I think that scepticism about the efficacy of Magic (Mageia, Magikê, Mageutikêe) stems from three misunderstandings, which can be called the Fallacies of Dualism, Individualism, and Egoism. These remarks are intended to dispel these fallacies from a Neo-Pythagorean perspective, but are based on ideas common to most ancient Hellenic philosophies.
In this context, Dualism is the view that there are two essentially different "stuffs": mind and matter, or something similar. Since the modern scientific worldview attaches more reality to matter (or the physical) than to mind (or the psychical), there is a tendency to suppose that Magic, which is primarily psychical, can have no effect on the physical world.
On the other hand, Monism is the view that there is one basic "stuff" in the universe, although it is experienced in two different ways. When it is experienced from the "inside" it is experienced as psychical, as our mental states and processes. When it is experienced from the "outside" it is experienced as physical, as material states and processes outside of us. From the monistic perspective, the mental is just as real as the material, because it is just the other side of the same reality.
The fallacy of Individualism is the supposition that each mind is separate from every other mind, that we are all individuals. However, many of the ancient philosophies teach that we each possess a spark of Divinity and that the divine parts of our souls connect us to the totality of Divinity. The analogy was made to a statue of Three-faced Hecate. Like the faces on the statue, each of our Egos looks out through a different set of eyes, and supposes that it is a separate being. But at the back of our heads (so to speak) we are all joined, we are all one.
In ancient Greek, Bathus means both high and deep, as does Latin Altus. Therefore, your Higher Mind, where you connect with Divinity and, through it, to all other minds, is also your Deeper Mind (the Collective Unconscious, in Jung's terms).
As you move Higher/Deeper beyond your individual Ego, you come to the Gods, who are the same for everyone. Pressing further, you come to the Monad, which is the unity of All Things (ta Panta, ta Hola). The Flow of The All is the Providence (Pronoia) or Destiny to which all things are subject, even the Gods. It is the Providential Flux of The All (though not an immutable predestination).
By the fallacy of Egoism I mean the assumption that one's conscious Ego is in charge. Rather, the Ego is the servant of the Higher/Deeper parts of the soul and, ultimately, the servant of the Gods. The Ego has an important role to play, or the Gods wouldn't have created it, but it is important to understand that it is a means to the ends of the Gods and Providence, the collective Divine Movement. The Gods have given us consciousness and free will so that we might aid in the accomplishment of Their goals and in the fulfilling of Universal Destiny.
Although you think of your Ego as "you," because it is the part of your soul most separated from others' souls, it is in fact the lowest/shallowest part of your psyche. Your Deeper/Higher Self, which is the true "you," is more closely united with the Deeper/Higher Selves of other people.
In true Magic, which is a sacred art, the Magus acts to fulfil the Destiny of The All. Therefore, it is important that the Magus be "enlightened," at least to the point that he or she serves the Higher/Deeper Self rather than the Ego. That is, as Magus you employ your Ego as a tool for bringing the Will of the Gods into conscious awareness so that, by symbolical acts, that Will may be more effectively accomplished. (This is, presumably, at least part of the reason the Gods created us.)
What are these symbolical acts? As in the physical world things affect each other by physical forces, so in the psychical world Ideas influence each other by symbols, signs, and sympathies. These are the raw materials with which the Magus works. If the basic currency of the physical world is energy, then the basic currency of the psychical world is Meaning. By manipulating connections and influences the Magus effects change in the psychical world, which is - be it remembered - as real as the physical world, by the Principle of Monism. That is, since the psyche is an authentic perspective on Reality, symbolic connections, perceived or constructed in the mind, are as real as physical connections.
Magic works most effectively when the Ego is in service to the Higher Self, which is in service to the Gods. Therefore Magic is most effective when it helps to fulfill Destiny. As a consequence, successful Magic often appears non-miraculous in hindsight because, in hindsight, the outcome seems probable or even inevitable.
Magic that attempts to thwart Universal Destiny is less successful. It is like trying to row against the current of a mighty river; one can do it for a time, but the river wins in the end. So also such Magic may create chaotic vortices in the Flow, but the effects are local and dissipate before long.
The true Magus does not fight the river, but works with it, helping to channel it in its destined direction. Therefore successful Magic entails knowledge of Providence and willingness to work with It. Fortunately, misguided Magic is usually ineffective. Sacred Magic is made powerful by its cooperation with Divine Providence.
The foregoing remarks do not imply that the true Magus never works Magic for his or her own benefit. Rather, you may work Magic for your own immediate good if that facilitates your Sacred Service to Providence. For example, you may use Magic to protect yourself from robbers, or to protect your land from invaders, if doing so helps you to fulfill your Sacred Charge. Of course, if Destiny is better fulfilled by your being robbed or by your land being overrun, then you may find that your Magic is ineffective, at least in the long run.
Practically, the Magus must try to divine the Will of the Gods; thus you may know the ends to which your Magic should be directed. Then you should put your Ego in service to your Higher Self and the Gods. By leaving the outcome of your Magic in the laps of the Gods, you will ensure that your Art is in conformity with Providence, and does not balk it.
The foregoing may be summarized in these Axioms of Magic: