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I have read about the notion of necessity in a logical sense. For example, 2+2=4 seems to be logically necessary.

But I have also read about the notion of metaphysical necessity. God, for example, is argued to be an example of one kind of metaphysical necessity. Full causal determinism is also often taken to be an example of this. If everything is determined, it becomes necessary.

But if one can imagine alternate states of affairs even if determinism is true or if there is some God who does certain things necessarily, isn’t the mere imagination evidence that it is contingent? For example, one can imagine different laws in the universe. Or one can imagine a different kind of god, or no god at all. There would presumably be no reason as to why a certain law would exist rather than another, even if everything was determined by certain laws.

But since there is no reason, wouldn’t it be a brute contingency rather than a necessity?

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Metaphysical necessity is a question on which philosophers continue to disagree.

Our use of language contains a great deal of modal terminology. We say that some things are necessary, some are possible, some propositions are true but only contingently, some things are true but might have been otherwise, etc. Modal talk is ubiquitous and significant and comes in many varieties. Scientists also use modal language when talking of laws of nature and causal relations.

It is conceivable that all this talk is mistaken, or that it can all be explained away in some fashion. But many philosophers hold that in order to do justice to it, we need a philosophical theory that allows that some modal judgments are true. Doing so does not (necessarily!) commit us to modal realism. We might speak of what is true in some possible world without believing there are any real possible worlds.

It is relatively uncontroversial to accept that there are physical or nomological necessities, e.g. it is impossible to travel faster than the speed of light, or it is impossible to build a perpetual motion machine. Some philosophers distinguish these from metaphysical necessities. We can coherently imagine the laws of nature being different from how they actually are. But other things are not so easy to conceive as being different without lapsing into absurdity. Of course this in turn raises the question of whether what is imaginable or conceivable is a satisfactory basis for making judgments about what is possible.

Several distinct positions arise.

  1. Some philosophers are skeptical about metaphysical necessity, or even about necessity in general. They prefer to dismiss it or recast it as a purely linguistic phenomenon.
  2. Some are necessitarians and hold that the way our universe is constitutes the only way it could be. They hold that there is no metaphysical necessity beyond what is physically necessary.
  3. There are essentialists such as Kripke who maintain that statements about the nature or origin of a thing are necessary but other properties are not. According to Kripke, I could have been a lawyer, but I couldn't have been born to different parents, or else I just wouldn't be me. Gold might have different properties in another possible world, such as being purple or being a liquid at room temperature, but gold must be element 79 or else we are talking about something else, not gold. Hesperus and Phosphorus are necessarily the same thing, because they (it) are identical.
  4. Some philosophers are modal realists who hold that there really are possible worlds and what goes on there is what grounds the truth of modal judgments in our world. For them, metaphysical necessities are literally true in all possible worlds.

Various other possible combinations of positions exist also. There is some useful coverage of this material in this Stanford Encyclopedia article.

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  • +1 for a good review, but I think "we can coherently imagine the laws of nature being different" (as opposed to imagining having observed some events without knowing the laws of nature which produced them or their other consequences) is deeply false. As would be the lesser claim that we can coherently imagine the laws of nature as they are.
    – g s
    Commented Jul 9 at 16:08
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Necessity is a logical device: necessity describes the dependencies of Logic.

For example, for all judgements on a book about The Laws of Thermodynamics to be valid, it is necessary for truth to be true. Without it, all rational and empirical judgements get destroyed. The book would have no meaning at all. By fulfilling necessity, we are fulfilling the requirements for Logic to be possible.

Now, consider the core domains of philosophy: physika (what we perceive with the senses, what is empirical) and meta ta physika (what we address mentally, independently of the senses).

It becomes evident that Logic is purely metaphysical (judgements, rules, entities, order, etc. are not physical, they have no substance, they occupy no space, they have no size, they can't be put inside a bottle). Same as Mathematics (numbers, symbols, variables, arithmetics, etc. are not physical).

Ergo, your answer:

Necessity is eminently metaphysical.

Ok. Now, you were thinking that necessity is not metaphysical, but it turned to be the complete opposite.

Is God a metaphysical fact? Perhaps not. In part, the idea of God raises from our knowledge of physical facts we have no explanations of. God's attributes are commonly related with physical intuitions (e.g. omnipotence, omnipresence, incorruptibility, immutability, etc.) Or perhaps it is, when it is perceived purely by reason.

So, what would be empirical necessity? I imagine, for example, that this is a physical necessity:

The egg is necessary for the chicken to exist.

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Energy itself is not mere imagination. In fact, if there were to be a notion that imagination even is, that it could even be or exist, it would require some sort of precursor. Thus far, in life, the only valid precursor we can truly understand is pure energy. Pure energy, light energy truly, allows for formation. Dark energy, on the contrary, does not. Rather, it is the absence of that which is created.

In the matter of numbers, yes 2 + 2 = 4. But such numbers could not be conceived unless we could use some sort of particle, like an atom, or even wave, like light, which are both energetically founded. Thusly, the only way we see logic itself, is by energy being. Therefore, metaphysical logic is the precursor to logic. We can even understand that if energy is required for logic, it must be required for metaphysical logic. In this understanding, I am implying that metaphysical logic is logic of the immaterial, not purely material.

The imagining of differing states is not necessarily logical, nor is it true. Rather, it is simply a proof that shows that one needs guides, metaphysical and physical, so that we do not get lost in the mucus that is perpetually being spewed via those that are incompetent.

Finally, understand that:

  • The concept or understanding of God is not incompetent, nor is Godess.

  • Imagination is for fiction, not non-fiction. Determined probabilities are prevalent, yet, must be navigated so that the truly best probability is expressed.

  • If I were to imagine that 2 + 2 = 5, then I could argue against logic altogether and even numbers themselves. The thing is, I can't, unless I'm a schizophrenic idiot that truly gives no care at all. This implies that factually, 2 + 2 = 4 metaphysically and physically, just as God must be real metaphysically and physically. This proof requires no imagination, rather, the elimination of it.

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