceptual level. That is accomplished by by means of causal reasoning.

Brittleness can be measured by fracture toughness. Fracture toughness of materials varies according to composition, mixture of multiple substances under certain conditions, pre-existing cracks, porosity, etc. Material potentials are a consequence of constitutive properties, i.e. of bonding, intermolecular forces, etc.

Any principle we name is made possible by concepts. In this example, we needed such concepts as fragility, composition, etc. A complete reduction will include reducing every key concept we uncover, as outlined at the beginning of this post.

I’ve mentioned lower-level principles vs higher-level principles. I see four levels before I reach the level of ordinary observations:

  1. The level of generalization about property, aka the level of inductive inference.

  2. The level of particular causations, where you perform causal reasoning.

  3. The level of rigorous testing, where you have a clear idea of the relationship involved.

  4. The level of play, where you come up with tentative principles.

  5. Observation of a chance event.

As I go through these levels, I write down notes. This makes three things explicit:

  • the hierarchy of principles,
  • the hierarchy of concepts, including explicit mention of genus and differentia
  • a map of causality.

The hierarchy of concepts includes genus and differentia.

The map of causality isn’t necessary for reducing the principle itself, but it is necessary for reducing the explanation associated with the principle. After all, intermolecular forces are NOT on the every-day perceptual level. And energy is so abstract that we can’t talk about it without invoking mathematics.

By forcing myself to study existents and re-engineer every concept I come across between the principle and the perceptual level, I guarantee valid definition for every concept identified.

This makes my method superior to simply defining a chain of terms without thinking clearly about the existents involved.

2

Are principles not concepts?

3

Principle: Styrofoam is brittle.

That is not a principle, that is a generalization about Styrofoam. Dr. Peikoff gives this definition:

Definition of Principle: a conceptual first cause which has many derivative generalizations; an integration of generalizations; the deepest level of integration possible within a given context ; no rule exists for how many generalizations make a principle (same for units making a concepts); principles are contextual

Definition of Generalization: a proposition that ascribes a characteristic to every member of an unlimited class, however a member is placed in time and space. Format: “All S is P”

Principles are also propositions, so they are constituted of concepts and the relation between them. Some principles are single words (such as the principle of relativity), but that highlights the relationship and method of thinking as its own abstraction in the manner of a name or proper noun; it still refers to and is constituted by concepts in relation.

4

I think you missed the point on “fragility.”

True, it is a property of materials, but the point is that the tendency to fracture, which all materials have, is related to the chemical composition of a material, as well as its geometry or architecture. The opposite of fragility is toughness. Jade is very tough, so it can be carved into intricate, pierced figures. It would be impossible to do the same with diamond, even though diamond is harder than jade, meaning it takes great force to scratch it.

Metals are normally tough, not fragile. They are also ductile, meaning they can be drawn out into wires, bent into sharp angles (without breaking,) or beaten into new shapes. You couldn’t do that with jade or diamond. Metals tend, however, to be soft, easily scratched. So, there are “strengths” of diamond that jade and metals lack; strengths of jade and metals which diamond lacks, and strengths of metals that diamond and jade lack.

An object is fragile only if its architecture, in combination with its molecular structure, both lend themselves to ease of fracture. You can’t abstract “fragility” from two sets of instances, one in which things break, and the other in which they don’t. If you take different materials in the same configuration and subject them to the same pressure differential, then you can say that the ones that break are more “fragile” than the ones that didn’t.

So, one can speak of whether or not concrete is a fragile material, or one can speak of whether or not a particular object, made of concrete, is fragile. Your examples of a mug’s breaking one time and not another, or concrete’s being fragile and then not being so do not define any characteristic.

– Mindy

5

Mindy,

First, strength has a very specific meaning in materials science and mechanical engineering. Calling hardness, ductility, and so on forms of strength confuses everything.

Second, different materials have different values for fracture toughness. If two parts are made exactly the same way, but out of different materials, one will be more resistant to fracture than another.

Third, two samples of the same material will show a difference in fracture point if one is subjected to special conditions. Embrittlement comes to mind.

Fourth, you’ve misunderstood me. I’m well aware of the necessity of commensurable characteristics.

I’m not suggesting you compare a mug to a piece of steel. I’m just suggesting you consider a wide variety of materials.

Nor am I suggesting you compare a mug now against the same mug later. That ignores things like material fatigue and crack propagation.

I’m suggesting that you study the constitutive properties behind the phenomenon of fracture, such as chemical structure, properties of grains (if there are any crystals), part design, the presence of initial cracks after creation of the material, etc.

6

Grames,

Good catch.

I meant “proposition”.

7

Two people have suggested that “fragility” refers exclusively to fracture toughness.

What is the word for the concept that is more abstract than fracture toughness and includes special conditions like heat-treatment and embrittlement in its estimate of what the thing can do?

8

Mindy,

First, strength has a very specific meaning in materials science and mechanical engineering. Calling hardness, ductility, and so on forms of strength confuses everything.

Second, different materials have different values for fracture toughness. If two parts are made exactly the same way, but out of different materials, one will be more resistant to fracture than another.

Third, two samples of the same material will show a difference in fracture point if one is subjected to special conditions. Embrittlement comes to mind.

Fourth, you’ve misunderstood me. I’m well aware of the necessity of commensurable characteristics.

I’m not suggesting you compare a mug to a piece of steel. I’m just suggesting you consider a wide variety of materials.

Nor am I suggesting you compare a mug now against the same mug later. That ignores things like material fatigue and crack propagation.

I’m suggesting that you study the constitutive properties behind the phenomenon of fracture, such as chemical structure, properties of grains (if there are any crystals), part design, the presence of initial cracks after creation of the material, etc.

Your instances of fragile and those of not-fragile each include mugs, glass, and concrete. Those groupings do not pick out fragility, but “having broken,” and “not having broken.” But the concept, “fragility” is not a synonym for “broken.” Not everything that breaks is therefore fragile!

Your instances should have reflected breaking under given circumstances, versus not breaking under the SAME circumstances. That is the difference “fragility” picks out.

– Mindy

9

Your instances of fragile and those of not-fragile each include mugs, glass, and concrete. Those groupings do not pick out fragility, but “having broken,” and “not having broken.” But the concept, “fragility” is not a synonym for “broken.” Not everything that breaks is therefore fragile!

Your instances should have reflected breaking under given circumstances, versus not breaking under the SAME circumstances. That is the difference “fragility” picks out.

– Mindy

They weren’t supposed to.

Fragility is a potential for action, namely the action of fracture.

My point is that you need to differentiate before you can integrate.

The step you mention was implied, but I should have been explicit. You are correct in bringing it up.